Black hole versus cosmological horizon entropy
International Nuclear Information System (INIS)
Davis, Tamara M; Davies, P C W; Lineweaver, Charles H
2003-01-01
The generalized second law of thermodynamics states that entropy always increases when all event horizons are attributed with an entropy proportional to their area. We test the generalized second law by investigating the change in entropy when dust, radiation and black holes cross a cosmological event horizon. We generalize for flat, open and closed Friedmann-Robertson-Walker universes by using numerical calculations to determine the cosmological horizon evolution. In most cases, the loss of entropy from within the cosmological horizon is more than balanced by an increase in cosmological event horizon entropy, maintaining the validity of the generalized second law of thermodynamics. However, an intriguing set of open universe models shows an apparent entropy decrease when black holes disappear over the cosmological event horizon. We anticipate that this apparent violation of the generalized second law will disappear when solutions are available for black holes embedded in arbitrary backgrounds
Entropy of black holes with multiple horizons
He, Yun; Ma, Meng-Sen; Zhao, Ren
2018-05-01
We examine the entropy of black holes in de Sitter space and black holes surrounded by quintessence. These black holes have multiple horizons, including at least the black hole event horizon and a horizon outside it (cosmological horizon for de Sitter black holes and "quintessence horizon" for the black holes surrounded by quintessence). Based on the consideration that the two horizons are not independent each other, we conjecture that the total entropy of these black holes should not be simply the sum of entropies of the two horizons, but should have an extra term coming from the correlations between the two horizons. Different from our previous works, in this paper we consider the cosmological constant as the variable and employ an effective method to derive the explicit form of the entropy. We also try to discuss the thermodynamic stabilities of these black holes according to the entropy and the effective temperature.
Entropy of black holes with multiple horizons
Directory of Open Access Journals (Sweden)
Yun He
2018-05-01
Full Text Available We examine the entropy of black holes in de Sitter space and black holes surrounded by quintessence. These black holes have multiple horizons, including at least the black hole event horizon and a horizon outside it (cosmological horizon for de Sitter black holes and “quintessence horizon” for the black holes surrounded by quintessence. Based on the consideration that the two horizons are not independent each other, we conjecture that the total entropy of these black holes should not be simply the sum of entropies of the two horizons, but should have an extra term coming from the correlations between the two horizons. Different from our previous works, in this paper we consider the cosmological constant as the variable and employ an effective method to derive the explicit form of the entropy. We also try to discuss the thermodynamic stabilities of these black holes according to the entropy and the effective temperature.
Horizon Entropy from Quantum Gravity Condensates.
Oriti, Daniele; Pranzetti, Daniele; Sindoni, Lorenzo
2016-05-27
We construct condensate states encoding the continuum spherically symmetric quantum geometry of a horizon in full quantum gravity, i.e., without any classical symmetry reduction, in the group field theory formalism. Tracing over the bulk degrees of freedom, we show how the resulting reduced density matrix manifestly exhibits a holographic behavior. We derive a complete orthonormal basis of eigenstates for the reduced density matrix of the horizon and use it to compute the horizon entanglement entropy. By imposing consistency with the horizon boundary conditions and semiclassical thermodynamical properties, we recover the Bekenstein-Hawking entropy formula for any value of the Immirzi parameter. Our analysis supports the equivalence between the von Neumann (entanglement) entropy interpretation and the Boltzmann (statistical) one.
NHEG mechanics: laws of near horizon extremal geometry (thermo)dynamics
International Nuclear Information System (INIS)
Hajian, K.; Seraj, A.; Sheikh-Jabbari, M.M.
2014-01-01
Near Horizon Extremal Geometries (NHEG) are solutions to gravity theories with SL(2,ℝ)×U(1) N (for some N) symmetry, are smooth geometries and have no event horizon, unlike black holes. Following the ideas by R. M. Wald, we derive laws of NHEG dynamics, the analogs of laws of black hole dynamics for the NHEG. Despite the absence of horizon in the NHEG, one may associate an entropy to the NHEG, as a Noether-Wald conserved charge. We work out “entropy” and “entropy perturbation” laws, which are respectively universal relations between conserved Noether charges corresponding to the NHEG and a system probing the NHEG. Our entropy law is closely related to Sen’s entropy function. We also discuss whether the laws of NHEG dynamics can be obtained from the laws of black hole thermodynamics in the extremal limit
Quantum statistical entropy corresponding to cosmic horizon in five-dimensional spacetime
Institute of Scientific and Technical Information of China (English)
2008-01-01
The generalized uncertainty relation is introduced to calculate the quantum statis-tical entropy corresponding to cosmic horizon. By using the new equation of state density motivated by the generalized uncertainty relation, we discuss entropies of Bose field and Fermi field on the background of five-dimensional spacetime. In our calculation, we need not introduce cutoff. There is no divergent logarithmic term in the original brick-wall method. And it is obtained that the quantum statistical en-tropy corresponding to cosmic horizon is proportional to the area of the horizon. Further it is shown that the entropy corresponding to cosmic horizon is the entropy of quantum state on the surface of horizon. The black hole’s entropy is the intrinsic property of the black hole. The entropy is a quantum effect. In our calculation, by using the quantum statistical method, we obtain the partition function of Bose field and Fermi field on the background of five-dimensional spacetime. We provide a way to study the quantum statistical entropy corresponding to cosmic horizon in the higher-dimensional spacetime.
Black hole entropy, universality, and horizon constraints
International Nuclear Information System (INIS)
Carlip, Steven
2006-01-01
To ask a question about a black hole in quantum gravity, one must restrict initial or boundary data to ensure that a black hole is actually present. For two-dimensional dilaton gravity, and probably a much wider class of theories, I show that the imposition of a 'stretched horizon' constraint modifies the algebra of symmetries at the horizon, allowing the use of conformal field theory techniques to determine the asymptotic density of states. The result reproduces the Bekenstein-Hawking entropy without any need for detailed assumptions about the microscopic theory. Horizon symmetries may thus offer an answer to the problem of universality of black hole entropy
Black hole entropy, universality, and horizon constraints
Energy Technology Data Exchange (ETDEWEB)
Carlip, Steven [Department of Physics, University of California, Davis, CA 95616 (United States)
2006-03-01
To ask a question about a black hole in quantum gravity, one must restrict initial or boundary data to ensure that a black hole is actually present. For two-dimensional dilaton gravity, and probably a much wider class of theories, I show that the imposition of a 'stretched horizon' constraint modifies the algebra of symmetries at the horizon, allowing the use of conformal field theory techniques to determine the asymptotic density of states. The result reproduces the Bekenstein-Hawking entropy without any need for detailed assumptions about the microscopic theory. Horizon symmetries may thus offer an answer to the problem of universality of black hole entropy.
Does horizon entropy satisfy a quantum null energy conjecture?
Fu, Zicao; Marolf, Donald
2016-12-01
A modern version of the idea that the area of event horizons gives 4G times an entropy is the Hubeny-Rangamani causal holographic information (CHI) proposal for holographic field theories. Given a region R of a holographic QFTs, CHI computes A/4G on a certain cut of an event horizon in the gravitational dual. The result is naturally interpreted as a coarse-grained entropy for the QFT. CHI is known to be finitely greater than the fine-grained Hubeny-Rangamani-Takayanagi (HRT) entropy when \\partial R lies on a Killing horizon of the QFT spacetime, and in this context satisfies other non-trivial properties expected of an entropy. Here we present evidence that it also satisfies the quantum null energy condition (QNEC), which bounds the second derivative of the entropy of a quantum field theory on one side of a non-expanding null surface by the flux of stress-energy across the surface. In particular, we show CHI to satisfy the QNEC in 1 + 1 holographic CFTs when evaluated in states dual to conical defects in AdS3. This surprising result further supports the idea that CHI defines a useful notion of coarse-grained holographic entropy, and suggests unprecedented bounds on the rate at which bulk horizon generators emerge from a caustic. To supplement our motivation, we include an appendix deriving a corresponding coarse-grained generalized second law for 1 + 1 holographic CFTs perturbatively coupled to dilaton gravity.
Entropy bound of horizons for accelerating, rotating and charged Plebanski–Demianski black hole
International Nuclear Information System (INIS)
Debnath, Ujjal
2016-01-01
We first review the accelerating, rotating and charged Plebanski–Demianski (PD) black hole, which includes the Kerr–Newman rotating black hole and the Taub-NUT spacetime. The main feature of this black hole is that it has 4 horizons like event horizon, Cauchy horizon and two accelerating horizons. In the non-extremal case, the surface area, entropy, surface gravity, temperature, angular velocity, Komar energy and irreducible mass on the event horizon and Cauchy horizon are presented for PD black hole. The entropy product, temperature product, Komar energy product and irreducible mass product have been found for event horizon and Cauchy horizon. Also their sums are found for both horizons. All these relations are dependent on the mass of the PD black hole and other parameters. So all the products are not universal for PD black hole. The entropy and area bounds for two horizons have been investigated. Also we found the Christodoulou–Ruffini mass for extremal PD black hole. Finally, using first law of thermodynamics, we also found the Smarr relation for PD black hole.
Entropy bound of horizons for accelerating, rotating and charged Plebanski–Demianski black hole
Energy Technology Data Exchange (ETDEWEB)
Debnath, Ujjal, E-mail: ujjaldebnath@yahoo.com
2016-09-15
We first review the accelerating, rotating and charged Plebanski–Demianski (PD) black hole, which includes the Kerr–Newman rotating black hole and the Taub-NUT spacetime. The main feature of this black hole is that it has 4 horizons like event horizon, Cauchy horizon and two accelerating horizons. In the non-extremal case, the surface area, entropy, surface gravity, temperature, angular velocity, Komar energy and irreducible mass on the event horizon and Cauchy horizon are presented for PD black hole. The entropy product, temperature product, Komar energy product and irreducible mass product have been found for event horizon and Cauchy horizon. Also their sums are found for both horizons. All these relations are dependent on the mass of the PD black hole and other parameters. So all the products are not universal for PD black hole. The entropy and area bounds for two horizons have been investigated. Also we found the Christodoulou–Ruffini mass for extremal PD black hole. Finally, using first law of thermodynamics, we also found the Smarr relation for PD black hole.
Gravitational entropy and thermodynamics away from the horizon
Energy Technology Data Exchange (ETDEWEB)
Brustein, Ram, E-mail: ramyb@bgu.ac.il [Department of Physics, Ben-Gurion University, Beer-Sheva 84105 (Israel); CAS, Ludwig-Maximilians-Universitaet Muenchen, 80333 Muenchen (Germany); Medved, A.J.M., E-mail: j.medved@ru.ac.za [Department of Physics and Electronics, Rhodes University, Grahamstown 6140 (South Africa)
2012-08-29
We define, by an integral of geometric quantities over a spherical shell of arbitrary radius, an invariant gravitational entropy. This definition relies on defining a gravitational energy and pressure, and it reduces at the horizon of both black branes and black holes to Wald's Noether charge entropy. We support the thermodynamic interpretation of the proposed entropy by showing that, for some cases, the field theory duals of the entropy, energy and pressure are the same as the corresponding quantities in the field theory. In this context, the Einstein equations are equivalent to the field theory thermodynamic relation TdS=dE+PdV supplemented by an equation of state.
Quantization of horizon entropy and the thermodynamics of spacetime
International Nuclear Information System (INIS)
Skakala, Jozef
2014-01-01
This is a review of my work published in the papers of Skakala (JHEP 1201:144, 2012; JHEP 1206:094, 2012) and Chirenti et al. (Phys. Rev. D 86:124008, 2012; Phys. Rev.D 87:044034, 2013). It offers a more detailed discussion of the results than the accounts in those papers, and it links my results to some conclusions recently reached by other authors. It also offers some new arguments supporting the conclusions in the cited articles. The fundamental idea of this work is that the semiclassical quantization of the black hole entropy, as suggested by Bekenstein (Phys. Rev. D 7:2333-2346, 1973), holds (at least) generically for the spacetime horizons. We support this conclusion by two separate arguments: (1) we generalize Bekenstein’s lower bound on the horizon area transition to a much wider class of horizons than only the black-hole horizon, and (2) we obtain the same entropy spectra via the asymptotic quasi-normal frequencies of some particular spherically symmetric multi horizon spacetimes (in the way proposed by Maggiore (Phys. Rev. Lett. 100:141301, 2008)). The main result of this paper supports the conclusions derived by Kothawalla et al. (Phys. Rev. D 78:104018, 2008) and Kwon and Nam (Class. Quant. Grav. 28:035007, 2011), on the basis of different arguments. (author)
Irreversible thermodynamics of dark energy on the entropy-corrected apparent horizon
Energy Technology Data Exchange (ETDEWEB)
Karami, K; Sahraei, N [Department of Physics, University of Kurdistan, Pasdaran Street, Sanandaj (Iran, Islamic Republic of); Jamil, M, E-mail: KKarami@uok.ac.i, E-mail: mjamil@camp.nust.edu.p [Center for Advanced Mathematics and Physics (CAMP), National University of Sciences and Technology (NUST), Islamabad (Pakistan)
2010-10-15
We study the irreversible (non-equilibrium) thermodynamics of the Friedmann-Robertson-Walker (FRW) universe containing only dark energy. Using the modified entropy-area relation that is motivated by loop quantum gravity, we calculate the entropy-corrected form of the apparent horizon of the FRW universe.
‘Quantum hairs’ and entropy of the quantum isolated horizon from Chern–Simons theory
International Nuclear Information System (INIS)
Majhi, Abhishek; Majumdar, Parthasarathi
2014-01-01
We articulate the fact that the loop quantum gravity (LQG) description of the quantum macrostates of black hole horizons, modeled as quantum isolated horizons (QIHs), is completely characterized in terms of two independent integer-valued ‘quantum hairs’, viz, the coupling constant (k) of the quantum SU(2) Chern–Simons (CS) theory describing QIH dynamics, and the number of punctures (N) produced by the bulk spin network edges piercing the isolated horizon (which act as pointlike sources for the CS fields). We demonstrate that the microcanonical entropy of macroscopic (both parameters assuming very large values) QIHs can be obtained directly from the microstates of this CS theory using standard statistical mechanical methods, without having to additionally postulate the horizon as an ideal gas of punctures, or incorporate any additional classical or semiclassical input from general relativity vis-a-vis the functional dependence of the isolated horizon mass on its area, or indeed, without having to restrict to any special class of spins. Requiring the validity of the Bekenstein–Hawking area law relates these two parameters (as an equilibrium ‘equation of state’), and consequently allows the Barbero–Immirzi parameter to take any real and positive value depending on the value of k/N. The logarithmic correction to the area law obtained a decade ago by R Kaul and one of us (PM), ensues straightforwardly, with precisely the coefficient −3/2, making it a signature of the LQG approach to black hole entropy. (paper)
Entanglement Entropy of Reissner—Nordström Black Hole and Quantum Isolated Horizon
International Nuclear Information System (INIS)
Ma Meng-Sen; Zhang Li-Chun; Zhao Ren
2014-01-01
Based on the work of Ghosh and Pereze, who view the black hole entropy as the logarithm of the number of quantum states on the Quantum Isolated Horizon (QIH) § the entropy of Reissner—Nordström black hole is studied. According to the Unruh temperature, the statistical entropy of quantum fields under the background of Reissner—Nordström spacetime is calculated by means of quantum statistics. In the calculations we take the integral from the position of QIH to infinity, so the obtained entropy is the entanglement entropy outside the QIH. In Reissner—Nordström spacetime it is shown that if only the position of QIH is properly chosen the leading term of logarithm of the number of quantum states on the QIH is equal to the leading term of the entanglement entropy outside the black hole horizon, and both are the Bekenstein—Hawking entropy. The results reveal the relation between the entanglement entropy of black hole and the logarithm of the number of quantum states. (general)
Isolated and Dynamical Horizons and Their Applications
Directory of Open Access Journals (Sweden)
Ashtekar Abhay
2004-12-01
Full Text Available Over the past three decades, black holes have played an important role in quantum gravity, mathematical physics, numerical relativity and gravitational wave phenomenology. However, conceptual settings and mathematical models used to discuss them have varied considerably from one area to another. Over the last five years a new, quasi-local framework was introduced to analyze diverse facets of black holes in a unified manner. In this framework, evolving black holes are modelled by dynamical horizons and black holes in equilibrium by isolated horizons. We review basic properties of these horizons and summarize applications to mathematical physics, numerical relativity, and quantum gravity. This paradigm has led to significant generalizations of several results in black hole physics. Specifically, it has introduced a more physical setting for black hole thermodynamics and for black hole entropy calculations in quantum gravity, suggested a phenomenological model for hairy black holes, provided novel techniques to extract physics from numerical simulations, and led to new laws governing the dynamics of black holes in exact general relativity.
Entropy of nonrotating isolated horizons in Lovelock theory from loop quantum gravity
Wang, Jing-Bo; Huang, Chao-Guang; Li, Lin
2016-08-01
In this paper, the BF theory method is applied to the nonrotating isolated horizons in Lovelock theory. The final entropy matches the Wald entropy formula for this theory. We also confirm the conclusion obtained by Bodendorfer et al. that the entropy is related to the flux operator rather than the area operator in general diffeomorphic-invariant theory. Supported by National Natural Science Foundation of China (11275207)
Black Hole Entropy from Bondi-Metzner-Sachs Symmetry at the Horizon.
Carlip, S
2018-03-09
Near the horizon, the obvious symmetries of a black hole spacetime-the horizon-preserving diffeomorphisms-are enhanced to a larger symmetry group with a three-dimensional Bondi-Metzner-Sachs algebra. Using dimensional reduction and covariant phase space techniques, I investigate this augmented symmetry and show that it is strong enough to determine the black hole entropy in any dimension.
Isolated Horizons and Black Hole Entropy in Loop Quantum Gravity
Directory of Open Access Journals (Sweden)
Jacobo Diaz-Polo
2012-08-01
Full Text Available We review the black hole entropy calculation in the framework of Loop Quantum Gravity based on the quasi-local definition of a black hole encoded in the isolated horizon formalism. We show, by means of the covariant phase space framework, the appearance in the conserved symplectic structure of a boundary term corresponding to a Chern-Simons theory on the horizon and present its quantization both in the U(1 gauge fixed version and in the fully SU(2 invariant one. We then describe the boundary degrees of freedom counting techniques developed for an infinite value of the Chern-Simons level case and, less rigorously, for the case of a finite value. This allows us to perform a comparison between the U(1 and SU(2 approaches and provide a state of the art analysis of their common features and different implications for the entropy calculations. In particular, we comment on different points of view regarding the nature of the horizon degrees of freedom and the role played by the Barbero-Immirzi parameter. We conclude by presenting some of the most recent results concerning possible observational tests for theory.
Parity horizons in shape dynamics
International Nuclear Information System (INIS)
Herczeg, Gabriel
2016-01-01
I introduce the notion of a parity horizon, and show that many simple solutions of shape dynamics possess them. I show that the event horizons of the known asymptotically flat black hole solutions of shape dynamics are parity horizons and that this notion of parity implies that these horizons possess a notion of CPT invariance that can in some cases be extended to the solution as a whole. I present three new solutions of shape dynamics with parity horizons and find that not only do event horizons become parity horizons in shape dynamics, but observer-dependent horizons and Cauchy horizons do as well. The fact that Cauchy horizons become (singular) parity horizons suggests a general chronology protection mechanism in shape dynamics that prevents the formation of closed timelike curves. (paper)
Statistical Entropy of the Kaluza－Klein Black Hole from the Horizon Conformal Field Theory
Institute of Scientific and Technical Information of China (English)
JING Ji-Liang; YAN Mu-Lin
2001-01-01
The statistical entropy of the Kaluza-Klein black hole is studied by counting the black hole states which form an algebra of diffeomorphism at Killing horizon with a central charge. It is shown that the entropy yielded by the standard Cardy formula agrees with the Bekenstein-Hawking entropy only if we take period T of function u as the periodicity of the Euclidean black hole. On the other hand, the first-order quantum correction to the entropy is proportional to the logarithm of the Bekenstein-Hawking entropy with a factor -1/2.
Quantum dynamical entropy revisited
International Nuclear Information System (INIS)
Hudetz, T.
1996-10-01
We define a new quantum dynamical entropy, which is a 'hybrid' of the closely related, physically oriented entropy introduced by Alicki and Fannes in 1994, and of the mathematically well-developed, single-argument entropy introduced by Connes, Narnhofer and Thirring in 1987. We show that this new quantum dynamical entropy has many properties similar to the ones of the Alicki-Fannes entropy, and also inherits some additional properties from the CNT entropy. In particular, the 'hybrid' entropy interpolates between the two different ways in which both the AF and the CNT entropy of the shift automorphism on the quantum spin chain agree with the usual quantum entropy density, resulting in even better agreement. Also, the new quantum dynamical entropy generalizes the classical dynamical entropy of Kolmogorov and Sinai in the same way as does the AF entropy. Finally, we estimate the 'hybrid' entropy both for the Powers-Price shift systems and for the noncommutative Arnold map on the irrational rotation C * -algebra, leaving some interesting open problems. (author)
International Nuclear Information System (INIS)
Chen Qiang; Ren Ji-Rong
2013-01-01
In this paper, we use the modified Hod's treatment and the Kunstatter's method to study the horizon area spectrum and entropy spectrum in Gauss—Bonnet de-Sitter space-time, which is regarded as the natural generalization of Einstein gravity by including higher derivative correction terms to the original Einstein—Hilbert action. The horizon areas have some properties that are very different from the vacuum solutions obtained from the frame of Einstein gravity. With the new physical interpretation of quasinormal modes, the area/entropy spectrum for the event horizon for near-extremal Gauss—Bonnet de Sitter black holes are obtained. Meanwhile, we also extend the discussion of area/entropy quantization to the non-extremal black holes solutions. (general)
Membrane viewpoint on black holes: Dynamical electromagnetic fields near the horizon
International Nuclear Information System (INIS)
Macdonald, D.A.; Suen, W.
1985-01-01
This paper is part of a series of papers with the aim of developing a complete self-consistent formalism for the treatment of electromagnetic and gravitational fields in the neighborhood of a black-hole horizon. In this membrane formalism, the horizon is treated as a closed two-dimensional membrane lying in a curved three-dimensional space, and endowed with familiar physical properties such as entropy and temperature, surface pressure and viscosity, and electrical conductivity, charge, and current. This paper develops the concept of the ''stretched horizon,'' which will be vital for both the electromagnetic and gravitational aspects of the formalism, and it presents several model problems illustrating the interaction of dynamical electromagnetic fields with stationary black-hole horizons: The field of a test charge in various states of motion outside the Schwarzschild horizon is analyzed in the near-horizon limit, where the spatial curvature may be ignored and the metric may be approximated by that of Rindler. This analysis elucidates the influence of the horizon on the shapes and motions of electric and magnetic field lines when external agents move the field lines in arbitrary manners. It also illustrates how the field lines interact with the horizon's charge and current to produce an exchange of energy and momentum between the external agent and the horizon. A numerical calculation of the dynamical relaxation of a magnetic field threading a Schwarzschild black hole is also presented, illustrating the ''cleaning'' of a complicated field structure by a black-hole horizon, and elucidating the constraints on the location of the stretched horizon
Energy Technology Data Exchange (ETDEWEB)
Schroer, Bert [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)]. E-mail: schroer@cbpf.br
2002-08-01
The lightfront quantization of the 70s is reviewed in the more rigorous setting of lightfront (LF) restriction of free fields in which the lightfront is considered to be linear extension of the upper causal horizon of a wedge region. Particular attention is given to the change of localization structure in passing from the wedge to its horizon which results in the emergence of a transverse quantum mechanical substructure of the QFT on the horizon and its lightfront extension. The vacuum fluctuations of QFT on the LF are compressed into the direction of the lightray (where they become associated with a chiral QFT) and lead to the notion of area density of a 'split localization' entropy. To overcome the limitation of this restriction approach and include interacting theories with non-canonical short distance behavior, we introduce a new concept of algebraic lightfront holography which uses ideas of algebraic QFT, in particular the modular structure of its associated local operator algebras. In this way the localization properties of LF degrees of freedom including the absence of transverse vacuum fluctuations are confirmed to be stable against interactions. The important universality aspect of lightfront holography is emphasized. Only in this way one is able to extract from the 'split-localization' entropy a split-independent additive entropy-like measure of the entanglement of the vacuum upon restriction to the horizon algebra. (author)
q-entropy for symbolic dynamical systems
International Nuclear Information System (INIS)
Zhao, Yun; Pesin, Yakov
2015-01-01
For symbolic dynamical systems we use the Carathéodory construction as described in (Pesin 1997 Dimension Theory in Dynamical Systems, ConTemporary Views and Applications (Chicago: University of Chicago Press)) to introduce the notions of q-topological and q-metric entropies. We describe some basic properties of these entropies and in particular, discuss relations between q-metric entropy and local metric entropy. Both q-topological and q-metric entropies are new invariants respectively under homeomorphisms and metric isomorphisms of dynamical systems. (paper)
Entropy equilibrium equation and dynamic entropy production in environment liquid
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The entropy equilibrium equation is the basis of the nonequilibrium state thermodynamics. But the internal energy implies the kinetic energy of the fluid micelle relative to mass center in the classical entropy equilibrium equation at present. This internal energy is not the mean kinetic energy of molecular movement in thermodynamics. Here a modified entropy equilibrium equation is deduced, based on the concept that the internal energy is just the mean kinetic energy of the molecular movement. A dynamic entropy production is introduced into the entropy equilibrium equation to describe the dynamic process distinctly. This modified entropy equilibrium equation can describe not only the entropy variation of the irreversible processes but also the reversible processes in a thermodynamic system. It is more reasonable and suitable for wider applications.
Dynamical entropy for infinite quantum systems
International Nuclear Information System (INIS)
Hudetz, T.
1990-01-01
We review the recent physical application of the so-called Connes-Narnhofer-Thirring entropy, which is the successful quantum mechanical generalization of the classical Kolmogorov-Sinai entropy and, by its very conception, is a dynamical entropy for infinite quantum systems. We thus comparingly review also the physical applications of the classical dynamical entropy for infinite classical systems. 41 refs. (Author)
Lemos, José P. S.; Minamitsuji, Masato; Zaslavskii, Oleg B.
2017-10-01
Using a thin shell, the first law of thermodynamics, and a unified approach, we study the thermodymanics and find the entropy of a (2 +1 )-dimensional extremal rotating Bañados-Teitelbom-Zanelli (BTZ) black hole. The shell in (2 +1 ) dimensions, i.e., a ring, is taken to be circularly symmetric and rotating, with the inner region being a ground state of the anti-de Sitter spacetime and the outer region being the rotating BTZ spacetime. The extremal BTZ rotating black hole can be obtained in three different ways depending on the way the shell approaches its own gravitational or horizon radius. These ways are explicitly worked out. The resulting three cases give that the BTZ black hole entropy is either the Bekenstein-Hawking entropy, S =A/+ 4 G , or an arbitrary function of A+, S =S (A+) , where A+=2 π r+ is the area, i.e., the perimeter, of the event horizon in (2 +1 ) dimensions. We speculate that the entropy of an extremal black hole should obey 0 ≤S (A+)≤A/+ 4 G . We also show that the contributions from the various thermodynamic quantities, namely, the mass, the circular velocity, and the temperature, for the entropy in all three cases are distinct. This study complements the previous studies in thin shell thermodynamics and entropy for BTZ black holes. It also corroborates the results found for a (3 +1 )-dimensional extremal electrically charged Reissner-Nordström black hole.
Phase space and black-hole entropy of higher genus horizons in loop quantum gravity
International Nuclear Information System (INIS)
Kloster, S; Brannlund, J; DeBenedictis, A
2008-01-01
In the context of loop quantum gravity, we construct the phase space of isolated horizons with genus greater than 0. Within the loop quantum gravity framework, these horizons are described by genus g surfaces with N punctures and the dimension of the corresponding phase space is calculated including the genus cycles as degrees of freedom. From this, the black-hole entropy can be calculated by counting the microstates which correspond to a black hole of fixed area. We find that the leading term agrees with the A/4 law and that the sub-leading contribution is modified by the genus cycles
The long string at the stretched horizon and the entropy of large non-extremal black holes
International Nuclear Information System (INIS)
Mertens, Thomas G.; Verschelde, Henri; Zakharov, Valentin I.
2016-01-01
We discuss how long strings can arise at the stretched horizon and how they can account for the Bekenstein-Hawking entropy. We use the thermal scalar field theory to derive the asymptotic density of states and corresponding stress tensor of a microcanonical long string gas in Rindler space. We show that the equality of the Hagedorn and Hawking temperatures gives rise to the tree-level entropy of large black holes in accordance with the Bekenstein-Hawking-Wald formula.
The long string at the stretched horizon and the entropy of large non-extremal black holes
Energy Technology Data Exchange (ETDEWEB)
Mertens, Thomas G. [Joseph Henry Laboratories, Princeton University,Washington Road, Princeton, NJ 08544 (United States); Ghent University, Department of Physics and Astronomy,Krijgslaan, 281-S9, 9000 Gent (Belgium); Verschelde, Henri [Ghent University, Department of Physics and Astronomy,Krijgslaan, 281-S9, 9000 Gent (Belgium); Zakharov, Valentin I. [ITEP,B. Cheremushkinskaya 25, Moscow 117218 (Russian Federation); Moscow Institute Phys. & Technol.,Dolgoprudny, Moscow Region 141700 (Russian Federation); School of Biomedicine, Far Eastern Federal University,Sukhanova str 8, Vladivostok 690950 (Russian Federation)
2016-02-04
We discuss how long strings can arise at the stretched horizon and how they can account for the Bekenstein-Hawking entropy. We use the thermal scalar field theory to derive the asymptotic density of states and corresponding stress tensor of a microcanonical long string gas in Rindler space. We show that the equality of the Hagedorn and Hawking temperatures gives rise to the tree-level entropy of large black holes in accordance with the Bekenstein-Hawking-Wald formula.
Quantum statistical entropy for Kerr-de Sitter black hole
Institute of Scientific and Technical Information of China (English)
Zhang Li-Chun; Wu Yue-Qin; Zhao Ren
2004-01-01
Improving the membrane model by which the entropy of the black hole is studied, we study the entropy of the black hole in the non-thermal equilibrium state. To give the problem stated here widespread meaning, we discuss the (n+2)-dimensional de Sitter spacetime. Through discussion, we obtain that the black hole's entropy which contains two horizons (a black hole's horizon and a cosmological horizon) in the non-thermal equilibrium state comprises the entropy corresponding to the black hole's horizon and the entropy corresponding to the cosmological horizon. Furthermore, the entropy of the black hole is a natural property of the black hole. The entropy is irrelevant to the radiation field out of the horizon. This deepens the understanding of the relationship between black hole's entropy and horizon's area. A way to study the bosonic and fermionic entropy of the black hole in high non-thermal equilibrium spacetime is given.
Gradient Dynamics and Entropy Production Maximization
Janečka, Adam; Pavelka, Michal
2018-01-01
We compare two methods for modeling dissipative processes, namely gradient dynamics and entropy production maximization. Both methods require similar physical inputs-how energy (or entropy) is stored and how it is dissipated. Gradient dynamics describes irreversible evolution by means of dissipation potential and entropy, it automatically satisfies Onsager reciprocal relations as well as their nonlinear generalization (Maxwell-Onsager relations), and it has statistical interpretation. Entropy production maximization is based on knowledge of free energy (or another thermodynamic potential) and entropy production. It also leads to the linear Onsager reciprocal relations and it has proven successful in thermodynamics of complex materials. Both methods are thermodynamically sound as they ensure approach to equilibrium, and we compare them and discuss their advantages and shortcomings. In particular, conditions under which the two approaches coincide and are capable of providing the same constitutive relations are identified. Besides, a commonly used but not often mentioned step in the entropy production maximization is pinpointed and the condition of incompressibility is incorporated into gradient dynamics.
Logical entropy of quantum dynamical systems
Directory of Open Access Journals (Sweden)
Ebrahimzadeh Abolfazl
2016-01-01
Full Text Available This paper introduces the concepts of logical entropy and conditional logical entropy of hnite partitions on a quantum logic. Some of their ergodic properties are presented. Also logical entropy of a quantum dynamical system is dehned and ergodic properties of dynamical systems on a quantum logic are investigated. Finally, the version of Kolmogorov-Sinai theorem is proved.
Entropy of dynamical social networks
Zhao, Kun; Karsai, Marton; Bianconi, Ginestra
2012-02-01
Dynamical social networks are evolving rapidly and are highly adaptive. Characterizing the information encoded in social networks is essential to gain insight into the structure, evolution, adaptability and dynamics. Recently entropy measures have been used to quantify the information in email correspondence, static networks and mobility patterns. Nevertheless, we still lack methods to quantify the information encoded in time-varying dynamical social networks. In this talk we present a model to quantify the entropy of dynamical social networks and use this model to analyze the data of phone-call communication. We show evidence that the entropy of the phone-call interaction network changes according to circadian rhythms. Moreover we show that social networks are extremely adaptive and are modified by the use of technologies such as mobile phone communication. Indeed the statistics of duration of phone-call is described by a Weibull distribution and is significantly different from the distribution of duration of face-to-face interactions in a conference. Finally we investigate how much the entropy of dynamical social networks changes in realistic models of phone-call or face-to face interactions characterizing in this way different type human social behavior.
Entropy for the Complexity of Physiological Signal Dynamics.
Zhang, Xiaohua Douglas
2017-01-01
Recently, the rapid development of large data storage technologies, mobile network technology, and portable medical devices makes it possible to measure, record, store, and track analysis of biological dynamics. Portable noninvasive medical devices are crucial to capture individual characteristics of biological dynamics. The wearable noninvasive medical devices and the analysis/management of related digital medical data will revolutionize the management and treatment of diseases, subsequently resulting in the establishment of a new healthcare system. One of the key features that can be extracted from the data obtained by wearable noninvasive medical device is the complexity of physiological signals, which can be represented by entropy of biological dynamics contained in the physiological signals measured by these continuous monitoring medical devices. Thus, in this chapter I present the major concepts of entropy that are commonly used to measure the complexity of biological dynamics. The concepts include Shannon entropy, Kolmogorov entropy, Renyi entropy, approximate entropy, sample entropy, and multiscale entropy. I also demonstrate an example of using entropy for the complexity of glucose dynamics.
Logarithmic black hole entropy corrections and holographic Renyi entropy
Energy Technology Data Exchange (ETDEWEB)
Mahapatra, Subhash [The Institute of Mathematical Sciences, Chennai (India); KU Leuven - KULAK, Department of Physics, Kortrijk (Belgium)
2018-01-15
The entanglement and Renyi entropies for spherical entangling surfaces in CFTs with gravity duals can be explicitly calculated by mapping these entropies first to the thermal entropy on hyperbolic space and then, using the AdS/CFT correspondence, to the Wald entropy of topological black holes. Here we extend this idea by taking into account corrections to the Wald entropy. Using the method based on horizon symmetries and the asymptotic Cardy formula, we calculate corrections to the Wald entropy and find that these corrections are proportional to the logarithm of the area of the horizon. With the corrected expression for the entropy of the black hole, we then find corrections to the Renyi entropies. We calculate these corrections for both Einstein and Gauss-Bonnet gravity duals. Corrections with logarithmic dependence on the area of the entangling surface naturally occur at the order G{sub D}{sup 0}. The entropic c-function and the inequalities of the Renyi entropy are also satisfied even with the correction terms. (orig.)
Logarithmic black hole entropy corrections and holographic Renyi entropy
International Nuclear Information System (INIS)
Mahapatra, Subhash
2018-01-01
The entanglement and Renyi entropies for spherical entangling surfaces in CFTs with gravity duals can be explicitly calculated by mapping these entropies first to the thermal entropy on hyperbolic space and then, using the AdS/CFT correspondence, to the Wald entropy of topological black holes. Here we extend this idea by taking into account corrections to the Wald entropy. Using the method based on horizon symmetries and the asymptotic Cardy formula, we calculate corrections to the Wald entropy and find that these corrections are proportional to the logarithm of the area of the horizon. With the corrected expression for the entropy of the black hole, we then find corrections to the Renyi entropies. We calculate these corrections for both Einstein and Gauss-Bonnet gravity duals. Corrections with logarithmic dependence on the area of the entangling surface naturally occur at the order G D 0 . The entropic c-function and the inequalities of the Renyi entropy are also satisfied even with the correction terms. (orig.)
Transplanckian entanglement entropy
International Nuclear Information System (INIS)
Chang, Darwin; Chu, C.-S.; Lin Fengli
2004-01-01
The entanglement entropy of the event horizon is known to be plagued by the UV divergence due to the infinitely blue-shifted near horizon modes. In this Letter we calculate the entanglement entropy using the transplanckian dispersion relation, which has been proposed to model the quantum gravity effects. We show that, very generally, the entropy is rendered UV finite due to the suppression of high energy modes effected by the transplanckian dispersion relation
Does black-hole entropy make sense
International Nuclear Information System (INIS)
Wilkins, D.
1979-01-01
Bekenstein and Hawking saved the second law of thermodynamics near a black hole by assigning to the hole an entropy Ssub(h) proportional to the area of its event horizon. It is tempting to assume that Ssub(h) possesses all the features commonly associated with the physical entropy. Kundt has shown, however, that Ssub(h) violates several reasonable physical expectations. This criticism is reviewed, augmenting it as follows: (a) Ssub(h) is a badly behaved state function requiring knowledge of the hole's future history; and (b) close analogs of event horizons in other space-times do not possess an 'entropy'. These questions are also discussed: (c) Is Ssub(h) suitable for all regions of a black-hole space-time. And (b) should Ssub(h) be attributed to the exterior of a white hole. One can retain Ssub(h) for the interior (respectively, exterior) of a black (respectively, white) hole, but is rejected as contrary to the information-theoretic derivation of horizon entropy given by Berkenstein. The total entropy defined by Kundt (all ordinary entropy on space-section cutting through the hole, no horizon term) and that of Bekenstein-Hawking (ordinary entropy outside horizon plus horizon term) appear to be complementary concepts with separate domains of validity. In the most natural choice, an observer inside a black hole will use Kundt's entropy, and one remaining outside that of Bekenstein-Hawking. (author)
Logarithmic black hole entropy corrections and holographic Rényi entropy
Mahapatra, Subhash
2018-01-01
The entanglement and Rényi entropies for spherical entangling surfaces in CFTs with gravity duals can be explicitly calculated by mapping these entropies first to the thermal entropy on hyperbolic space and then, using the AdS/CFT correspondence, to the Wald entropy of topological black holes. Here we extend this idea by taking into account corrections to the Wald entropy. Using the method based on horizon symmetries and the asymptotic Cardy formula, we calculate corrections to the Wald entropy and find that these corrections are proportional to the logarithm of the area of the horizon. With the corrected expression for the entropy of the black hole, we then find corrections to the Rényi entropies. We calculate these corrections for both Einstein and Gauss-Bonnet gravity duals. Corrections with logarithmic dependence on the area of the entangling surface naturally occur at the order GD^0. The entropic c-function and the inequalities of the Rényi entropy are also satisfied even with the correction terms.
The dynamical entropy of quantum systems
International Nuclear Information System (INIS)
Connes, A.; Narnhofer, H.; Thirring, W.
1987-01-01
The definition of the dynamical entropy for automorphisms of C * - algebras is represented. Several properties are discussed; especially it is argued that the entropy of the shift can be shown in special cases to be equal with the entropy density. (Author)
Aur, Dorian; Vila-Rodriguez, Fidel
2017-01-01
Complexity measures for time series have been used in many applications to quantify the regularity of one dimensional time series, however many dynamical systems are spatially distributed multidimensional systems. We introduced Dynamic Cross-Entropy (DCE) a novel multidimensional complexity measure that quantifies the degree of regularity of EEG signals in selected frequency bands. Time series generated by discrete logistic equations with varying control parameter r are used to test DCE measures. Sliding window DCE analyses are able to reveal specific period doubling bifurcations that lead to chaos. A similar behavior can be observed in seizures triggered by electroconvulsive therapy (ECT). Sample entropy data show the level of signal complexity in different phases of the ictal ECT. The transition to irregular activity is preceded by the occurrence of cyclic regular behavior. A significant increase of DCE values in successive order from high frequencies in gamma to low frequencies in delta band reveals several phase transitions into less ordered states, possible chaos in the human brain. To our knowledge there are no reliable techniques able to reveal the transition to chaos in case of multidimensional times series. In addition, DCE based on sample entropy appears to be robust to EEG artifacts compared to DCE based on Shannon entropy. The applied technique may offer new approaches to better understand nonlinear brain activity. Copyright Â© 2016 Elsevier B.V. All rights reserved.
Entropy of Vaidya-deSitter Spacetime
Institute of Scientific and Technical Information of China (English)
LI Xiang; ZHAO Zheng
2001-01-01
As a statistical model of black hole entropy, the brick-wall method based on the thermal equilibrium in a large scale cannot be applied to the cases out of equilibrium, such as the non-static hole or the case with two horizons.However, the leading term of hole entropy called the Bekenstein-Hawking entropy comes from the contribution of the field near the horizon. According to this idea, the entropy of Vaidya-deSitter spacetime is calculated. A difference from the static case is that the result proportional to the area of horizon relies on a time-dependent cut-off. The condition of local equilibrium near the horizon is used as a working postulate.
Hawking radiation from quasilocal dynamical horizons
Indian Academy of Sciences (India)
2016-01-06
Jan 6, 2016 ... Abstract. In completely local settings, we establish that a dynamically evolving spherically symmetric black hole horizon can be assigned a Hawking temperature and with the emission of flux, radius of the horizon shrinks.
Gravitational entropy of nonstationary black holes and spherical shells
International Nuclear Information System (INIS)
Hiscock, W.A.
1989-01-01
The problem of defining the gravitational entropy of a nonstationary black hole is considered in a simple model consisting of a spherical shell which collapses into a preexisting black hole. The second law of black-hole mechanics strongly suggests identifying one-quarter of the area of the event horizon as the gravitational entropy of the system. It is, however, impossible to accurately locate the position of the global event horizon using only local measurements. In order to maintain a local thermodynamics, it is suggested that the entropy of the black hole be identified with one-quarter the area of the apparent horizon. The difference between the event-horizon entropy (to the extent it can be determined) and the apparent-horizon entropy may then be interpreted as the gravitational entropy of the collapsing shell. The total (event-horizon) gravitational entropy evolves in a smooth (C 0 ) fashion, even in the presence of δ-functional shells of matter
Entropy in the classical and quantum polymer black hole models
International Nuclear Information System (INIS)
Livine, Etera R; Terno, Daniel R
2012-01-01
We investigate the entropy counting for black hole horizons in loop quantum gravity (LQG). We argue that the space of 3D closed polyhedra is the classical counterpart of the space of SU(2) intertwiners at the quantum level. Then computing the entropy for the boundary horizon amounts to calculating the density of polyhedra or the number of intertwiners at fixed total area. Following the previous work (Bianchi 2011 Class. Quantum Grav. 28 114006) we dub these the classical and quantum polymer models for isolated horizons in LQG. We provide exact micro-canonical calculations for both models and we show that the classical counting of polyhedra accounts for most of the features of the intertwiner counting (leading order entropy and log-correction), thus providing us with a simpler model to further investigate correlations and dynamics. To illustrate this, we also produce an exact formula for the dimension of the intertwiner space as a density of ‘almost-closed polyhedra’. (paper)
Trajectories entropy in dynamical graphs with memory
Directory of Open Access Journals (Sweden)
Francesco eCaravelli
2016-04-01
Full Text Available In this paper we investigate the application of non-local graph entropy to evolving and dynamical graphs. The measure is based upon the notion of Markov diffusion on a graph, and relies on the entropy applied to trajectories originating at a specific node. In particular, we study the model of reinforcement-decay graph dynamics, which leads to scale free graphs. We find that the node entropy characterizes the structure of the network in the two parameter phase-space describing the dynamical evolution of the weighted graph. We then apply an adapted version of the entropy measure to purely memristive circuits. We provide evidence that meanwhile in the case of DC voltage the entropy based on the forward probability is enough to characterize the graph properties, in the case of AC voltage generators one needs to consider both forward and backward based transition probabilities. We provide also evidence that the entropy highlights the self-organizing properties of memristive circuits, which re-organizes itself to satisfy the symmetries of the underlying graph.
Dynamical entropy, quantum K-systems and clustering
International Nuclear Information System (INIS)
Narnhofer, H.
1989-01-01
The two possibilities to define a quantum K-system, either using algebraic relations or using properties of the dynamical entropy, are compared. It is shown that under the additional assumption of strong asymptotic abelianess the algebraic relations imply the properties of the dynamical entropy. 14 refs. (Author)
Dynamical entropy of C* algebras and Von Neumann algebras
International Nuclear Information System (INIS)
Connes, A.; Narnhofer, H.; Thirring, W.
1986-01-01
The definition of the dynamical entropy is extended for automorphism groups of C * algebras. As example the dynamical entropy of the shift of a lattice algebra is studied and it is shown that in some cases it coincides with the entropy density. (Author)
Quantum Statistical Entropy of Five-Dimensional Black Hole
Institute of Scientific and Technical Information of China (English)
ZHAO Ren; WU Yue-Qin; ZHANG Sheng-Li
2006-01-01
The generalized uncertainty relation is introduced to calculate quantum statistic entropy of a black hole.By using the new equation of state density motivated by the generalized uncertainty relation, we discuss entropies of Bose field and Fermi field on the background of the five-dimensional spacetime. In our calculation, we need not introduce cutoff. There is not the divergent logarithmic term as in the original brick-wall method. And it is obtained that the quantum statistic entropy corresponding to black hole horizon is proportional to the area of the horizon. Further it is shown that the entropy of black hole is the entropy of quantum state on the surface of horizon. The black hole's entropy is the intrinsic property of the black hole. The entropy is a quantum effect. It makes people further understand the quantum statistic entropy.
Quantum Statistical Entropy of Five-Dimensional Black Hole
International Nuclear Information System (INIS)
Zhao Ren; Zhang Shengli; Wu Yueqin
2006-01-01
The generalized uncertainty relation is introduced to calculate quantum statistic entropy of a black hole. By using the new equation of state density motivated by the generalized uncertainty relation, we discuss entropies of Bose field and Fermi field on the background of the five-dimensional spacetime. In our calculation, we need not introduce cutoff. There is not the divergent logarithmic term as in the original brick-wall method. And it is obtained that the quantum statistic entropy corresponding to black hole horizon is proportional to the area of the horizon. Further it is shown that the entropy of black hole is the entropy of quantum state on the surface of horizon. The black hole's entropy is the intrinsic property of the black hole. The entropy is a quantum effect. It makes people further understand the quantum statistic entropy.
Bianchi, Eugenio; De Lorenzo, Tommaso; Smerlak, Matteo
2015-06-01
We study the dynamics of vacuum entanglement in the process of gravitational collapse and subsequent black hole evaporation. In the first part of the paper, we introduce a covariant regularization of entanglement entropy tailored to curved spacetimes; this regularization allows us to propose precise definitions for the concepts of black hole "exterior entropy" and "radiation entropy." For a Vaidya model of collapse we find results consistent with the standard thermodynamic properties of Hawking radiation. In the second part of the paper, we compute the vacuum entanglement entropy of various spherically-symmetric spacetimes of interest, including the nonsingular black hole model of Bardeen, Hayward, Frolov and Rovelli-Vidotto and the "black hole fireworks" model of Haggard-Rovelli. We discuss specifically the role of event and trapping horizons in connection with the behavior of the radiation entropy at future null infinity. We observe in particular that ( i) in the presence of an event horizon the radiation entropy diverges at the end of the evaporation process, ( ii) in models of nonsingular evaporation (with a trapped region but no event horizon) the generalized second law holds only at early times and is violated in the "purifying" phase, ( iii) at late times the radiation entropy can become negative (i.e. the radiation can be less correlated than the vacuum) before going back to zero leading to an up-down-up behavior for the Page curve of a unitarily evaporating black hole.
Entropy of Kerr-de Sitter black hole
Li, Huai-Fan; Ma, Meng-Sen; Zhang, Li-Chun; Zhao, Ren
2017-07-01
Based on the consideration that the black hole horizon and the cosmological horizon of Kerr-de Sitter black hole are not independent of each other, we conjecture the total entropy of the system should have an extra term contributed from the correlations between the two horizons, except for the sum of the two horizon entropies. By employing globally effective first law and effective thermodynamic quantities, we obtain the corrected total entropy and find that the region of stable state for Kerr-de Sitter is related to the angular velocity parameter a, i.e., the region of stable state becomes bigger as the rotating parameters a is increases.
Notes on entropy force in general spherically symmetric spacetimes
International Nuclear Information System (INIS)
Cai Ronggen; Cao Liming; Ohta, Nobuyoshi
2010-01-01
In a recent paper [arXiv:1001.0785], Verlinde has shown that the Newton gravity appears as an entropy force. In this paper we show how gravity appears as entropy force in Einstein's equation of gravitational field in a general spherically symmetric spacetime. We mainly focus on the trapping horizon of the spacetime. We find that when matter fields are absent, the change of entropy associated with the trapping horizon indeed can be identified with an entropy force. When matter fields are present, we see that heat flux of matter fields also leads to the change of entropy. Applying arguments made by Verlinde and Smolin, respectively, to the trapping horizon, we find that the entropy force is given by the surface gravity of the horizon. The cases in the untrapped region of the spacetime are also discussed.
Crossing the entropy barrier of dynamical zeta functions
International Nuclear Information System (INIS)
Aurich, R.; Bolte, J.; Matthies, C.; Sieber, M.; Steiner, F.
1992-01-01
Dynamical zeta functions are an important tool to quantize chaotic dynamical systems. The basic quantization rules require the computation of the zeta functions on the real energy axis, where the Euler product representations running over the classical periodic orbits usually do not converge due to the existence of the so-called entropy barrier determined by the topological entropy of the classical system. We shown that the convergence properties of the dynamical zeta functions rewritten as Dirichlet series are governed not only by the well-known topological and metric entropy, but depend crucially on subtle statistical properties of the Maslow indices and of the multiplicities of the periodic orbits that are measured by a new parameter for which we introduce the notion of a third entropy. If and only if the third entropy is nonvanishing, one can cross the entropy barrier; if it exceeds a certain value, one can even compute the zeta function in the physical region by means of a convergent Dirichlet series. A simple statistical model is presented which allows to compute the third entropy. Four examples of chaotic systems are studied in detail to test the model numerically. (orig.)
Crossing the entropy barrier of dynamical zeta functions
Energy Technology Data Exchange (ETDEWEB)
Aurich, R.; Bolte, J.; Matthies, C.; Sieber, M.; Steiner, F. (Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik)
1992-01-01
Dynamical zeta functions are an important tool to quantize chaotic dynamical systems. The basic quantization rules require the computation of the zeta functions on the real energy axis, where the Euler product representations running over the classical periodic orbits usually do not converge due to the existence of the so-called entropy barrier determined by the topological entropy of the classical system. We shown that the convergence properties of the dynamical zeta functions rewritten as Dirichlet series are governed not only by the well-known topological and metric entropy, but depend crucially on subtle statistical properties of the Maslow indices and of the multiplicities of the periodic orbits that are measured by a new parameter for which we introduce the notion of a third entropy. If and only if the third entropy is nonvanishing, one can cross the entropy barrier; if it exceeds a certain value, one can even compute the zeta function in the physical region by means of a convergent Dirichlet series. A simple statistical model is presented which allows to compute the third entropy. Four examples of chaotic systems are studied in detail to test the model numerically. (orig.).
LOCAL ENTROPY FUNCTION OF DYNAMICAL SYSTEM
Directory of Open Access Journals (Sweden)
İsmail TOK
2013-05-01
Full Text Available In this work, we first,define the entropy function of the topological dynamical system and investigate basic properties of this function without going into details. Let (X,A,T be a probability measure space and consider P = { pl5p2,...,pn} a finite measurable partition of all sub-sets of topological dynamical system (X,T.Then,the quantity H (P = ^ zpt is called the i=1 entropy function of finite measurable partition P.Where f-1 log t if 0 0.If diam(P < s,then the quantity L^ (T = h^ (T - h^ (T,P is called a local entropy function of topological dynamical system (X,T . In conclusion, Let (X,T and (Y,S be two topological dynamical system. If TxS is a transformation defined on the product space (XxY,TxS with (TxS(x , y = (Tx,Sy for all (x,y X x Y.Then L ^^ (TxS = L^d(T + L (S .and, we prove some fundamental properties of this function.
Entropy of Reissner–Nordström–de Sitter black hole
Energy Technology Data Exchange (ETDEWEB)
Zhang, Li-Chun [Department of Physics, Shanxi Datong University, Datong 037009 (China); Institute of Theoretical Physics, Shanxi Datong University, Datong 037009 (China); Zhao, Ren [Institute of Theoretical Physics, Shanxi Datong University, Datong 037009 (China); Ma, Meng-Sen, E-mail: mengsenma@gmail.com [Department of Physics, Shanxi Datong University, Datong 037009 (China); Institute of Theoretical Physics, Shanxi Datong University, Datong 037009 (China)
2016-10-10
Based on the consideration that the black hole horizon and the cosmological horizon of Reissner–Nordström black hole in de Sitter space are not independent each other, we conjecture the total entropy of the system should have an extra term contributed from the entanglement between the two horizons, except for the sum of the two horizon entropies. Making use of the globally effective first law and the effective thermodynamic quantities, we derive the total entropy and find that it will diverge as the two horizons tend to coincide.
International Nuclear Information System (INIS)
Bianchi, Eugenio; Lorenzo, Tommaso De; Smerlak, Matteo
2015-01-01
We study the dynamics of vacuum entanglement in the process of gravitational collapse and subsequent black hole evaporation. In the first part of the paper, we introduce a covariant regularization of entanglement entropy tailored to curved spacetimes; this regularization allows us to propose precise definitions for the concepts of black hole “exterior entropy” and “radiation entropy.” For a Vaidya model of collapse we find results consistent with the standard thermodynamic properties of Hawking radiation. In the second part of the paper, we compute the vacuum entanglement entropy of various spherically-symmetric spacetimes of interest, including the nonsingular black hole model of Bardeen, Hayward, Frolov and Rovelli-Vidotto and the “black hole fireworks” model of Haggard-Rovelli. We discuss specifically the role of event and trapping horizons in connection with the behavior of the radiation entropy at future null infinity. We observe in particular that (i) in the presence of an event horizon the radiation entropy diverges at the end of the evaporation process, (ii) in models of nonsingular evaporation (with a trapped region but no event horizon) the generalized second law holds only at early times and is violated in the “purifying” phase, (iii) at late times the radiation entropy can become negative (i.e. the radiation can be less correlated than the vacuum) before going back to zero leading to an up-down-up behavior for the Page curve of a unitarily evaporating black hole.
Fundamental limits on quantum dynamics based on entropy change
Das, Siddhartha; Khatri, Sumeet; Siopsis, George; Wilde, Mark M.
2018-01-01
It is well known in the realm of quantum mechanics and information theory that the entropy is non-decreasing for the class of unital physical processes. However, in general, the entropy does not exhibit monotonic behavior. This has restricted the use of entropy change in characterizing evolution processes. Recently, a lower bound on the entropy change was provided in the work of Buscemi, Das, and Wilde [Phys. Rev. A 93(6), 062314 (2016)]. We explore the limit that this bound places on the physical evolution of a quantum system and discuss how these limits can be used as witnesses to characterize quantum dynamics. In particular, we derive a lower limit on the rate of entropy change for memoryless quantum dynamics, and we argue that it provides a witness of non-unitality. This limit on the rate of entropy change leads to definitions of several witnesses for testing memory effects in quantum dynamics. Furthermore, from the aforementioned lower bound on entropy change, we obtain a measure of non-unitarity for unital evolutions.
Energy Technology Data Exchange (ETDEWEB)
Xu, Kaixuan, E-mail: kaixuanxubjtu@yeah.net; Wang, Jun
2017-02-26
In this paper, recently introduced permutation entropy and sample entropy are further developed to the fractional cases, weighted fractional permutation entropy (WFPE) and fractional sample entropy (FSE). The fractional order generalization of information entropy is utilized in the above two complexity approaches, to detect the statistical characteristics of fractional order information in complex systems. The effectiveness analysis of proposed methods on the synthetic data and the real-world data reveals that tuning the fractional order allows a high sensitivity and more accurate characterization to the signal evolution, which is useful in describing the dynamics of complex systems. Moreover, the numerical research on nonlinear complexity behaviors is compared between the returns series of Potts financial model and the actual stock markets. And the empirical results confirm the feasibility of the proposed model. - Highlights: • Two new entropy approaches for estimation of nonlinear complexity are proposed for the financial market. • Effectiveness analysis of proposed methods is presented and their respective features are studied. • Empirical research of proposed analysis on seven world financial market indices. • Numerical simulation of Potts financial dynamics is preformed for nonlinear complexity behaviors.
International Nuclear Information System (INIS)
Xu, Kaixuan; Wang, Jun
2017-01-01
In this paper, recently introduced permutation entropy and sample entropy are further developed to the fractional cases, weighted fractional permutation entropy (WFPE) and fractional sample entropy (FSE). The fractional order generalization of information entropy is utilized in the above two complexity approaches, to detect the statistical characteristics of fractional order information in complex systems. The effectiveness analysis of proposed methods on the synthetic data and the real-world data reveals that tuning the fractional order allows a high sensitivity and more accurate characterization to the signal evolution, which is useful in describing the dynamics of complex systems. Moreover, the numerical research on nonlinear complexity behaviors is compared between the returns series of Potts financial model and the actual stock markets. And the empirical results confirm the feasibility of the proposed model. - Highlights: • Two new entropy approaches for estimation of nonlinear complexity are proposed for the financial market. • Effectiveness analysis of proposed methods is presented and their respective features are studied. • Empirical research of proposed analysis on seven world financial market indices. • Numerical simulation of Potts financial dynamics is preformed for nonlinear complexity behaviors.
Entropy of Reissner-Nordstrom-De Sitter Black Hole in Nonthermal Equilibrium
Institute of Scientific and Technical Information of China (English)
ZHAO Ren; ZHANG Jun-Fang; ZHANG Li-Chun
2002-01-01
By making use of the method of quantum statistics, we directly derive the partition function of bosonic and fermionic fields in Reissner-Nordstrom-De Sitter black hole and obtain the integral expression of black hole's entropy and the entropy to which the cosmic horizon surface corresponds. It avoids the difficulty in solving the wave equation of various particles. Then via the improved brick-wall method, i.e. the membrane model, we calculate black hole's entropy and cosmic entropy and find out that if we let the integral upper limit and lower limit both tend to the horizon, the entropy of black hole is proportional to the area of horizon and the entropy to which cosmic horizon surface corresponds is proportional to the area of cosmic horizon. In our result, the stripped term and the divergent logarithmic term in the original brick-wall method no longer exist. In the whole process, the physical idea is clear and the calculation is simple.We offer a new simple and direct way for calculating the entropy of different complicated black holes.
Information entropy for static spherically symmetric black holes
Institute of Scientific and Technical Information of China (English)
Jiang Ji-Jian; Li Chuan-An
2009-01-01
By using the new equation of state density derived from the generalized uncertainty relation, the number of the quantum states near event horizon is obtained, with which then the information entropy of static spherically symmetric black holes has been discussed. It is found that the divergent integral of quantum states near the event horizon can be naturally avoided if using the new equation of state density without introducing the ultraviolet cut-off. The information entropy of black holes can be obtained precisely by the residue theorem, which is shown to be proportional to the horizon area. The information entropy of black holes obtained agrees with the Bechenstein-Hawking entropy when the suitable cutoff factor is adopted.
Information entropy for static spherically symmetric black holes
International Nuclear Information System (INIS)
Ji-Jian, Jiang; Chuan-An, Li
2009-01-01
By using the new equation of state density derived from the generalized uncertainty relation, the number of the quantum states near event horizon is obtained, with which then the information entropy of static spherically symmetric black holes has been discussed. It is found that the divergent integral of quantum states near the event horizon can be naturally avoided if using the new equation of state density without introducing the ultraviolet cut-off. The information entropy of black holes can be obtained precisely by the residue theorem, which is shown to be proportional to the horizon area. The information entropy of black holes obtained agrees with the Bechenstein–Hawking entropy when the suitable cutoff factor is adopted. (general)
Invariant of dynamical systems: A generalized entropy
International Nuclear Information System (INIS)
Meson, A.M.; Vericat, F.
1996-01-01
In this work the concept of entropy of a dynamical system, as given by Kolmogorov, is generalized in the sense of Tsallis. It is shown that this entropy is an isomorphism invariant, being complete for Bernoulli schemes. copyright 1996 American Institute of Physics
Quantum Entropy of Black Hole with Internal Global Monopole
Institute of Scientific and Technical Information of China (English)
HAN Yi-Wen; YANG Shu-Zheng; LIU Wen-Biao
2005-01-01
Using the generalized uncertainty relation, the new equation of state density is obtained, and then the entropy of black hole with an internal global monopole is discussed. The divergence that appears in black hole entropy calculation through original brick-wall model is overcome. The result of the direct proportion between black hole entropy and its event horizon area is drawn and given. The result shows that the black hole entropy must be the entropy of quantum state near the event horizon.
The information entropy of a static dilaton black hole
Institute of Scientific and Technical Information of China (English)
2008-01-01
In accordance with holographic principle, by calculating the statistical entropy of the quantum field just at the event horizon of the Garfinkle-Horowitz-Strominger dilaton black hole, the information entropy of the black hole was investigated and the Bekenstein-Hawking formula was obtained. The results show that black hole entropy is identical with the statistical entropy of the quantum field at the horizon. Using the generalized uncertainty relation, the divergence of the state density near the event horizon in usual quantum field theory was removed, and the cutoffs and the little mass approximation in the heat gas method of black hole entropy were avoided. Thus, the microstates of the massive scalar field just at the event horizon of the static dilaton black hole were studied directly and a description on holograph principle was presented. By using residue theorem, the integral difficulty in the calculation was overcome, and the information entropy and the Bekenstein-Hawking formula were obtained quantitatively. Compared with the black hole entropy from the loop quantum gravity, the consistency of methods and results of calculating black hole entropy in non-commutative quantum field theory and loop quantum gravity was investigated. By this, the gravity correction constant in the generalized uncertainty relation was suggested and the sense of holographic principle was discussed.
Radiation from quantum weakly dynamical horizons in loop quantum gravity.
Pranzetti, Daniele
2012-07-06
We provide a statistical mechanical analysis of quantum horizons near equilibrium in the grand canonical ensemble. By matching the description of the nonequilibrium phase in terms of weakly dynamical horizons with a local statistical framework, we implement loop quantum gravity dynamics near the boundary. The resulting radiation process provides a quantum gravity description of the horizon evaporation. For large black holes, the spectrum we derive presents a discrete structure which could be potentially observable.
A note on entanglement entropy and quantum geometry
International Nuclear Information System (INIS)
Bodendorfer, N
2014-01-01
It has been argued that the entropy computed in the isolated horizon framework of loop quantum gravity is closely related to the entanglement entropy of the gravitational field, and that the calculation performed is not restricted to horizons. We recall existing work on this issue and explain how recent work on generalizing these computations to arbitrary spacetime dimensions D+1⩾3 supports this point of view and makes the duality between entanglement entropy and the entropy computed from counting boundary states manifest. In a certain semiclassical regime in 3+1 dimensions, this entropy is given by the Bekenstein–Hawking formula. (paper)
Where are the black-hole entropy degrees of freedom?
International Nuclear Information System (INIS)
Das, Saurya; Shankaranarayanan, S
2007-01-01
Understanding the area proportionality of black-hole entropy (the 'area law') from an underlying fundamental theory has been one of the goals of all models of quantum gravity. A key question that one asks is: where are the degrees of freedom giving rise to black-hole entropy located? Taking the point of view that entanglement between field degrees of freedom inside and outside the horizon can be a source of this entropy, we show that when the field is in its ground state, the degrees of freedom near the horizon contribute most to the entropy, and the area law is obeyed. However, when it is in an excited state, degrees of freedom far from the horizon contribute more significantly, and deviations from the area law are observed. In other words, we demonstrate that horizon degrees of freedom are responsible for the area law
Relationship between dynamical entropy and energy dissipation far from thermodynamic equilibrium
Green, Jason R.; Costa, Anthony B.; Grzybowski, Bartosz A.; Szleifer, Igal
2013-01-01
Connections between microscopic dynamical observables and macroscopic nonequilibrium (NE) properties have been pursued in statistical physics since Boltzmann, Gibbs, and Maxwell. The simulations we describe here establish a relationship between the Kolmogorov–Sinai entropy and the energy dissipated as heat from a NE system to its environment. First, we show that the Kolmogorov–Sinai or dynamical entropy can be separated into system and bath components and that the entropy of the system characterizes the dynamics of energy dissipation. Second, we find that the average change in the system dynamical entropy is linearly related to the average change in the energy dissipated to the bath. The constant energy and time scales of the bath fix the dynamical relationship between these two quantities. These results provide a link between microscopic dynamical variables and the macroscopic energetics of NE processes. PMID:24065832
Black hole entropy functions and attractor equations
International Nuclear Information System (INIS)
Lopes Cardoso, Gabriel; Wit, Bernard de; Mahapatra, Swapna
2007-01-01
The entropy and the attractor equations for static extremal black hole solutions follow from a variational principle based on an entropy function. In the general case such an entropy function can be derived from the reduced action evaluated in a near-horizon geometry. BPS black holes constitute special solutions of this variational principle, but they can also be derived directly from a different entropy function based on supersymmetry enhancement at the horizon. Both functions are consistent with electric/magnetic duality and for BPS black holes their corresponding OSV-type integrals give identical results at the semi-classical level. We clarify the relation between the two entropy functions and the corresponding attractor equations for N = 2 supergravity theories with higher-derivative couplings in four space-time dimensions. We discuss how non-holomorphic corrections will modify these entropy functions
Distance-Based Configurational Entropy of Proteins from Molecular Dynamics Simulations.
Fogolari, Federico; Corazza, Alessandra; Fortuna, Sara; Soler, Miguel Angel; VanSchouwen, Bryan; Brancolini, Giorgia; Corni, Stefano; Melacini, Giuseppe; Esposito, Gennaro
2015-01-01
Estimation of configurational entropy from molecular dynamics trajectories is a difficult task which is often performed using quasi-harmonic or histogram analysis. An entirely different approach, proposed recently, estimates local density distribution around each conformational sample by measuring the distance from its nearest neighbors. In this work we show this theoretically well grounded the method can be easily applied to estimate the entropy from conformational sampling. We consider a set of systems that are representative of important biomolecular processes. In particular: reference entropies for amino acids in unfolded proteins are obtained from a database of residues not participating in secondary structure elements;the conformational entropy of folding of β2-microglobulin is computed from molecular dynamics simulations using reference entropies for the unfolded state;backbone conformational entropy is computed from molecular dynamics simulations of four different states of the EPAC protein and compared with order parameters (often used as a measure of entropy);the conformational and rototranslational entropy of binding is computed from simulations of 20 tripeptides bound to the peptide binding protein OppA and of β2-microglobulin bound to a citrate coated gold surface. This work shows the potential of the method in the most representative biological processes involving proteins, and provides a valuable alternative, principally in the shown cases, where other approaches are problematic.
Nernst Theorem and Statistical Entropy of 5-Dimensional Rotating Black Hole
Institute of Scientific and Technical Information of China (English)
ZHAO Ren; WU Yue-Qin; ZHANG Li-Chun
2003-01-01
In this paper, by using quantum statistical method, we obtain the partition function of Bose field and Fermi field on the background of the 5-dimensional rotating black hole. Then via the improved brick-wall method and membrane model, we calculate the entropy of Bose field and Fermi field of the black hole. And it is obtained that the entropy of the black hole is not only related to the area of the outer horizon but also is the function of inner horizon's area. In our results, there are not the left out term and the divergent logarithmic term in the original brick-wall method.The doubt that why the entropy of the scalar or Dirac field outside the event horizon is the entropy of the black hole in the original brick-wall method does not exist. The influence of spinning degeneracy of particles on entropy of the black hole is also given. It is shown that the entropy determined by the areas of the inner and outer horizons will approach zero,when the radiation temperature of the black hole approaches absolute zero. It satisfies Nernst theorem. The entropy can be taken as the Planck absolute entropy. We provide a way to study higher dimensional black hole.
Thermodynamics of the Apparent Horizon in FRW Universe with Massive Gravity
International Nuclear Information System (INIS)
Li Hui; Zhang Yi
2013-01-01
Applying Clausius relation with energy-supply defined by the unified first law of thermodynamics formalism to the apparent horizon of a massive gravity model in cosmology proposed lately, the corrected entropic formula of the apparent horizon is obtained with the help of the modified Friedmann equations. This entropy-area relation, together with the identified Misner-Sharp internal energy, verifies the first law of thermodynamics for the apparent horizon with a volume change term for consistency. On the other hand, by means of the corrected entropy-area formula and the Clausius relation δQ = T d S, where the heat Bow δQ is the energy-supply of pure matter projecting on the vector ξ tangent to the apparent horizon and should be looked on as the amount of energy crossing the apparent horizon during the time interval dt and the temperature of the apparent horizon for energy crossing during the same interval is 1/(2πr A ), the modified Friedmann equations governing the dynamical evolution of the universe are reproduced with the known energy density and pressure of massive graviton. The integration constant is found to correspond to a cosmological term which could be absorbed into the energy density of matter. Having established the correspondence of massive cosmology with the unified first law of thermodynamics on the apparent horizon, the validity of the generalized second law of thermodynamics is also discussed by assuming the thermal equilibrium between the apparent horizon and the matter field bounded by the apparent horizon. It is found that, in the limit H c → 0, which recovers the Minkowski reference metric solution in the fiat case, the generalized second law of thermodynamics holds if α 3 + 4α 4 3 = α 4 = 0, the generalized second law of thermodynamics could be violated. (general)
International Nuclear Information System (INIS)
Booth, Ivan; Fairhurst, Stephen
2007-01-01
We study the geometry and dynamics of both isolated and dynamical trapping horizons by considering the allowed variations of their foliating two-surfaces. This provides a common framework that may be used to consider both their possible evolutions and their deformations as well as derive the well-known flux laws. Using this framework, we unify much of what is already known about these objects as well as derive some new results. In particular we characterize and study the ''almost isolated'' trapping horizons known as slowly evolving horizons. It is for these horizons that a dynamical first law holds and this is analogous and closely related to the Hawking-Hartle formula for event horizons
The covariant entropy bound in gravitational collapse
International Nuclear Information System (INIS)
Gao, Sijie; Lemos, Jose P. S.
2004-01-01
We study the covariant entropy bound in the context of gravitational collapse. First, we discuss critically the heuristic arguments advanced by Bousso. Then we solve the problem through an exact model: a Tolman-Bondi dust shell collapsing into a Schwarzschild black hole. After the collapse, a new black hole with a larger mass is formed. The horizon, L, of the old black hole then terminates at the singularity. We show that the entropy crossing L does not exceed a quarter of the area of the old horizon. Therefore, the covariant entropy bound is satisfied in this process. (author)
Investigating dynamical complexity in the magnetosphere using various entropy measures
Balasis, Georgios; Daglis, Ioannis A.; Papadimitriou, Constantinos; Kalimeri, Maria; Anastasiadis, Anastasios; Eftaxias, Konstantinos
2009-09-01
The complex system of the Earth's magnetosphere corresponds to an open spatially extended nonequilibrium (input-output) dynamical system. The nonextensive Tsallis entropy has been recently introduced as an appropriate information measure to investigate dynamical complexity in the magnetosphere. The method has been employed for analyzing Dst time series and gave promising results, detecting the complexity dissimilarity among different physiological and pathological magnetospheric states (i.e., prestorm activity and intense magnetic storms, respectively). This paper explores the applicability and effectiveness of a variety of computable entropy measures (e.g., block entropy, Kolmogorov entropy, T complexity, and approximate entropy) to the investigation of dynamical complexity in the magnetosphere. We show that as the magnetic storm approaches there is clear evidence of significant lower complexity in the magnetosphere. The observed higher degree of organization of the system agrees with that inferred previously, from an independent linear fractal spectral analysis based on wavelet transforms. This convergence between nonlinear and linear analyses provides a more reliable detection of the transition from the quiet time to the storm time magnetosphere, thus showing evidence that the occurrence of an intense magnetic storm is imminent. More precisely, we claim that our results suggest an important principle: significant complexity decrease and accession of persistency in Dst time series can be confirmed as the magnetic storm approaches, which can be used as diagnostic tools for the magnetospheric injury (global instability). Overall, approximate entropy and Tsallis entropy yield superior results for detecting dynamical complexity changes in the magnetosphere in comparison to the other entropy measures presented herein. Ultimately, the analysis tools developed in the course of this study for the treatment of Dst index can provide convenience for space weather
Effective first law of thermodynamics of black holes with two horizons
International Nuclear Information System (INIS)
Yi-Huan, Wei
2009-01-01
For a black hole with two horizons, the effective entropy is assumed to be a linear combination of the two entropies of the outer and inner horizons. In terms of the effective thermodynamic quantities the effective Bekenstein–Smarr formula and the effective first law of thermodynamics are derived. (geophysics, astronomy and astrophysics)
A note on entropy of de Sitter black holes
Energy Technology Data Exchange (ETDEWEB)
Bhattacharya, Sourav [University of Crete, ITCP and Department of Physics, Heraklion (Greece); Inter-University Centre for Astronomy and Astrophysics (IUCAA), Pune (India)
2016-03-15
A de Sitter black hole or a black hole spacetime endowed with a positive cosmological constant has two Killing horizons - a black hole and a cosmological event horizon surrounding it. It is natural to expect that the total Bekenstein-Hawking entropy of such spacetimes should be the sum of the two horizons' areas. In this work we apply the recently developed formalism using the Gibbons-Hawking-York boundary term and the near horizon symmetries to derive the total entropy of such two horizon spacetimes. We construct a suitable general geometric set up for general stationary axisymmetric spacetimes with two or more than two commuting Killing vector fields in an arbitrary spacetime dimensions. This framework helps us to deal with both horizons on an equal footing. We show that in order to obtain the total entropy of such spacetimes, the near horizon mode functions for the diffeomorphism generating vector fields have to be restricted in a certain manner, compared to the single horizon spacetimes. We next discuss specific known exact solutions belonging to the Kerr-Newman or the Plebanski-Demianski-de Sitter families to show that they fall into the category of our general framework. We end with a sketch of further possible extensions of this work. (orig.)
Holographic charged Rényi entropies
Belin, Alexandre; Hung, Ling-Yan; Maloney, Alexander; Matsuura, Shunji; Myers, Robert C.; Sierens, Todd
2013-12-01
We construct a new class of entanglement measures by extending the usual definition of Rényi entropy to include a chemical potential. These charged Rényi entropies measure the degree of entanglement in different charge sectors of the theory and are given by Euclidean path integrals with the insertion of a Wilson line encircling the entangling surface. We compute these entropies for a spherical entangling surface in CFT's with holographic duals, where they are related to entropies of charged black holes with hyperbolic horizons. We also compute charged Rényi entropies in free field theories.
Institute of Scientific and Technical Information of China (English)
XU Dian-Yan
2003-01-01
The free energy and entropy of Reissner-Nordstrom black holes in higher-dimensional space-time are calculated by the quantum statistic method with a brick wall model. The space-time of the black holes is divided into three regions: region 1, (r > r0); region 2, (r0 > r > n); and region 3, (T-J > r > 0), where r0 is the radius of the outer event horizon, and r, is the radius of the inner event horizon. Detailed calculation shows that the entropy contributed by region 2 is zero, the entropy contributed by region 1 is positive and proportional to the outer event horizon area, the entropy contributed by region 3 is negative and proportional to the inner event horizon area. The total entropy contributed by all the three regions is positive and proportional to the area difference between the outer and inner event horizons. As rt approaches r0 in the nearly extreme case, the total quantum statistical entropy approaches zero.
Entropy of charged dilaton-axion black hole
International Nuclear Information System (INIS)
Ghosh, Tanwi; SenGupta, Soumitra
2008-01-01
Using the brick wall method, the entropy of the charged dilaton-axion black hole is determined for both asymptotically flat and nonflat cases. The entropy turns out to be proportional to the horizon area of the black hole confirming the Bekenstein-Hawking area-entropy formula for black holes. The leading order logarithmic corrections to the entropy are also derived for such black holes.
Two Notes on Measure-Theoretic Entropy of Random Dynamical Systems
Institute of Scientific and Technical Information of China (English)
YuJun ZHU
2009-01-01
In this paper, Brin-Katok local entropy formula and Katok's definition of the measure theoretic entropy using spanning set are established for the random dynamical system over an invertible ergodic system.
Topological derivation of black hole entropy by analogy with a chain polymer
International Nuclear Information System (INIS)
Siino, Masaru
2002-01-01
The generic crease set of an event horizon possesses anisotropic structure although most black holes are dynamically stable. This fact suggests that a generic almost spherical black hole has a very crumpled crease set on a microscopic scale although the crease set is similar to a pointwise crease set on a macroscopic scale. In the present article, we count the number of such microstates of an almost spherical black hole by analogy with an elastic chain polymer. This estimation of black hole entropy reproduces the well-known Bekenstein-Hawking entropy of a Schwarzschild black hole
International Nuclear Information System (INIS)
Guo Yongfeng; Xu Wei; Li Dongxi; Xie Wenxian
2008-01-01
A stochastic dissipative dynamical system driven by non-Gaussian noise is investigated. A general approximate Fokker-Planck equation of the system is derived through a path-integral approach. Based on the definition of Shannon's information entropy, the exact time dependence of entropy flux and entropy production of the system is calculated both in the absence and in the presence of non-equilibrium constraint. The present calculation can be used to interpret the interplay of the dissipative constant and non-Gaussian noise on the entropy flux and entropy production
Hair-brane ideas on the horizon
International Nuclear Information System (INIS)
Martinec, Emil J.; Niehoff, Ben E.
2015-01-01
We continue an examination of the microstate geometries program begun in arXiv:1409.6017, focussing on the role of branes that wrap the cycles which degenerate when a throat in the geometry deepens and a horizon forms. An associated quiver quantum mechanical model of minimally wrapped branes exhibits a non-negligible fraction of the gravitational entropy, which scales correctly as a function of the charges. The results suggest a picture of AdS_3/CFT_2 duality wherein the long string that accounts for BTZ black hole entropy in the CFT description, can also be seen to inhabit the horizon of BPS black holes on the gravity side.
Hair-brane ideas on the horizon
Energy Technology Data Exchange (ETDEWEB)
Martinec, Emil J. [Enrico Fermi Institute and Department of Physics, University of Chicago, 5640 S. Ellis Ave., Chicago, IL 60637-1433 (United States); Niehoff, Ben E. [Department of Applied Mathematics and Theoretical Physics, University of Cambridge,Centre for Mathematical Sciences,Wilberforce Rd., Cambridge, CB3 0WA (United Kingdom)
2015-11-27
We continue an examination of the microstate geometries program begun in arXiv:1409.6017, focussing on the role of branes that wrap the cycles which degenerate when a throat in the geometry deepens and a horizon forms. An associated quiver quantum mechanical model of minimally wrapped branes exhibits a non-negligible fraction of the gravitational entropy, which scales correctly as a function of the charges. The results suggest a picture of AdS{sub 3}/CFT{sub 2} duality wherein the long string that accounts for BTZ black hole entropy in the CFT description, can also be seen to inhabit the horizon of BPS black holes on the gravity side.
Attractor horizons in six-dimensional type IIB supergravity
Energy Technology Data Exchange (ETDEWEB)
Astefanesei, Dumitru, E-mail: dumitru.astefanesei@ucv.cl [Instituto de Fisica, Pontificia Universidad Catolica de Valparaiso, Casilla 4059, Valparaiso (Chile); Miskovic, Olivera, E-mail: olivera.miskovic@ucv.cl [Instituto de Fisica, Pontificia Universidad Catolica de Valparaiso, Casilla 4059, Valparaiso (Chile); Olea, Rodrigo, E-mail: rodrigo.olea@unab.cl [Universidad Andres Bello, Departamento de Ciencias Fisicas, Republica 220, Santiago (Chile)
2012-08-14
We consider near horizon geometries of extremal black holes in six-dimensional type IIB supergravity. In particular, we use the entropy function formalism to compute the charges and thermodynamic entropy of these solutions. We also comment on the role of attractor mechanism in understanding the entropy of the Hopf T-dual solutions in type IIA supergravity.
Gravitational surface Hamiltonian and entropy quantization
Directory of Open Access Journals (Sweden)
Ashish Bakshi
2017-02-01
Full Text Available The surface Hamiltonian corresponding to the surface part of a gravitational action has xp structure where p is conjugate momentum of x. Moreover, it leads to TS on the horizon of a black hole. Here T and S are temperature and entropy of the horizon. Imposing the hermiticity condition we quantize this Hamiltonian. This leads to an equidistant spectrum of its eigenvalues. Using this we show that the entropy of the horizon is quantized. This analysis holds for any order of Lanczos–Lovelock gravity. For general relativity, the area spectrum is consistent with Bekenstein's observation. This provides a more robust confirmation of this earlier result as the calculation is based on the direct quantization of the Hamiltonian in the sense of usual quantum mechanics.
Institute of Scientific and Technical Information of China (English)
Xie Wen-Xian; Xu Wei; Cai Li
2007-01-01
This paper shows the Fokker-Planck equation of a dynamical system driven by coloured cross-correlated white noises in the absence and presence of a small external force. Based on the Fokker-Planck equation and the definition of Shannon's information entropy, the time dependence of entropy flux and entropy production can be calculated. The present results can be used to explain the extremal behaviour of time dependence of entropy flux and entropy production in view of the dissipative parameter γ of the system, coloured cross-correlation time τ and coloured cross-correlation strength λ.
Temperature and entropy of Schwarzschild-de Sitter space-time
International Nuclear Information System (INIS)
Shankaranarayanan, S.
2003-01-01
In the light of recent interest in quantum gravity in de Sitter space, we investigate semiclassical aspects of four-dimensional Schwarzschild-de Sitter space-time using the method of complex paths. The standard semiclassical techniques (such as Bogoliubov coefficients and Euclidean field theory) have been useful to study quantum effects in space-times with single horizons; however, none of these approaches seem to work for Schwarzschild-de Sitter space-time or, in general, for space-times with multiple horizons. We extend the method of complex paths to space-times with multiple horizons and obtain the spectrum of particles produced in these space-times. We show that the temperature of radiation in these space-times is proportional to the effective surface gravity--the inverse harmonic sum of surface gravity of each horizon. For the Schwarzschild-de Sitter space-time, we apply the method of complex paths to three different coordinate systems--spherically symmetric, Painleve, and Lemaitre. We show that the equilibrium temperature in Schwarzschild-de Sitter space-time is the harmonic mean of cosmological and event horizon temperatures. We obtain Bogoliubov coefficients for space-times with multiple horizons by analyzing the mode functions of the quantum fields near the horizons. We propose a new definition of entropy for space-times with multiple horizons, analogous to the entropic definition for space-times with a single horizon. We define entropy for these space-times to be inversely proportional to the square of the effective surface gravity. We show that this definition of entropy for Schwarzschild-de Sitter space-time satisfies the D-bound conjecture
Examples of algebrae with equal dynamic entropy
International Nuclear Information System (INIS)
Narnhofer, H.
1988-01-01
For given dynamical entropy we construct uncountably many examples of corresponding algebras, some of them are quantum K systems, whereas at least one explicit example is not. Consequences for cluster properties are studied. 12 refs. (Author)
Arithmetic of quantum entropy function
International Nuclear Information System (INIS)
Sen, Ashoke
2009-01-01
Quantum entropy function is a proposal for computing the entropy associated with the horizon of a black hole in the extremal limit, and is related via AdS/CFT correspondence to the dimension of the Hilbert space in a dual quantum mechanics. We show that in N = 4 supersymmetric string theories, quantum entropy function formalism naturally explains the origin of the subtle differences between the microscopic degeneracies of quarter BPS dyons carrying different torsion, i.e. different arithmetical properties. These arise from additional saddle points in the path integral - whose existence depends on the arithmetical properties of the black hole charges - constructed as freely acting orbifolds of the original AdS 2 x S 2 near horizon geometry. During this analysis we demonstrate that the quantum entropy function is insensitive to the details of the infrared cutoff used in the computation, and the details of the boundary terms added to the action. We also discuss the role of the asymptotic symmetries of AdS 2 in carrying out the path integral in the definition of quantum entropy function. Finally we show that even though quantum entropy function is expected to compute the absolute degeneracy in a given charge and angular momentum sector, it can also be used to compute the index. This can then be compared with the microscopic computation of the index.
An improved thin film brick-wall model of black hole entropy
Liu Wen Biao
2001-01-01
The authors improve the brick-wall model to take only the contribution of a thin film near the event horizon into account. This improvement not only gives them a satisfactory result, but also avoids some drawbacks in the original brick-wall method such as the little mass approximation, neglecting logarithm term, and taking the term L/sup 3/ as the contribution of the vacuum surrounding a black hole. It is found that there is an intrinsic relation between the event horizon and the entropy. The event horizon is the characteristic of a black hole, so the entropy calculating of a black hole is also naturally related to its horizon. (12 refs).
Statistical-mechanical entropy by the thin-layer method
International Nuclear Information System (INIS)
Feng, He; Kim, Sung Won
2003-01-01
G. Hooft first studied the statistical-mechanical entropy of a scalar field in a Schwarzschild black hole background by the brick-wall method and hinted that the statistical-mechanical entropy is the statistical origin of the Bekenstein-Hawking entropy of the black hole. However, according to our viewpoint, the statistical-mechanical entropy is only a quantum correction to the Bekenstein-Hawking entropy of the black-hole. The brick-wall method based on thermal equilibrium at a large scale cannot be applied to the cases out of equilibrium such as a nonstationary black hole. The statistical-mechanical entropy of a scalar field in a nonstationary black hole background is calculated by the thin-layer method. The condition of local equilibrium near the horizon of the black hole is used as a working postulate and is maintained for a black hole which evaporates slowly enough and whose mass is far greater than the Planck mass. The statistical-mechanical entropy is also proportional to the area of the black hole horizon. The difference from the stationary black hole is that the result relies on a time-dependent cutoff
Ugarte, Juan P.; Orozco-Duque, Andrés; Tobón, Catalina; Kremen, Vaclav; Novak, Daniel; Saiz, Javier; Oesterlein, Tobias; Schmitt, Clauss; Luik, Armin; Bustamante, John
2014-01-01
There is evidence that rotors could be drivers that maintain atrial fibrillation. Complex fractionated atrial electrograms have been located in rotor tip areas. However, the concept of electrogram fractionation, defined using time intervals, is still controversial as a tool for locating target sites for ablation. We hypothesize that the fractionation phenomenon is better described using non-linear dynamic measures, such as approximate entropy, and that this tool could be used for locating the rotor tip. The aim of this work has been to determine the relationship between approximate entropy and fractionated electrograms, and to develop a new tool for rotor mapping based on fractionation levels. Two episodes of chronic atrial fibrillation were simulated in a 3D human atrial model, in which rotors were observed. Dynamic approximate entropy maps were calculated using unipolar electrogram signals generated over the whole surface of the 3D atrial model. In addition, we optimized the approximate entropy calculation using two real multi-center databases of fractionated electrogram signals, labeled in 4 levels of fractionation. We found that the values of approximate entropy and the levels of fractionation are positively correlated. This allows the dynamic approximate entropy maps to localize the tips from stable and meandering rotors. Furthermore, we assessed the optimized approximate entropy using bipolar electrograms generated over a vicinity enclosing a rotor, achieving rotor detection. Our results suggest that high approximate entropy values are able to detect a high level of fractionation and to locate rotor tips in simulated atrial fibrillation episodes. We suggest that dynamic approximate entropy maps could become a tool for atrial fibrillation rotor mapping. PMID:25489858
Ugarte, Juan P; Orozco-Duque, Andrés; Tobón, Catalina; Kremen, Vaclav; Novak, Daniel; Saiz, Javier; Oesterlein, Tobias; Schmitt, Clauss; Luik, Armin; Bustamante, John
2014-01-01
There is evidence that rotors could be drivers that maintain atrial fibrillation. Complex fractionated atrial electrograms have been located in rotor tip areas. However, the concept of electrogram fractionation, defined using time intervals, is still controversial as a tool for locating target sites for ablation. We hypothesize that the fractionation phenomenon is better described using non-linear dynamic measures, such as approximate entropy, and that this tool could be used for locating the rotor tip. The aim of this work has been to determine the relationship between approximate entropy and fractionated electrograms, and to develop a new tool for rotor mapping based on fractionation levels. Two episodes of chronic atrial fibrillation were simulated in a 3D human atrial model, in which rotors were observed. Dynamic approximate entropy maps were calculated using unipolar electrogram signals generated over the whole surface of the 3D atrial model. In addition, we optimized the approximate entropy calculation using two real multi-center databases of fractionated electrogram signals, labeled in 4 levels of fractionation. We found that the values of approximate entropy and the levels of fractionation are positively correlated. This allows the dynamic approximate entropy maps to localize the tips from stable and meandering rotors. Furthermore, we assessed the optimized approximate entropy using bipolar electrograms generated over a vicinity enclosing a rotor, achieving rotor detection. Our results suggest that high approximate entropy values are able to detect a high level of fractionation and to locate rotor tips in simulated atrial fibrillation episodes. We suggest that dynamic approximate entropy maps could become a tool for atrial fibrillation rotor mapping.
Planning horizon affects prophylactic decision-making and epidemic dynamics.
Nardin, Luis G; Miller, Craig R; Ridenhour, Benjamin J; Krone, Stephen M; Joyce, Paul; Baumgaertner, Bert O
2016-01-01
The spread of infectious diseases can be impacted by human behavior, and behavioral decisions often depend implicitly on a planning horizon-the time in the future over which options are weighed. We investigate the effects of planning horizons on epidemic dynamics. We developed an epidemiological agent-based model (along with an ODE analog) to explore the decision-making of self-interested individuals on adopting prophylactic behavior. The decision-making process incorporates prophylaxis efficacy and disease prevalence with the individuals' payoffs and planning horizon. Our results show that for short and long planning horizons individuals do not consider engaging in prophylactic behavior. In contrast, individuals adopt prophylactic behavior when considering intermediate planning horizons. Such adoption, however, is not always monotonically associated with the prevalence of the disease, depending on the perceived protection efficacy and the disease parameters. Adoption of prophylactic behavior reduces the epidemic peak size while prolonging the epidemic and potentially generates secondary waves of infection. These effects can be made stronger by increasing the behavioral decision frequency or distorting an individual's perceived risk of infection.
Kinetics of the Dynamical Information Shannon Entropy for Complex Systems
International Nuclear Information System (INIS)
Yulmetyev, R.M.; Yulmetyeva, D.G.
1999-01-01
Kinetic behaviour of dynamical information Shannon entropy is discussed for complex systems: physical systems with non-Markovian property and memory in correlation approximation, and biological and physiological systems with sequences of the Markovian and non-Markovian random noises. For the stochastic processes, a description of the information entropy in terms of normalized time correlation functions is given. The influence and important role of two mutually dependent channels of the entropy change, correlation (creation or generation of correlations) and anti-correlation (decay or annihilation of correlation) is discussed. The method developed here is also used in analysis of the density fluctuations in liquid cesium obtained from slow neutron scattering data, fractal kinetics of the long-range fluctuation in the short-time human memory and chaotic dynamics of R-R intervals of human ECG. (author)
The Thermal Entropy Density of Spacetime
Directory of Open Access Journals (Sweden)
Rongjia Yang
2013-01-01
Full Text Available Introducing the notion of thermal entropy density via the first law of thermodynamics and assuming the Einstein equation as an equation of thermal state, we obtain the thermal entropy density of any arbitrary spacetime without assuming a temperature or a horizon. The results confirm that there is a profound connection between gravity and thermodynamics.
Implication of Negative Temperature in the Inner Horizon of Reissner-Nordström Black Hole
Directory of Open Access Journals (Sweden)
Yuant Tiandho
2017-12-01
Full Text Available This paper reconsiders the properties of Hawking radiation in the inner horizon of a Reissner-Nordström black hole. Through the correlation between temperature and surface gravity, it is concluded that the temperature of the inner horizon is always negative and that of the outer horizon is always positive. Since negative temperature is hotter than any positive temperature, it is predicted that particle radiation from the inner horizon will move toward the outer horizon. However, unlike temperature, entropy in both horizons remains positive. Following the definition of negative temperature in the inner horizon, it is assured that the entropy of a black hole within a closed system can never decrease. By analyzing the conditions of an extremal black hole, the third law of black hole thermodynamics can be extended to multi-horizon black holes.
Reissner-Nordstrom Black Hole Entropy Inside and Outside the Brick Wall
Institute of Scientific and Technical Information of China (English)
刘文彪
2003-01-01
Applying the generalized uncertainty relation to the calculation of the free energy and entropy of a Reissner Nordstrom black hole inside the brick wall, the entropy proportional to the horizon area is derived from the contribution of the vicinity of the horizon. This is compared with the entropy calculated via the original brick wall model. The entropy given by the original brick wall model comes from the outside of the brick wall seemingly.The inside result using generalized uncertainty relation is similar to the outside result using original uncertainty relation, and the divergence inside the brick wall disappears. It is apparent that the cutoff is something related to the quantum theory of gravity.
Corrected entropy of Friedmann-Robertson-Walker universe in tunneling method
International Nuclear Information System (INIS)
Zhu, Tao; Ren, Ji-Rong; Li, Ming-Fan
2009-01-01
In this paper, we study the thermodynamic quantities of Friedmann-Robertson-Walker (FRW) universe by using the tunneling formalism beyond semiclassical approximation developed by Banerjee and Majhi [25]. For this we first calculate the corrected Hawking-like temperature on apparent horizon by considering both scalar particle and fermion tunneling. With this corrected Hawking-like temperature, the explicit expressions of the corrected entropy of apparent horizon for various gravity theories including Einstein gravity, Gauss-Bonnet gravity, Lovelock gravity, f(R) gravity and scalar-tensor gravity, are computed. Our results show that the corrected entropy formula for different gravity theories can be written into a general expression (4.39) of a same form. It is also shown that this expression is also valid for black holes. This might imply that the expression for the corrected entropy derived from tunneling method is independent of gravity theory, spacetime and dimension of the spacetime. Moreover, it is concluded that the basic thermodynamical property that the corrected entropy on apparent horizon is a state function is satisfied by the FRW universe
Dynamics of entropy perturbations in assisted dark energy with mixed kinetic terms
International Nuclear Information System (INIS)
Karwan, Khamphee
2011-01-01
We study dynamics of entropy perturbations in the two-field assisted dark energy model. Based on the scenario of assisted dark energy, in which one scalar field is subdominant compared with the other in the early epoch, we show that the entropy perturbations in this two-field system tend to be constant on large scales in the early epoch and hence survive until the present era for a generic evolution of both fields during the radiation and matter eras. This behaviour of the entropy perturbations is preserved even when the fields are coupled via kinetic interaction. Since, for assisted dark energy, the subdominant field in the early epoch becomes dominant at late time, the entropy perturbations can significantly influence the dynamics of density perturbations in the universe. Assuming correlations between the entropy and curvature perturbations, the entropy perturbations can enhance the integrated Sachs-Wolfe (ISW) effect if the signs of the contributions from entropy perturbations and curvature perturbations are opposite after the matter era, otherwise the ISW contribution is suppressed. For canonical scalar field the effect of entropy perturbations on ISW effect is small because the initial value of the entropy perturbations estimated during inflation cannot be sufficiently large. However, in the case of k-essence, the initial value of the entropy perturbations can be large enough to affect the ISW effect to leave a significant imprint on the CMB power spectrum
Gravitational black hole hair from event horizon supertranslations
Energy Technology Data Exchange (ETDEWEB)
Averin, Artem [Arnold-Sommerfeld-Center for Theoretical Physics,Ludwig-Maximilians-Universität, 80333 München (Germany); Max-Planck-Institut für Physik, Werner-Heisenberg-Institut,80805 München (Germany); Dvali, Gia [Arnold-Sommerfeld-Center for Theoretical Physics,Ludwig-Maximilians-Universität, 80333 München (Germany); Max-Planck-Institut für Physik, Werner-Heisenberg-Institut,80805 München (Germany); Center for Cosmology and Particle Physics, Department of Physics, New York University,4 Washington Place, New York, NY 10003 (United States); Gomez, Cesar [Instituto de Física Teórica UAM-CSIC, C-XVI, Universidad Autónoma de Madrid,Cantoblanco, 28049 Madrid (Spain); Lüst, Dieter [Arnold-Sommerfeld-Center for Theoretical Physics,Ludwig-Maximilians-Universität, 80333 München (Germany); Max-Planck-Institut für Physik, Werner-Heisenberg-Institut,80805 München (Germany)
2016-06-16
We discuss BMS supertranslations both at null-infinity BMS{sup −} and on the horizon BMS{sup H} for the case of the Schwarzschild black hole. We show that both kinds of supertranslations lead to infinetly many gapless physical excitations. On this basis we construct a quotient algebra A≡BMS{sup H}/BMS{sup −} using suited superpositions of both kinds of transformations which cannot be compensated by an ordinary BMS-supertranslation and therefore are intrinsically due to the presence of an event horizon. We show that transformations in A are physical and generate gapless excitations on the horizon that can account for the gravitational hair as well as for the black hole entropy. We identify the physics of these modes as associated with Bogolioubov-Goldstone modes due to quantum criticality. Classically the number of these gapless modes is infinite. However, we show that due to quantum criticality the actual amount of information-carriers becomes finite and consistent with Bekenstein entropy. Although we only consider the case of Schwarzschild geometry, the arguments are extendable to arbitrary space-times containing event horizons.
Gravitational black hole hair from event horizon supertranslations
International Nuclear Information System (INIS)
Averin, Artem; Dvali, Gia; Gomez, Cesar; Lüst, Dieter
2016-01-01
We discuss BMS supertranslations both at null-infinity BMS"− and on the horizon BMS"H for the case of the Schwarzschild black hole. We show that both kinds of supertranslations lead to infinetly many gapless physical excitations. On this basis we construct a quotient algebra A≡BMS"H/BMS"− using suited superpositions of both kinds of transformations which cannot be compensated by an ordinary BMS-supertranslation and therefore are intrinsically due to the presence of an event horizon. We show that transformations in A are physical and generate gapless excitations on the horizon that can account for the gravitational hair as well as for the black hole entropy. We identify the physics of these modes as associated with Bogolioubov-Goldstone modes due to quantum criticality. Classically the number of these gapless modes is infinite. However, we show that due to quantum criticality the actual amount of information-carriers becomes finite and consistent with Bekenstein entropy. Although we only consider the case of Schwarzschild geometry, the arguments are extendable to arbitrary space-times containing event horizons.
Falling through the black hole horizon
International Nuclear Information System (INIS)
Brustein, Ram; Medved, A.J.M.
2015-01-01
We consider the fate of a small classical object, a “stick”, as it falls through the horizon of a large black hole (BH). Classically, the equivalence principle dictates that the stick is affected by small tidal forces, and Hawking’s quantum-mechanical model of BH evaporation makes essentially the same prediction. If, on the other hand, the BH horizon is surrounded by a “firewall”, the stick will be consumed as it falls through. We have recently extended Hawking’s model by taking into account the quantum fluctuations of the geometry and the classical back-reaction of the emitted particles. Here, we calculate the strain exerted on the falling stick for our model. The strain depends on the near-horizon state of the Hawking pairs. We find that, after the Page time when the state of the pairs deviates significantly from maximal entanglement (as required by unitarity), the induced strain in our semiclassical model is still parametrically small. This is because the number of the disentangled pairs is parametrically smaller than the BH entropy. A firewall does, however, appear if the number of disentangled pairs near the horizon is of order of the BH entropy, as implicitly assumed in previous discussions in the literature.
Soft hairy warped black hole entropy
Grumiller, Daniel; Hacker, Philip; Merbis, Wout
2018-02-01
We reconsider warped black hole solutions in topologically massive gravity and find novel boundary conditions that allow for soft hairy excitations on the horizon. To compute the associated symmetry algebra we develop a general framework to compute asymptotic symmetries in any Chern-Simons-like theory of gravity. We use this to show that the near horizon symmetry algebra consists of two u (1) current algebras and recover the surprisingly simple entropy formula S = 2 π( J 0 + + J 0 - ), where J 0 ± are zero mode charges of the current algebras. This provides the first example of a locally non-maximally symmetric configuration exhibiting this entropy law and thus non-trivial evidence for its universality.
Stretched horizons, quasiparticles, and quasinormal modes
International Nuclear Information System (INIS)
Iizuka, Norihiro; Kabat, Daniel; Lifschytz, Gilad; Lowe, David A.
2003-01-01
We propose that stretched horizons can be described in terms of a gas of noninteracting quasiparticles. The quasiparticles are unstable, with a lifetime set by the imaginary part of the lowest quasinormal mode frequency. If the horizon arises from an AdS-CFT style duality the quasiparticles are also the effective low-energy degrees of freedom of the finite-temperature CFT. We analyze a large class of models including Schwarzschild black holes, nonextremal Dp-branes, the rotating BTZ black hole and de Sitter space, and we comment on degenerate horizons. The quasiparticle description makes manifest the relationship between entropy and area
Unified first law and the thermodynamics of the apparent horizon in the FRW universe
International Nuclear Information System (INIS)
Cai Ronggen; Cao Liming
2007-01-01
In this paper we revisit the relation between the Friedmann equations and the first law of thermodynamics. We find that the unified first law first proposed by Hayward to treat the outertrapping horizon of a dynamical black hole can be used to the apparent horizon (a kind of inner trapping horizon in the context of the FRW cosmology) of the FRW universe. We discuss three kinds of gravity theorties: Einstein theory, Lovelock thoery, and scalar-tensor theory. In Einstein theory, the first law of thermodynamics is always satisfied on the apparent horizon. In Lovelock theory, treating the higher derivative terms as an effective energy-momentum tensor, we find that this method can give the same entropy formula for the apparent horizon as that of black hole horizon. This implies that the Clausius relation holds for the Lovelock theory. In scalar-tensor gravity, we find, by using the same procedure, the Clausius relation no longer holds. This indicates that the apparent horizon of the FRW universe in the scalar-tensor gravity corresponds to a system of nonequilibrium thermodynamics. We show this point by using the method developed recently by Eling et al. for dealing with the f(R) gravity
Cosmological event horizons, thermodynamics, and particle creation
International Nuclear Information System (INIS)
Gibbons, G.W.; Hawking, S.W.
1977-01-01
It is shown that the close connection between event horizons and thermodynamics which has been found in the case of black holes can be extended to cosmological models with a repulsive cosmological constant. An observer in these models will have an event horizon whose area can be interpreted as the entropy or lack of information of the observer about the regions which he cannot see. Associated with the event horizon is a surface gravity kappa which enters a classical ''first law of event horizons'' in a manner similar to that in which temperature occurs in the first law of thermodynamics. It is shown that this similarity is more than an analogy: An observer with a particle detector will indeed observe a background of thermal radiation coming apparently from the cosmological event horizon. If the observer absorbs some of this radiation, he will gain energy and entropy at the expense of the region beyond his ken and the event horizon will shrink. The derivation of these results involves abandoning the idea that particles should be defined in an observer-independent manner. They also suggest that one has to use something like the Everett-Wheeler interpretation of quantum mechanics because the back reaction and hence the spacetime metric itself appear to be observer-dependent, if one assumes, as seems reasonable, that the detection of a particle is accompanied by a change in the gravitational field
Two dissimilar approaches to dynamical systems on hyper MV -algebras and their information entropy
Mehrpooya, Adel; Ebrahimi, Mohammad; Davvaz, Bijan
2017-09-01
Measuring the flow of information that is related to the evolution of a system which is modeled by applying a mathematical structure is of capital significance for science and usually for mathematics itself. Regarding this fact, a major issue in concern with hyperstructures is their dynamics and the complexity of the varied possible dynamics that exist over them. Notably, the dynamics and uncertainty of hyper MV -algebras which are hyperstructures and extensions of a central tool in infinite-valued Lukasiewicz propositional calculus that models many valued logics are of primary concern. Tackling this problem, in this paper we focus on the subject of dynamical systems on hyper MV -algebras and their entropy. In this respect, we adopt two varied approaches. One is the set-based approach in which hyper MV -algebra dynamical systems are developed by employing set functions and set partitions. By the other method that is based on points and point partitions, we establish the concept of hyper injective dynamical systems on hyper MV -algebras. Next, we study the notion of entropy for both kinds of systems. Furthermore, we consider essential ergodic characteristics of those systems and their entropy. In particular, we introduce the concept of isomorphic hyper injective and hyper MV -algebra dynamical systems, and we demonstrate that isomorphic systems have the same entropy. We present a couple of theorems in order to help calculate entropy. In particular, we prove a contemporary version of addition and Kolmogorov-Sinai Theorems. Furthermore, we provide a comparison between the indispensable properties of hyper injective and semi-independent dynamical systems. Specifically, we present and prove theorems that draw comparisons between the entropies of such systems. Lastly, we discuss some possible relationships between the theories of hyper MV -algebra and MV -algebra dynamical systems.
Entropy of a rotating and charged black string to all orders in the Planck length
International Nuclear Information System (INIS)
Ren, Zhao; Yue-Qin, Wu; Li-Chun, Zhang
2009-01-01
By using the entanglement entropy method, this paper calculates the statistical entropy of the Bose and Fermi fields in thin films, and derives the Bekenstein–Hawking entropy and its correction term on the background of a rotating and charged black string. Here, the quantum field is entangled with quantum states in the black string and thin film to the event horizon from outside the rotating and charged black string. Taking into account the effect of the generalized uncertainty principle on quantum state density, it removes the difficulty of the divergence of state density near the event horizon in the brick-wall model. These calculations and discussions imply that high density quantum states near the event horizon of a black string are strongly correlated with the quantum states in a black string and that black string entropy is a quantum effect. The ultraviolet cut-off in the brick-wall model is not reasonable. The generalized uncertainty principle should be considered in the high energy quantum field near the event horizon. From the viewpoint of quantum statistical mechanics, the correction value of Bekenstein–Hawking entropy is obtained. This allows the fundamental recognition of the correction value of black string entropy at nonspherical coordinates
Gul, Ahmet; Erman, Burak
2018-03-01
Prediction of peptide binding on specific human leukocyte antigens (HLA) has long been studied with successful results. We herein describe the effects of entropy and dynamics by investigating the binding stabilities of 10 nanopeptides on various HLA Class I alleles using a theoretical model based on molecular dynamics simulations. The fluctuational entropies of the peptides are estimated over a temperature range of 310-460 K. The estimated entropies correlate well with experimental binding affinities of the peptides: peptides that have higher binding affinities have lower entropies compared to non-binders, which have significantly larger entropies. The computation of the entropies is based on a simple model that requires short molecular dynamics trajectories and allows for approximate but rapid determination. The paper draws attention to the long neglected dynamic aspects of peptide binding, and provides a fast computation scheme that allows for rapid scanning of large numbers of peptides on selected HLA antigens, which may be useful in defining the right peptides for personal immunotherapy.
International Nuclear Information System (INIS)
Porteus, E.
1982-01-01
The study of infinite-horizon nonstationary dynamic programs using the operator approach is continued. The point of view here differs slightly from that taken by others, in that Denardo's local income function is not used as a starting point. Infinite-horizon values are defined as limits of finite-horizon values, as the horizons get long. Two important conditions of an earlier paper are weakened, yet the optimality equations, the optimality criterion, and the existence of optimal ''structured'' strategies are still obtained
Directory of Open Access Journals (Sweden)
Chellaboina Vijaysekhar
2005-01-01
Full Text Available We develop thermodynamic models for discrete-time large-scale dynamical systems. Specifically, using compartmental dynamical system theory, we develop energy flow models possessing energy conservation, energy equipartition, temperature equipartition, and entropy nonconservation principles for discrete-time, large-scale dynamical systems. Furthermore, we introduce a new and dual notion to entropy; namely, ectropy, as a measure of the tendency of a dynamical system to do useful work and grow more organized, and show that conservation of energy in an isolated thermodynamic system necessarily leads to nonconservation of ectropy and entropy. In addition, using the system ectropy as a Lyapunov function candidate, we show that our discrete-time, large-scale thermodynamic energy flow model has convergent trajectories to Lyapunov stable equilibria determined by the system initial subsystem energies.
Dynamical maximum entropy approach to flocking.
Cavagna, Andrea; Giardina, Irene; Ginelli, Francesco; Mora, Thierry; Piovani, Duccio; Tavarone, Raffaele; Walczak, Aleksandra M
2014-04-01
We derive a new method to infer from data the out-of-equilibrium alignment dynamics of collectively moving animal groups, by considering the maximum entropy model distribution consistent with temporal and spatial correlations of flight direction. When bird neighborhoods evolve rapidly, this dynamical inference correctly learns the parameters of the model, while a static one relying only on the spatial correlations fails. When neighbors change slowly and the detailed balance is satisfied, we recover the static procedure. We demonstrate the validity of the method on simulated data. The approach is applicable to other systems of active matter.
Black brane entropy and hydrodynamics: The boost-invariant case
International Nuclear Information System (INIS)
Booth, Ivan; Heller, Michal P.; Spalinski, Michal
2009-01-01
The framework of slowly evolving horizons is generalized to the case of black branes in asymptotically anti-de Sitter spaces in arbitrary dimensions. The results are used to analyze the behavior of both event and apparent horizons in the gravity dual to boost-invariant flow. These considerations are motivated by the fact that at second order in the gradient expansion the hydrodynamic entropy current in the dual Yang-Mills theory appears to contain an ambiguity. This ambiguity, in the case of boost-invariant flow, is linked with a similar freedom on the gravity side. This leads to a phenomenological definition of the entropy of black branes. Some insights on fluid/gravity duality and the definition of entropy in a time-dependent setting are elucidated.
Loop quantum gravity and black hole entropy quantization
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
Using the spin networks and the asymptotic quasinormal mode frequencies of black holes given by loop quantum gravity,the minimum horizon area gap is obtained.Then the quantum area spectrum of black holes is derived and the black hole entropy is a realized quantization.The results show that the black hole entropy given by loop quantum gravity is in full accord with the Bekenstein-Hawking entropy with a suitable Immirzi.
International Nuclear Information System (INIS)
Goswami, Gurupada; Mukherjee, Biswajit; Bag, Bidhan Chandra
2005-01-01
We have studied the relaxation of non-Markovian and thermodynamically closed system both in the absence and presence of non-equilibrium constraint in terms of the information entropy flux and entropy production based on the Fokker-Planck and the entropy balance equations. Our calculation shows how the relaxation time depends on noise correlation time. It also considers how the non-equilibrium constraint is affected by system parameters such as noise correlation time, strength of dissipation and frequency of dynamical system. The interplay of non-equilibrium constraint, frictional memory kernel, noise correlation time and frequency of dynamical system reveals the extremum nature of the entropy production
Goswami, Gurupada; Mukherjee, Biswajit; Bag, Bidhan Chandra
2005-06-01
We have studied the relaxation of non-Markovian and thermodynamically closed system both in the absence and presence of non-equilibrium constraint in terms of the information entropy flux and entropy production based on the Fokker-Planck and the entropy balance equations. Our calculation shows how the relaxation time depends on noise correlation time. It also considers how the non-equilibrium constraint is affected by system parameters such as noise correlation time, strength of dissipation and frequency of dynamical system. The interplay of non-equilibrium constraint, frictional memory kernel, noise correlation time and frequency of dynamical system reveals the extremum nature of the entropy production.
Topological Aspects of Entropy and Phase Transition of Kerr Black Holes
Institute of Scientific and Technical Information of China (English)
YANG Guo-Hong; YAN Ji-Jiang; TIAN Li-Jun; DUAN Yi-Shi
2005-01-01
In the light of topological current and the relationship between the entropy and the Euler characteristic, the topological aspects of entropy and phase transition of Kerr black holes are studied. From Gauss-Bonnet-Chern theorem,it is shown that the entropy of Kerr black holes is determined by the singularities of the Killing vector field of spacetime.By calculating the Hopf indices and Brouwer degrees of the Killing vector field at the singularities, the entropy S = A/4for nonextreme Kerr black holes and S = 0 for extreme ones are obtained, respectively. It is also discussed that, with the change of the ratio of mass to angular momentum for unit mass, the Euler characteristic and the entropy of Kerr black holes will change discontinuously when the singularities on Cauchy horizon merge with the singularities on event horizon, which will lead to the first-order phase transition of Kerr black holes.
Emergent horizon, Hawking radiation and chaos in the collapsed polymer model of a black hole
International Nuclear Information System (INIS)
Brustein, Ram; Medved, A.J.M.
2017-01-01
We have proposed that the interior of a macroscopic Schwarzschild black hole (BH) consists of highly excited, long, closed, interacting strings and, as such, can be modeled as a collapsed polymer. It was previously shown that the scaling relations of the collapsed-polymer model agree with those of the BH. The current paper further substantiates this proposal with an investigation into some of its dynamical consequences. In particular, we show that the model predicts, without relying on gravitational effects, an emergent horizon. We further show that the horizon fluctuates quantum mechanically as it should and that the strength of the fluctuations is inversely proportional to the BH entropy. It is then demonstrated that the emission of Hawking radiation is realized microscopically by the quantum-induced escape of small pieces of string, with the rate of escape and the energy per emitted piece both parametrically matching the Hawking temperature. We also show, using standard methods from statistical mechanics and chaos theory, how our model accounts for some other known properties of BHs. These include the accepted results for the scrambling time and the viscosity-to-entropy ratio, which in our model apply not only at the horizon but throughout the BH interior. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Emergent horizon, Hawking radiation and chaos in the collapsed polymer model of a black hole
Energy Technology Data Exchange (ETDEWEB)
Brustein, Ram [Department of Physics, Ben-Gurion University, Beer-Sheva (Israel); Medved, A.J.M. [Department of Physics and Electronics, Rhodes University, Grahamstown (South Africa); National Institute for Theoretical Physics (NITheP), Western Cape (South Africa)
2017-02-15
We have proposed that the interior of a macroscopic Schwarzschild black hole (BH) consists of highly excited, long, closed, interacting strings and, as such, can be modeled as a collapsed polymer. It was previously shown that the scaling relations of the collapsed-polymer model agree with those of the BH. The current paper further substantiates this proposal with an investigation into some of its dynamical consequences. In particular, we show that the model predicts, without relying on gravitational effects, an emergent horizon. We further show that the horizon fluctuates quantum mechanically as it should and that the strength of the fluctuations is inversely proportional to the BH entropy. It is then demonstrated that the emission of Hawking radiation is realized microscopically by the quantum-induced escape of small pieces of string, with the rate of escape and the energy per emitted piece both parametrically matching the Hawking temperature. We also show, using standard methods from statistical mechanics and chaos theory, how our model accounts for some other known properties of BHs. These include the accepted results for the scrambling time and the viscosity-to-entropy ratio, which in our model apply not only at the horizon but throughout the BH interior. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Notes on entanglement entropy in string theory
International Nuclear Information System (INIS)
He, Song; Numasawa, Tokiro; Takayanagi, Tadashi; Watanabe, Kento
2015-01-01
In this paper, we study the conical entropy in string theory in the simplest setup of dividing the nine dimensional space into two halves. This corresponds to the leading quantum correction to the horizon entropy in string theory on the Rindler space. This entropy is also called the conical entropy and includes surface term contributions. We first derive a new simple formula of the conical entropy for any free higher spin fields. Then we apply this formula to computations of conical entropy in open and closed superstring. In our analysis of closed string, we study the twisted conical entropy defined by making use of string theory on Melvin backgrounds. This quantity is easier to calculate owing to the folding trick. Our analysis shows that the conical entropy in closed superstring is UV finite owing to the string scale cutoff.
Entanglement Entropy for the charged BTZ black hole
International Nuclear Information System (INIS)
Larrañaga, A.
2011-01-01
Using the AdS/CFT correspondence we calculate the explicit form of the entanglement entropy for the charged BTZ (Banados-Teitelboim-Zanelli) black hole. The leading term in the large temperature expansion of the entropy function for this black hole reproduces its Bekenstein-Hawking entropy and the subleading term, representing the first corrections due to quantum entanglement, behaves as a logarithm of the BH entropy. It has also been obtained an inverse of area term in subleading order similar to the reported when considering Hawking radiation as quantum tunneling of particles through the event horizon
Area law for localization-entropy in local quantum physics
Energy Technology Data Exchange (ETDEWEB)
Schroer, Bert [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)]. E-mail: schroer@cbpf.br
2002-02-01
The previously developed algebraic lightfront holography is used in conjunction with the tensor splitting of the chiral theory on the causal horizon. In this way a universal area law for the entanglement entropy of the vacuum relative to the split (tensor factorized) vacuum is obtained. The universality of the area law is a result of the kinematical structure of the properly defined lightfront degrees of freedom. We consider this entropy associated with causal horizon of the wedge algebra in Minkowski spacetime as an analog of the quantum Bekenstein black hole entropy similar to the way in which the Unruh temperature for the wedge algebra may be viewed as an analog in Minkowski spacetime of the Hawking thermal behavior. My more recent preprint hep-th/20202085 presents other aspects of the same problem. (author)
How the change in horizon area drives black hole evaporation
International Nuclear Information System (INIS)
Massar, S.; Parentani, R.
2000-01-01
We rephrase the derivation of black hole radiation so as to take into account, at the level of transition amplitudes, the change of the geometry induced by the emission process. This enlarged description reveals that the dynamical variables which govern the emission are the horizon area and its conjugate time variable. Their conjugation is established through the boundary term at the horizon which must be added to the canonical action of general relativity in order to obtain a well defined action principle when the area varies. These coordinates have already been used by Teitelboim and collaborators to compute the partition function of a black hole. We use them to show that the probability to emit a particle is given by e -ΔA/4 , where ΔA is the decrease in horizon area induced by the emission. This expression improves Hawking result which is governed by a temperature (given by the surface gravity) in that the specific heat of the black hole is no longer neglected. The present derivation of quantum black hole radiation is based on the same principles which are used to derive the first law of classical black hole thermodynamics. Moreover, it also applies to quantum processes associated with cosmological or acceleration horizons. These two results indicate that not only black holes but all event horizons possess an entropy which governs processes according to quantum statistical thermodynamics
Discussion of a Possible Corrected Black Hole Entropy
Directory of Open Access Journals (Sweden)
Miao He
2018-01-01
Full Text Available Einstein’s equation could be interpreted as the first law of thermodynamics near the spherically symmetric horizon. Through recalling the Einstein gravity with a more general static spherical symmetric metric, we find that the entropy would have a correction in Einstein gravity. By using this method, we investigate the Eddington-inspired Born-Infeld (EiBI gravity. Without matter field, we can also derive the first law in EiBI gravity. With an electromagnetic field, as the field equations have a more general spherically symmetric solution in EiBI gravity, we find that correction of the entropy could be generalized to EiBI gravity. Furthermore, we point out that the Einstein gravity and EiBI gravity might be equivalent on the event horizon. At last, under EiBI gravity with the electromagnetic field, a specific corrected entropy of black hole is given.
Supertranslations and Superrotations at the Black Hole Horizon.
Donnay, Laura; Giribet, Gaston; González, Hernán A; Pino, Miguel
2016-03-04
We show that the asymptotic symmetries close to nonextremal black hole horizons are generated by an extension of supertranslations. This group is generated by a semidirect sum of Virasoro and Abelian currents. The charges associated with the asymptotic Killing symmetries satisfy the same algebra. When considering the special case of a stationary black hole, the zero mode charges correspond to the angular momentum and the entropy at the horizon.
Conformal Killing horizons and their thermodynamics
Nielsen, Alex B.; Shoom, Andrey A.
2018-05-01
Certain dynamical black hole solutions can be mapped to static spacetimes by conformal metric transformations. This mapping provides a physical link between the conformal Killing horizon of the dynamical black hole and the Killing horizon of the static spacetime. Using the Vaidya spacetime as an example, we show how this conformal relation can be used to derive thermodynamic properties of such dynamical black holes. Although these horizons are defined quasi-locally and can be located by local experiments, they are distinct from other popular notions of quasi-local horizons such as apparent horizons. Thus in the dynamical Vaidya spacetime describing constant accretion of null dust, the conformal Killing horizon, which is null by construction, is the natural horizon to describe the black hole.
Entropy function and universality of entropy-area relation for small black holes
International Nuclear Information System (INIS)
Cai Ronggen; Chen, C.-M.; Maeda, Kei-ichi; Ohta, Nobuyoshi; Pang Dawei
2008-01-01
We discuss the entropy-area relation for the small black holes with higher curvature corrections by using the entropy function formalism and field redefinition method. We show that the entropy S BH of the small black hole is proportional to its horizon area A. In particular, we find a universal result that S BH =A/2G, the ratio is 2 times of Bekenstein-Hawking entropy-area formula in many cases of physical interest. In four dimensions, the universal relation is always true irrespective of the coefficients of the higher-order terms if the dilaton couplings are the same, which is the case for string effective theory, while in five dimensions, the relation again holds irrespective of the overall coefficient if the higher-order corrections are in the GB combination. We also discuss how this result generalizes to known physically interesting cases with Lovelock correction terms in various dimensions, and possible implications of the universal relation.
Stochastic Dynamics of Clay Translocation and Formation of Argillic Horizons
Calabrese, S.; Richter, D. D., Jr.; Porporato, A. M.
2017-12-01
The formation of argillic horizons in vertical soil profiles is mainly attributed to lessivage, namely the transport of clay from an upper E horizon to a deeper illuviated horizon. Because of the long timescales involved in this phenomenon, quantitative modeling is useful to explore the role of clay lessivage on soil formation and sub-surface clay accumulation. The limitations of detailed models of colloidal transport to short timescales make it necessary to resort to simple models. Here, we present a parsimonious model of clay transport in which lessivage is interpreted stochastically. Clay particles approach the soil surface at a speed equal to the erosion rate and are intermittently transported to deeper soil layers when percolation events occur or removed by erosion. Along with the evolution of clay particles trajectories, the model predicts the vertical clay profile, the depth of the B horizon, and the mean time to erosion. Dimensional analysis reveals the two dimensionless parameters governing the dynamics, leading to a new classification of soil types based on erosion rates and intensity of lessivage.
CFT and Logarithmic Corrections to the Black Hole Entropy Product Formula
Directory of Open Access Journals (Sweden)
Parthapratim Pradhan
2017-01-01
Full Text Available We examine the logarithmic corrections to the black hole (BH entropy product formula of outer horizon and inner horizon by taking into account the effects of statistical quantum fluctuations around the thermal equilibrium and via conformal field theory (CFT. We argue that, in logarithmic corrections to the BH entropy product formula when calculated using CFT and taking into account the effects of quantum fluctuations around the thermal equilibrium, the formula should not be universal and it also should not be quantized. These results have been explicitly checked by giving several examples.
Physical entropy, information entropy and their evolution equations
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Inspired by the evolution equation of nonequilibrium statistical physics entropy and the concise statistical formula of the entropy production rate, we develop a theory of the dynamic information entropy and build a nonlinear evolution equation of the information entropy density changing in time and state variable space. Its mathematical form and physical meaning are similar to the evolution equation of the physical entropy: The time rate of change of information entropy density originates together from drift, diffusion and production. The concise statistical formula of information entropy production rate is similar to that of physical entropy also. Furthermore, we study the similarity and difference between physical entropy and information entropy and the possible unification of the two statistical entropies, and discuss the relationship among the principle of entropy increase, the principle of equilibrium maximum entropy and the principle of maximum information entropy as well as the connection between them and the entropy evolution equation.
Planck absolute entropy of a rotating BTZ black hole
Riaz, S. M. Jawwad
2018-04-01
In this paper, the Planck absolute entropy and the Bekenstein-Smarr formula of the rotating Banados-Teitelboim-Zanelli (BTZ) black hole are presented via a complex thermodynamical system contributed by its inner and outer horizons. The redefined entropy approaches zero as the temperature of the rotating BTZ black hole tends to absolute zero, satisfying the Nernst formulation of a black hole. Hence, it can be regarded as the Planck absolute entropy of the rotating BTZ black hole.
Devil's carpet of topological entropy and complexity of global dynamical behavior
International Nuclear Information System (INIS)
Cao, K.-F.; Zhang, X.-S.; Zhou Zhong; Peng, S.-L.
2003-01-01
For bimodal maps the concept of an equal topological entropy class (ETEC) is established by the dual star products. All the infinitely many ETEC plateaus and single points are harmonically organized in the kneading parameter plane, they construct a multifractal devil's carpet, which possesses a perfect subregion similarity and a dual central symmetry. The entropy devil's carpet reveals the complexity of global dynamical behavior in the whole parameter plane of bimodal systems
Logarithmic corrections to gravitational entropy and the null energy condition
Energy Technology Data Exchange (ETDEWEB)
Parikh, Maulik, E-mail: maulik.parikh@asu.edu; Svesko, Andrew
2016-10-10
Using a relation between the thermodynamics of local horizons and the null energy condition, we consider the effects of quantum corrections to the gravitational entropy. In particular, we find that the geometric form of the null energy condition is not affected by the inclusion of logarithmic corrections to the Bekenstein–Hawking entropy.
The entropy function for the black holes of Nariai class
International Nuclear Information System (INIS)
Cho, Jin-Ho; Nam, Soonkeon
2008-01-01
Based on the fact that the near horizon geometry of the extremal Schwarzschild-de Sitter black holes is Nariai geometry, we define the black holes of Nariai class as the configuration whose near-horizon geometry is factorized as two dimensional de Sitter space-time and some compact topology, that is Nariai geometry. We extend the entropy function formalism to the case of the black holes of Nariai class. The conventional entropy function (for the extremal black holes) is defined as Legendre transformation of Lagrangian density, thus the 'Routhian density', over two dimensional anti-de Sitter. As for the black holes of Nariai class, it is defined as minus 'Routhian density' over two dimensional de Sitter space-time. We found an exact agreement of the result with Bekenstein-Hawking entropy. The higher order corrections are nontrivial only when the space-time dimension is over four, that is, d>4. There is a subtlety as regards the temperature of the black holes of Nariai class. We show that in order to be consistent with the near horizon geometry, the temperature should be non-vanishing despite the extremality of the black holes
Preimage entropy dimension of topological dynamical systems
Liu, Lei; Zhou, Xiaomin; Zhou, Xiaoyao
2014-01-01
We propose a new definition of preimage entropy dimension for continuous maps on compact metric spaces, investigate fundamental properties of the preimage entropy dimension, and compare the preimage entropy dimension with the topological entropy dimension. The defined preimage entropy dimension holds various basic properties of topological entropy dimension, for example, the preimage entropy dimension of a subsystem is bounded by that of the original system and topologically conjugated system...
Minimum entropy production principle from a dynamical fluctuation law
Czech Academy of Sciences Publication Activity Database
Maes, C.; Netočný, Karel
2007-01-01
Roč. 48, č. 5 (2007), 053306/1-053306/12 ISSN 0022-2488 R&D Projects: GA ČR GA202/07/0404 Institutional research plan: CEZ:AV0Z10100520 Keywords : dynamical fluctuations * entropy production Subject RIV: BE - Theoretical Physics Impact factor: 1.137, year: 2007
International Nuclear Information System (INIS)
Park, Mu-In
2008-01-01
Recently, the Banados-Teitelboim-Zanelli (BTZ) black hole in the presence of the gravitational Chern-Simons term has been studied, and it is found that the usual thermodynamic quantities, like the black hole mass, angular momentum, and entropy, are modified. But, for large values of the gravitational Chern-Simons coupling where the modification terms dominate the original terms some exotic behaviors occur, like the roles of the mass and angular momentum are interchanged and the entropy depends more on the inner horizon area than the outer one. A basic physical problem of this system is that the form of entropy does not guarantee the second law of thermodynamics, in contrast to the Bekenstein-Hawking entropy. Moreover, this entropy does not agree with the statistical entropy, in contrast to a good agreement for small values of the gravitational Chern-Simons coupling. Here I find that there is another entropy formula where the usual Bekenstein-Hawking form dominates the inner-horizon term again, as in the small gravitational Chern-Simons coupling case, such that the second law of thermodynamics can be guaranteed. I also find that the new entropy formula agrees with the statistical entropy based on the holographic anomalies for the whole range of the gravitational Chern-Simons coupling. This reproduces, in the limit of a vanishing Einstein-Hilbert term, the recent result about the exotic BTZ black holes, where their masses and angular momenta are completely interchanged and the entropies depend only on the area of the inner horizon. I compare the result of the holographic approach with the classical-symmetry-algebra-based approach, and I find exact agreements even with the higher-derivative corrections of the gravitational Chern-Simons term. This provides a nontrivial check of the AdS/CFT correspondence, in the presence of higher-derivative terms in the gravity action
Membrane paradigm and entropy of black holes in the Euclidean action approach
International Nuclear Information System (INIS)
Lemos, Jose P. S.; Zaslavskii, Oleg B.
2011-01-01
The membrane paradigm approach to black holes fixes in the vicinity of the event horizon a fictitious surface, the stretched horizon, so that the spacetime outside remains unchanged and the spacetime inside is vacuum. Using this powerful method, several black hole properties have been found and settled, such as the horizon's viscosity, electrical conductivity, resistivity, as well as other properties. On the other hand, the Euclidean action approach to black hole spacetimes has been very fruitful in understanding black hole entropy. Combining both the Euclidean action and membrane paradigm approaches, a direct derivation of the black hole entropy is given. In the derivation, it is considered that the only fields present are the gravitational and matter fields, with no electric field.
Logarithmic corrections to gravitational entropy and the null energy condition
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Maulik Parikh
2016-10-01
Full Text Available Using a relation between the thermodynamics of local horizons and the null energy condition, we consider the effects of quantum corrections to the gravitational entropy. In particular, we find that the geometric form of the null energy condition is not affected by the inclusion of logarithmic corrections to the Bekenstein–Hawking entropy.
Near the horizon of 5D black rings
International Nuclear Information System (INIS)
Loran, Farhang; Soltanpanahi, Hesam
2009-01-01
For the five dimensional N = 2 black rings, we study the supersymmetry enhancement and identify the global supergroup of the near horizon geometry. We show that the global part of the supergroup is OSp(4*|2) x U(1) which is similar to the small black string. We show that results obtained by applying the entropy function formalism, the c-extremization approach and the Brown-Henneaux method to the black ring solution are in agreement with the microscopic entropy calculation.
Excess entropy scaling for the segmental and global dynamics of polyethylene melts.
Voyiatzis, Evangelos; Müller-Plathe, Florian; Böhm, Michael C
2014-11-28
The range of validity of the Rosenfeld and Dzugutov excess entropy scaling laws is analyzed for unentangled linear polyethylene chains. We consider two segmental dynamical quantities, i.e. the bond and the torsional relaxation times, and two global ones, i.e. the chain diffusion coefficient and the viscosity. The excess entropy is approximated by either a series expansion of the entropy in terms of the pair correlation function or by an equation of state for polymers developed in the context of the self associating fluid theory. For the whole range of temperatures and chain lengths considered, the two estimates of the excess entropy are linearly correlated. The scaled bond and torsional relaxation times fall into a master curve irrespective of the chain length and the employed scaling scheme. Both quantities depend non-linearly on the excess entropy. For a fixed chain length, the reduced diffusion coefficient and viscosity scale linearly with the excess entropy. An empirical reduction to a chain length-independent master curve is accessible for both dynamic quantities. The Dzugutov scheme predicts an increased value of the scaled diffusion coefficient with increasing chain length which contrasts physical expectations. The origin of this trend can be traced back to the density dependence of the scaling factors. This finding has not been observed previously for Lennard-Jones chain systems (Macromolecules, 2013, 46, 8710-8723). Thus, it limits the applicability of the Dzugutov approach to polymers. In connection with diffusion coefficients and viscosities, the Rosenfeld scaling law appears to be of higher quality than the Dzugutov approach. An empirical excess entropy scaling is also proposed which leads to a chain length-independent correlation. It is expected to be valid for polymers in the Rouse regime.
Entropy in Spacetime and Topological Hair
Hyun, Young-Hwan; Kim, Yoonbai
2018-01-01
Global topological soliton of the hedgehog ansatz is added to de Sitter spacetime in arbitrary dimensions larger than three, and then thermodynamic law is checked at the cosmological horizon. All geometric and thermodynamic quantities are varied in the presence of a long-range interacting matter distribution with negative pressure, however the entropy-area relation is satisfied in the exact form. Its geometry involves deficit solid angle but maintains a single horizon which allows unique temperature normalization, different from the case of Schwarzschild-de Sitter spacetime.
Static Isolated Horizons: SU(2 Invariant Phase Space, Quantization, and Black Hole Entropy
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Alejandro Perez
2011-03-01
Full Text Available We study the classical field theoretical formulation of static generic isolated horizons in a manifestly SU(2 invariant formulation. We show that the usual classical description requires revision in the non-static case due to the breaking of diffeomorphism invariance at the horizon leading to the non-conservation of the usual pre-symplectic structure. We argue how this difficulty could be avoided by a simple enlargement of the field content at the horizon that restores diffeomorphism invariance. Restricting our attention to static isolated horizons we study the effective theories describing the boundary degrees of freedom. A quantization of the horizon degrees of freedom is proposed. By defining a statistical mechanical ensemble where only the area aH of the horizon is fixed macroscopically—states with fluctuations away from spherical symmetry are allowed—we show that it is possible to obtain agreement with the Hawkings area law (S = aH /(4l 2p without fixing the Immirzi parameter to any particular value: consistency with the area law only imposes a relationship between the Immirzi parameter and the level of the Chern-Simons theory involved in the effective description of the horizon degrees of freedom.
A Dynamic and Adaptive Selection Radar Tracking Method Based on Information Entropy
Directory of Open Access Journals (Sweden)
Ge Jianjun
2017-12-01
Full Text Available Nowadays, the battlefield environment has become much more complex and variable. This paper presents a quantitative method and lower bound for the amount of target information acquired from multiple radar observations to adaptively and dynamically organize the detection of battlefield resources based on the principle of information entropy. Furthermore, for minimizing the given information entropy’s lower bound for target measurement at every moment, a method to dynamically and adaptively select radars with a high amount of information for target tracking is proposed. The simulation results indicate that the proposed method has higher tracking accuracy than that of tracking without adaptive radar selection based on entropy.
Dynamic ultraslow optical-matter wave analog of an event horizon.
Zhu, C J; Deng, L; Hagley, E W; Ge, Mo-Lin
2014-08-29
We investigate theoretically the effects of a dynamically increasing medium index on optical-wave propagation in a rubidium condensate. A long pulsed pump laser coupling a D2 line transition produces a rapidly growing internally generated field. This results in a significant optical self-focusing effect and creates a dynamically growing medium index anomaly that propagates ultraslowly with the internally generated field. When a fast probe pulse injected after a delay catches up with the dynamically increasing index anomaly, it is forced to slow down and is prohibited from crossing the anomaly, thereby realizing an ultraslow optical-matter wave analog of a dynamic white-hole event horizon.
Empirical study on entropy models of cellular manufacturing systems
Institute of Scientific and Technical Information of China (English)
Zhifeng Zhang; Renbin Xiao
2009-01-01
From the theoretical point of view,the states of manufacturing resources can be monitored and assessed through the amount of information needed to describe their technological structure and operational state.The amount of information needed to describe cellular manufacturing systems is investigated by two measures:the structural entropy and the operational entropy.Based on the Shannon entropy,the models of the structural entropy and the operational entropy of cellular manufacturing systems are developed,and the cognizance of the states of manufacturing resources is also illustrated.Scheduling is introduced to measure the entropy models of cellular manufacturing systems,and the feasible concepts of maximum schedule horizon and schedule adherence are advanced to quantitatively evaluate the effectiveness of schedules.Finally,an example is used to demonstrate the validity of the proposed methodology.
On extremals of the entropy production by ‘Langevin–Kramers’ dynamics
International Nuclear Information System (INIS)
Muratore-Ginanneschi, Paolo
2014-01-01
We refer as ‘Langevin–Kramers’ dynamics to a class of stochastic differential systems exhibiting a degenerate ‘metriplectic’ structure. This means that the drift field can be decomposed into a symplectic and a gradient-like component with respect to a pseudo-metric tensor associated with random fluctuations affecting increments of only a sub-set of the degrees of freedom. Systems in this class are often encountered in applications as elementary models of Hamiltonian dynamics in a heat bath eventually relaxing to a Boltzmann steady state. Entropy production control in Langevin–Kramers models differs from the now well-understood case of Langevin–Smoluchowski dynamics for two reasons. First, the definition of entropy production stemming from fluctuation theorems specifies a cost functional which does not act coercively on all degrees of freedom of control protocols. Second, the presence of a symplectic structure imposes a non-local constraint on the class of admissible controls. Using Pontryagin control theory and restricting the attention to additive noise, we show that smooth protocols attaining extremal values of the entropy production appear generically in continuous parametric families as a consequence of a trade-off between smoothness of the admissible protocols and non-coercivity of the cost functional. Uniqueness is, however, always recovered in the over-damped limit as extremal equations reduce at leading order to the Monge–Ampère–Kantorovich optimal mass-transport equations. (paper)
Entropy corresponding to the interior of a Schwarzschild black hole
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Bibhas Ranjan Majhi
2017-07-01
Full Text Available Interior volume within the horizon of a black hole is a non-trivial concept which turns out to be very important to explain several issues in the context of quantum nature of black hole. Here we show that the entropy, contained by the maximum interior volume for massless modes, is proportional to the Bekenstein–Hawking expression. The proportionality constant is less than unity implying the horizon bears maximum entropy than that by the interior. The derivation is very systematic and free of any ambiguity. To do so the precise value of the energy of the modes, living in the interior, is derived by constraint analysis. Finally, the implications of the result are discussed.
Entropy corresponding to the interior of a Schwarzschild black hole
Majhi, Bibhas Ranjan; Samanta, Saurav
2017-07-01
Interior volume within the horizon of a black hole is a non-trivial concept which turns out to be very important to explain several issues in the context of quantum nature of black hole. Here we show that the entropy, contained by the maximum interior volume for massless modes, is proportional to the Bekenstein-Hawking expression. The proportionality constant is less than unity implying the horizon bears maximum entropy than that by the interior. The derivation is very systematic and free of any ambiguity. To do so the precise value of the energy of the modes, living in the interior, is derived by constraint analysis. Finally, the implications of the result are discussed.
A Spacetime Foam Approach to the Schwarzschild-de Sitter Entropy
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Remo Garattini
2000-03-01
Full Text Available The entropy for a black hole in a de Sitter space is approached within the framework of spacetime foam. A simple model made by N wormholes in a semiclassical approximation, is taken under examination to compute the entropy for such a case. An extension to the extreme case when the black hole and cosmological horizons are equal is discussed.
Thermodynamics of event horizons in (2+1)-dimensional gravity
International Nuclear Information System (INIS)
Reznik, B.
1992-01-01
Although gravity in 2+1 dimensions is very different in nature from gravity in 3+1 dimensions, it is shown that the laws of thermodynamics for event horizons can be manifested also for (2+1)-dimensional gravity. The validity of the classical laws of horizon mechanics is verified in general and exemplified for the (2+1)-dimensional analogues of Reissner-Nordstroem and Schwarzschild--de Sitter spacetimes. We find that the entropy is given by 1/4L, where L is the length of the horizon. A consequence of having consistent thermodynamics is that the second law fixes the sign of Newton's constant to be positive
Black Hole Horizons and Thermodynamics: A Quantum Approach
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Nicola Pinamonti
2010-07-01
Full Text Available We focus on quantization of the metric of a black hole restricted to the Killing horizon with universal radius r0. After imposing spherical symmetry and after restriction to the Killing horizon, the metric is quantized employing the chiral currents formalism. Two "components of the metric" are indeed quantized: The former behaves as an affine scalar field under changes of coordinates, the latter is instead a proper scalar field. The action of the symplectic group on both fields is realized in terms of certain horizon diffeomorphisms. Depending on the choice of the vacuum state, such a representation is unitary. If the reference state of the scalar field is a coherent state rather than a vacuum, spontaneous breaking of conformal symmetry arises and the state contains a Bose-Einstein condensate. In this case the order parameter fixes the actual size of the black hole with respect to r0. Both the constructed state together with the one associated with the affine scalar are thermal states (KMS with respect to Schwarzschild Killing time when restricted to half horizon. The value of the order parameter fixes the temperature at the Hawking value as well. As a result, it is found that the quantum energy and entropy densities coincide with the black hole mass and entropy, provided the universal parameter r0 is suitably chosen, not depending on the size of the actual black hole in particular.
Dynamical symmetry enhancement near IIA horizons
International Nuclear Information System (INIS)
Gran, University; Gutowski, J.; Kayani, University; Papadopoulos, G.
2015-01-01
We show that smooth type IIA Killing horizons with compact spatial sections preserve an even number of supersymmetries, and that the symmetry algebra of horizons with non-trivial fluxes includes an sl(2,ℝ) subalgebra. This confirms the conjecture of http://dx.doi.org/10.1007/JHEP11(2013)104 for type IIA horizons. As an intermediate step in the proof, we also demonstrate new Lichnerowicz type theorems for spin bundle connections whose holonomy is contained in a general linear group.
Braneworld black holes and entropy bounds
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Y. Heydarzade
2018-01-01
Full Text Available The Bousso's D-bound entropy for the various possible black hole solutions on a 4-dimensional brane is checked. It is found that the D-bound entropy here is apparently different from that of obtained for the 4-dimensional black hole solutions. This difference is interpreted as the extra loss of information, associated to the extra dimension, when an extra-dimensional black hole is moved outward the observer's cosmological horizon. Also, it is discussed that N-bound entropy is hold for the possible solutions here. Finally, by adopting the recent Bohr-like approach to black hole quantum physics for the excited black holes, the obtained results are written also in terms of the black hole excited states.
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Tommaso Toffoli
2016-06-01
Full Text Available Here we deconstruct, and then in a reasoned way reconstruct, the concept of “entropy of a system”, paying particular attention to where the randomness may be coming from. We start with the core concept of entropy as a count associated with a description; this count (traditionally expressed in logarithmic form for a number of good reasons is in essence the number of possibilities—specific instances or “scenarios”—that match that description. Very natural (and virtually inescapable generalizations of the idea of description are the probability distribution and its quantum mechanical counterpart, the density operator. We track the process of dynamically updating entropy as a system evolves. Three factors may cause entropy to change: (1 the system’s internal dynamics; (2 unsolicited external influences on it; and (3 the approximations one has to make when one tries to predict the system’s future state. The latter task is usually hampered by hard-to-quantify aspects of the original description, limited data storage and processing resource, and possibly algorithmic inadequacy. Factors 2 and 3 introduce randomness—often huge amounts of it—into one’s predictions and accordingly degrade them. When forecasting, as long as the entropy bookkeping is conducted in an honest fashion, this degradation will always lead to an entropy increase. To clarify the above point we introduce the notion of honest entropy, which coalesces much of what is of course already done, often tacitly, in responsible entropy-bookkeping practice. This notion—we believe—will help to fill an expressivity gap in scientific discourse. With its help, we shall prove that any dynamical system—not just our physical universe—strictly obeys Clausius’s original formulation of the second law of thermodynamics if and only if it is invertible. Thus this law is a tautological property of invertible systems!
Mechanism of the generation of black hole entropy in Sakharov's induced gravity
International Nuclear Information System (INIS)
Frolov, V.P.; Fursaev, D.V.
1997-01-01
The mechanism of the generation of Bekenstein-Hawking entropy S BH of a black hole in the Sakharov's induced gravity is proposed. It is suggested that the physical degrees of freedom, which explain the entropy S BH , form only a finite subset of the standard Rindler-like modes defined outside the black hole horizon. The entropy S R of the Rindler modes, or entanglement entropy, is always ultraviolet divergent, while the entropy of the physical modes is finite and coincides in the induced gravity with S BH . The two entropies S BH and S R differ by a surface integral Q interpreted as a Noether charge of nonminimally coupled scalar constituents of the model. We demonstrate that energy E and Hamiltonian H of the fields localized in a part of space-time, restricted by the Killing horizon Σ, differ by the quantity T H Q, where T H is the temperature of a black hole. The first law of black hole thermodynamics enables one to relate the probability distribution of fluctuations of the black hole mass, caused by the quantum fluctuations of the fields, to the probability distribution of physical modes over energy E. The latter turns out to be different from the distribution of the Rindler modes. We show that the probability distribution of the physical degrees of freedom has a sharp peak at E=0 with the width proportional to the Planck mass. The logarithm of number of physical states at the peak coincides exactly with the black hole entropy S BH . This enables us to argue that the energy distribution of the physical modes and distribution of the black hole mass are equivalent in induced gravity. Finally it is shown that the Noether charge Q is related to the entropy of the low-frequency modes propagating in the vicinity of the bifurcation surface Σ of the horizon. (Abstract Truncated)
Upper bounds on the entropy of radiation systems
Institute of Scientific and Technical Information of China (English)
汪定雄
1997-01-01
The upper bounds on the entropy of a radiation system confined to a spherical box are calculated in six cases by using the equation of state of radiation in flat spacetime and the equation of state of radiation near black-hole horizon,which was derived by Li and Liu (hereafter the Li-Liu equation).It turns out that the Li-Liu equation does have unique advantage in dealing with the entropy bound of critical self-gravitating radiation systems,while the usual equation of state will result in entropy divergence.In the case of non-self-gravitating radiation systems and non-critical self-gravitating radiation systems,there is no difference in the entropy bounds derived by these two equations of state.
The Thermodynamic Evolution of the Cosmological Event Horizon
Funkhouser, Scott
2012-04-01
By manipulating the integral expression for the proper radius R e of the cosmological event horizon (CEH) in a Friedmann-Robertson-Walker (FRW) universe we obtain an analytical expression for the change δR e in response to a uniform fluctuation δρ in the average cosmic background density ρ. We stipulate that the fluctuation arises within a vanishing interval of proper time, during which the CEH is approximately stationary, and evolves subsequently such that δρ/ ρ is constant. The respective variations 2 πR e δR e and δE e in the horizon entropy S e and enclosed energy E e should be therefore related through the cosmological Clausius relation. In that manner we find that the temperature T e of the CEH at an arbitrary time in a flat FRW universe is E e / S e , which recovers asymptotically the usual static de Sitter temperature. Furthermore it is proven that during radiation-dominance and in late times the CEH conforms to the fully dynamical First Law T e d S e = Pd V e -d E e , where V e is the enclosed volume and P is the average cosmic pressure.
Directory of Open Access Journals (Sweden)
Hang Liu
2016-08-01
Full Text Available In this paper, we investigate the angular momentum independence of the entropy sum and product for AdS rotating black holes based on the first law of thermodynamics and a mathematical lemma related to Vandermonde determinant. The advantage of this method is that the explicit forms of the spacetime metric, black hole mass and charge are not needed but the Hawking temperature and entropy formula on the horizons are necessary for static black holes, while our calculations require the expressions of metric and angular velocity formula. We find that the entropy sum is always independent of angular momentum for all dimensions and the angular momentum-independence of entropy product only holds for the dimensions d>4 with at least one rotation parameter ai=0, while the mass-free of entropy sum and entropy product for rotating black holes only stand for higher dimensions (d>4 and for all dimensions, respectively. On the other hand, we find that the introduction of a negative cosmological constant does not affect the angular momentum-free of entropy sum and product but the criterion for angular momentum-independence of entropy product will be affected.
Logarithmic corrections to entropy of magnetically charged AdS4 black holes
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Imtak Jeon
2017-11-01
Full Text Available Logarithmic terms are quantum corrections to black hole entropy determined completely from classical data, thus providing a strong check for candidate theories of quantum gravity purely from physics in the infrared. We compute these terms in the entropy associated to the horizon of a magnetically charged extremal black hole in AdS×4S7 using the quantum entropy function and discuss the possibility of matching against recently derived microscopic expressions.
The Finite-Horizon Singular H∞ Control Problem With Dynamic Measurement Feedback
Stoorvogel, A.A.; Trentelman, H.L.
1993-01-01
This paper is concerned with the finite-horizon version of the H∞ problem with measurement feedback. Given a finite-dimensional linear, time-varying system, together with a positive real number γ, we obtain necessary and sufficient conditions for the existence of a possibly time-varying dynamic
Revisiting event horizon finders
International Nuclear Information System (INIS)
Cohen, Michael I; Pfeiffer, Harald P; Scheel, Mark A
2009-01-01
Event horizons are the defining physical features of black hole spacetimes, and are of considerable interest in studying black hole dynamics. Here, we reconsider three techniques to find event horizons in numerical spacetimes: integrating geodesics, integrating a surface, and integrating a level-set of surfaces over a volume. We implement the first two techniques and find that straightforward integration of geodesics backward in time is most robust. We find that the exponential rate of approach of a null surface towards the event horizon of a spinning black hole equals the surface gravity of the black hole. In head-on mergers we are able to track quasi-normal ringing of the merged black hole through seven oscillations, covering a dynamic range of about 10 5 . Both at late times (when the final black hole has settled down) and at early times (before the merger), the apparent horizon is found to be an excellent approximation of the event horizon. In the head-on binary black hole merger, only some of the future null generators of the horizon are found to start from past null infinity; the others approach the event horizons of the individual black holes at times far before merger.
Entropy Inequality Violations from Ultraspinning Black Holes.
Hennigar, Robie A; Mann, Robert B; Kubizňák, David
2015-07-17
We construct a new class of rotating anti-de Sitter (AdS) black hole solutions with noncompact event horizons of finite area in any dimension and study their thermodynamics. In four dimensions these black holes are solutions to gauged supergravity. We find that their entropy exceeds the maximum implied from the conjectured reverse isoperimetric inequality, which states that for a given thermodynamic volume, the black hole entropy is maximized for Schwarzschild-AdS space. We use this result to suggest more stringent conditions under which this conjecture may hold.
Scale-invariant entropy-based theory for dynamic ordering
International Nuclear Information System (INIS)
Mahulikar, Shripad P.; Kumari, Priti
2014-01-01
Dynamically Ordered self-organized dissipative structure exists in various forms and at different scales. This investigation first introduces the concept of an isolated embedding system, which embeds an open system, e.g., dissipative structure and its mass and/or energy exchange with its surroundings. Thereafter, scale-invariant theoretical analysis is presented using thermodynamic principles for Order creation, existence, and destruction. The sustainability criterion for Order existence based on its structured mass and/or energy interactions with the surroundings is mathematically defined. This criterion forms the basis for the interrelationship of physical parameters during sustained existence of dynamic Order. It is shown that the sufficient condition for dynamic Order existence is approached if its sustainability criterion is met, i.e., its destruction path is blocked. This scale-invariant approach has the potential to unify the physical understanding of universal dynamic ordering based on entropy considerations
The Cardy-Verlinde formula and entropy of topological Kerr-Newman black holes in de Sitter spaces
International Nuclear Information System (INIS)
Setare, M.R.; Altaie, M.B.
2003-01-01
In this paper we show that the entropy of a cosmological horizon in 4-dimensional topological Kerr-Newman-de Sitter spaces can be described by the Cardy-Verlinde formula, which is supposed to be an entropy formula of conformal field theory in any number of dimensions. Furthermore, we find that the entropy of a black hole horizon can also be rewritten in terms of the Cardy-Verlinde formula for these black holes in de Sitter spaces, if we use the definition due to Abbott and Deser for conserved charges in asymptotically de Sitter spaces. Such results presume a well-defined dS/CFT correspondence, which has not yet attained the credibility of its AdS analogue. (orig.)
Cosmological and black hole apparent horizons
Faraoni, Valerio
2015-01-01
This book overviews the extensive literature on apparent cosmological and black hole horizons. In theoretical gravity, dynamical situations such as gravitational collapse, black hole evaporation, and black holes interacting with non-trivial environments, as well as the attempts to model gravitational waves occurring in highly dynamical astrophysical processes, require that the concept of event horizon be generalized. Inequivalent notions of horizon abound in the technical literature and are discussed in this manuscript. The book begins with a quick review of basic material in the first one and a half chapters, establishing a unified notation. Chapter 2 reminds the reader of the basic tools used in the analysis of horizons and reviews the various definitions of horizons appearing in the literature. Cosmological horizons are the playground in which one should take baby steps in understanding horizon physics. Chapter 3 analyzes cosmological horizons, their proposed thermodynamics, and several coordinate systems....
On the entropy of four-dimensional near-extremal N = 2 black holes with R2-terms
International Nuclear Information System (INIS)
Gruss, Eyal; Oz, Yaron
2007-01-01
We consider the entropy of four-dimensional near-extremal N = 2 black holes. The Bekenstein-Hawking entropy formula has the structure of the extremal black holes entropy with a shift of the charges depending on the non-extremality parameter and the moduli at infinity. We construct a class of near-extremal horizon solutions with R 2 -terms, and show that the generalized Wald entropy formula exhibits the same property
IMPROVED ENTROPY-ULTRA-BEE SCHEME FOR THE EULER SYSTEM OF GAS DYNAMICS
Institute of Scientific and Technical Information of China (English)
Rongsan Chen; Dekang Mao
2017-01-01
The Entropy-Ultra-Bee scheme was developed for the linear advection equation and extended to the Euler system of gas dynamics in [13].It was expected that the technology be applied only to the second characteristic field of the system and the computation in the other two nonlinear fields be implemented by the Godunov scheme.However,the numerical experiments in [13] showed that the scheme,though having improved the wave resolution in the second field,produced numerical oscillations in the other two nonlinear fields.Sophisticated entropy increaser was designed to suppress the spurious oscillations by increasing the entropy when there are waves in the two nonlinear fields presented.However,the scheme is then not efficient neither robust with problem-related parameters.The purpose of this paper is to fix this problem.To this end,we first study a 3 × 3 linear system and apply the technology precisely to its second characteristic field while maintaining the computation in the other two fields be implemented by the Godunov scheme.We then follow the discussion for the linear system to apply the Entropy-Ultra-Bee technology to the second characteristic field of the Euler system in a linearlized field-byfield fashion to develop a modified Entropy-Ultra-Bee scheme for the system.Meanwhile a remark is given to explain the problem of the previous Entropy-Ultra-Bee scheme in [13].A reference solution is constructed for computing the numerical entropy,which maintains the feature of the density and flats the velocity and pressure to constants.The numerical entropy is then computed as the entropy cell-average of the reference solution.Several limitations are adopted in the construction of the reference solution to further stabilize the scheme.Designed in such a way,the modified Entropy-Ultra-Bee scheme has a unified form with no problem-related parameters.Numerical experiments show that all the spurious oscillations in smooth regions are gone and the results are better than that
Horizon thermodynamics and gravitational field equations in Horava-Lifshitz gravity
International Nuclear Information System (INIS)
Cai Ronggen; Ohta, Nobuyoshi
2010-01-01
We explore the relationship between the first law of thermodynamics and gravitational field equation at a static, spherically symmetric black hole horizon in Horava-Lifshitz theory with/without detailed balance. It turns out that as in the cases of Einstein gravity and Lovelock gravity, the gravitational field equation can be cast to a form of the first law of thermodynamics at the black hole horizon. This way we obtain the expressions for entropy and mass in terms of black hole horizon, consistent with those from other approaches. We also define a generalized Misner-Sharp energy for static, spherically symmetric spacetimes in Horava-Lifshitz theory. The generalized Misner-Sharp energy is conserved in the case without matter field, and its variation gives the first law of black hole thermodynamics at the black hole horizon.
Entropic dynamics: From entropy and information geometry to Hamiltonians and quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Caticha, Ariel; Bartolomeo, Daniel [Department of Physics, University at Albany-SUNY, Albany, NY 12222 (United States); Reginatto, Marcel [Physicalisch-Technische Bundesanstalt, 38116 Braunschweig (Germany)
2015-01-13
Entropic Dynamics is a framework in which quantum theory is derived as an application of entropic methods of inference. There is no underlying action principle. Instead, the dynamics is driven by entropy subject to the appropriate constraints. In this paper we show how a Hamiltonian dynamics arises as a type of non-dissipative entropic dynamics. We also show that the particular form of the 'quantum potential' that leads to the Schrödinger equation follows naturally from information geometry.
Entropic dynamics: From entropy and information geometry to Hamiltonians and quantum mechanics
International Nuclear Information System (INIS)
Caticha, Ariel; Bartolomeo, Daniel; Reginatto, Marcel
2015-01-01
Entropic Dynamics is a framework in which quantum theory is derived as an application of entropic methods of inference. There is no underlying action principle. Instead, the dynamics is driven by entropy subject to the appropriate constraints. In this paper we show how a Hamiltonian dynamics arises as a type of non-dissipative entropic dynamics. We also show that the particular form of the 'quantum potential' that leads to the Schrödinger equation follows naturally from information geometry
Microcanonical entropy of a black hole
International Nuclear Information System (INIS)
Bhaduri, Rajat K.; Tran, Muoi N.; Das, Saurya
2004-01-01
It has been suggested recently that the microcanonical entropy of a system may be accurately reproduced by including a logarithmic correction to the canonical entropy. In this paper we test this claim both analytically and numerically by considering three simple thermodynamic models whose energy spectrum may be defined in terms of one quantum number only, as in a non-rotating black hole. The first two pertain to collections of noninteracting bosons, with logarithmic and power-law spectra. The last is an area ensemble for a black hole with equi-spaced area spectrum. In this case, the many-body degeneracy factor can be obtained analytically in a closed form. We also show that in this model, the leading term in the entropy is proportional to the horizon area A, and the next term is ln A with a negative coefficient
Effect of entropy on anomalous transport in ITG-modes of magneto-plasma
Yaqub Khan, M.; Qaiser Manzoor, M.; Haq, A. ul; Iqbal, J.
2017-04-01
The ideal gas equation and S={{c}v}log ≤ft(P/ρ \\right) (where S is entropy, P is pressure and ρ is the mass density) define the interconnection of entropy with the temperature and density of plasma. Therefore, different phenomena relating to plasma and entropy need to be investigated. By employing the Braginskii transport equations for a nonuniform electron-ion magnetoplasma, two new parameters—the entropy distribution function and the entropy gradient drift—are defined, a new dispersion relation is obtained, and the dependence of anomalous transport on entropy is also proved. Some results, like monotonicity, the entropy principle and the second law of thermodynamics, are proved with a new definition of entropy. This work will open new horizons in fusion processes, not only by controlling entropy in tokamak plasmas—particularly in the pedestal regions of the H-mode and space plasmas—but also in engineering sciences.
Inflation via logarithmic entropy-corrected holographic dark energy model
Energy Technology Data Exchange (ETDEWEB)
Darabi, F.; Felegary, F. [Azarbaijan Shahid Madani University, Department of Physics, Tabriz (Iran, Islamic Republic of); Setare, M.R. [University of Kurdistan, Department of Science, Bijar (Iran, Islamic Republic of)
2016-12-15
We study the inflation in terms of the logarithmic entropy-corrected holographic dark energy (LECHDE) model with future event horizon, particle horizon, and Hubble horizon cut-offs, and we compare the results with those obtained in the study of inflation by the holographic dark energy HDE model. In comparison, the spectrum of primordial scalar power spectrum in the LECHDE model becomes redder than the spectrum in the HDE model. Moreover, the consistency with the observational data in the LECHDE model of inflation constrains the reheating temperature and Hubble parameter by one parameter of holographic dark energy and two new parameters of logarithmic corrections. (orig.)
Inflation via logarithmic entropy-corrected holographic dark energy model
International Nuclear Information System (INIS)
Darabi, F.; Felegary, F.; Setare, M.R.
2016-01-01
We study the inflation in terms of the logarithmic entropy-corrected holographic dark energy (LECHDE) model with future event horizon, particle horizon, and Hubble horizon cut-offs, and we compare the results with those obtained in the study of inflation by the holographic dark energy HDE model. In comparison, the spectrum of primordial scalar power spectrum in the LECHDE model becomes redder than the spectrum in the HDE model. Moreover, the consistency with the observational data in the LECHDE model of inflation constrains the reheating temperature and Hubble parameter by one parameter of holographic dark energy and two new parameters of logarithmic corrections. (orig.)
da Rocha-Neto, J. F.; Morais, B. R.
2018-04-01
In the context of the teleparallel equivalent of general relativity the concept of gravitational pressure and gravitational energy-momentum arisen in a natural way. In the case of a Friedmann-Lemaitre-Robertson-Walker space FLRW we obtain the total energy contained inside the apparent horizon and the radial pressure over the apparent horizon area. We use these definitions to written a thermodynamics relation TAdSA = dEA+PAdVA at the apparent horizon, where EA is the total energy inside the apparent horizon, VA is the areal volume of the apparent horizon, PA is the radial pressure over the apparent horizon area, SA is the entropy which can be assumed as one quarter of the apparent horizon area only for a non stationary apparent horizon. We identify TA as the temperature at the surface of the apparent horizon. We shown that for all expanding accelerated FLRW model of universe the radial pressure is positive.
CFT/gravity correspondence on the isolated horizon
Energy Technology Data Exchange (ETDEWEB)
Ghosh, Amit, E-mail: amit.ghosh@saha.ac.in [Saha Institute of Nuclear Physics, 1/AF Bidhan Nagar, 700064 Kolkata (India); Pranzetti, Daniele, E-mail: daniele.pranzetti@gravity.fau.de [Institute for Quantum Gravity, University of Erlangen-Nürnberg (FAU), Staudtstrasse 7/B2, 91058 Erlangen (Germany)
2014-12-15
A quantum isolated horizon can be modelled by an SU(2) Chern–Simons theory on a punctured 2-sphere. We show how a local 2-dimensional conformal symmetry arises at each puncture inducing an infinite set of new observables localised at the horizon which satisfy a Kac–Moody algebra. By means of the isolated horizon boundary conditions, we represent the gravitational flux degrees of freedom in terms of the zero modes of the Kac–Moody algebra defined on the boundary of a punctured disk. In this way, our construction encodes a precise notion of CFT/gravity correspondence. The higher modes in the algebra represent new nongeometric charges which can be represented in terms of free matter field degrees of freedom. When computing the CFT partition function of the system, these new states induce an extra degeneracy factor, representing the density of horizon states at a given energy level, which reproduces the Bekenstein's holographic bound for an imaginary Immirzi parameter. This allows us to recover the Bekenstein–Hawking entropy formula without the large quantum gravity corrections associated with the number of punctures.
International Nuclear Information System (INIS)
Maes, Christian
2012-01-01
In contrast to the quite unique entropy concept useful for systems in (local) thermodynamic equilibrium, there is a variety of quite distinct nonequilibrium entropies, reflecting different physical points. We disentangle these entropies as they relate to heat, fluctuations, response, time asymmetry, variational principles, monotonicity, volume contraction or statistical forces. However, not all of those extensions yield state quantities as understood thermodynamically. At the end we sketch how aspects of dynamical activity can take over for obtaining an extended Clausius relation.
Black hole entropy and the problem of universality
International Nuclear Information System (INIS)
Carlip, Steven
2007-01-01
A key test of any quantum theory of gravity is its ability to reproduce the known thermodynamic properties of black holes. A statistical mechanical description of the Bekenstein-Hawking entropy once seemed remote, but today we suffer an embarrassment of riches: many different approaches to quantum gravity yield the same entropy, despite counting very different states. This 'universality' suggests that some underlying feature of the classical theory may control the quantum density of states. I discuss the possibility that this feature is an approximate two-dimensional conformal symmetry near the horizon
Black hole entropy and the problem of universality
Energy Technology Data Exchange (ETDEWEB)
Carlip, Steven [Physics Department, 1 Shields Ave., University of California at Davis, Davis, CA 95616 (United States)
2007-05-15
A key test of any quantum theory of gravity is its ability to reproduce the known thermodynamic properties of black holes. A statistical mechanical description of the Bekenstein-Hawking entropy once seemed remote, but today we suffer an embarrassment of riches: many different approaches to quantum gravity yield the same entropy, despite counting very different states. This 'universality' suggests that some underlying feature of the classical theory may control the quantum density of states. I discuss the possibility that this feature is an approximate two-dimensional conformal symmetry near the horizon.
International Nuclear Information System (INIS)
Kim, Wontae; Oh, John J.
2008-01-01
We derive the formula of the black hole entropy with a minimal length of the Planck size by counting quantum modes of scalar fields in the vicinity of the black hole horizon, taking into account the generalized uncertainty principle (GUP). This formula is applied to some intriguing examples of black holes - the Schwarzschild black hole, the Reissner-Nordstrom black hole, and the magnetically charged dilatonic black hole. As a result, it is shown that the GUP parameter can be determined by imposing the black hole entropy-area relationship, which has a Planck length scale and a universal form within the near-horizon expansion
Empty black holes, firewalls, and the origin of Bekenstein-Hawking entropy
Saravani, Mehdi; Afshordi, Niayesh; Mann, Robert B.
2014-01-01
We propose a novel solution for the endpoint of gravitational collapse, in which spacetime ends (and is orbifolded) at a microscopic distance from black hole event horizons. This model is motivated by the emergence of singular event horizons in the gravitational aether theory, a semiclassical solution to the cosmological constant problem(s) and thus suggests a catastrophic breakdown of general relativity close to black hole event horizons. A similar picture emerges in fuzzball models of black holes in string theory, as well as the recent firewall proposal to resolve the information paradox. We then demonstrate that positing a surface fluid in thermal equilibrium with Hawking radiation, with vanishing energy density (but nonvanishing pressure) at the new boundary of spacetime, which is required by Israel junction conditions, yields a thermodynamic entropy that is identical to the Bekenstein-Hawking area law, SBH, for charged rotating black holes. To our knowledge, this is the first derivation of black hole entropy that only employs local thermodynamics. Furthermore, a model for the microscopic degrees of freedom of the surface fluid (which constitute the microstates of the black hole) is suggested, which has a finite, but Lorentz-violating, quantum field theory. Finally, we comment on the effects of physical boundary on Hawking radiation and show that relaxing the assumption of equilibrium with Hawking radiation sets SBH as an upper limit for Black Hole entropy.
On unified-entropy characterization of quantum channels
International Nuclear Information System (INIS)
Rastegin, A E
2012-01-01
We consider properties of quantum channels with the use of unified entropies. Extremal unravelings of quantum channel with respect to these entropies are examined. The concept of map entropy is extended in terms of the unified entropies. The map (q, s)-entropy is naturally defined as the unified (q, s)-entropy of a rescaled dynamical matrix of given quantum channel. Inequalities of Fannes type are obtained for introduced entropies in terms of both the trace and Frobenius norms of difference between corresponding dynamical matrices. Additivity properties of introduced map entropies are discussed. The known inequality of Lindblad with the entropy exchange is generalized to many of the unified entropies. For the tensor product of a pair of quantum channels, we derive a two-sided estimate on the output entropy of a maximally entangled input state. (paper)
Using entropy measures to characterize human locomotion.
Leverick, Graham; Szturm, Tony; Wu, Christine Q
2014-12-01
Entropy measures have been widely used to quantify the complexity of theoretical and experimental dynamical systems. In this paper, the value of using entropy measures to characterize human locomotion is demonstrated based on their construct validity, predictive validity in a simple model of human walking and convergent validity in an experimental study. Results show that four of the five considered entropy measures increase meaningfully with the increased probability of falling in a simple passive bipedal walker model. The same four entropy measures also experienced statistically significant increases in response to increasing age and gait impairment caused by cognitive interference in an experimental study. Of the considered entropy measures, the proposed quantized dynamical entropy (QDE) and quantization-based approximation of sample entropy (QASE) offered the best combination of sensitivity to changes in gait dynamics and computational efficiency. Based on these results, entropy appears to be a viable candidate for assessing the stability of human locomotion.
Connecting horizon pixels and interior voxels of a black hole
International Nuclear Information System (INIS)
Nicolini, Piero; Singleton, Douglas
2014-01-01
In this paper we discuss to what extent one can infer details of the interior structure of a black hole based on its horizon. Recalling that black hole thermal properties are connected to the non-classical nature of gravity, we circumvent the restrictions of the no-hair theorem by postulating that the black hole interior is singularity free due to violations of the usual energy conditions. Further these conditions allow one to establish a one-to-one, holographic projection between Planckian areal “bits” on the horizon and “voxels”, representing the gravitational degrees of freedom in the black hole interior. We illustrate the repercussions of this idea by discussing an example of the black hole interior consisting of a de Sitter core postulated to arise from the local graviton quantum vacuum energy. It is shown that the black hole entropy can emerge as the statistical entropy of a gas of voxels
Subleading contributions to the black hole entropy in the brick wall approach
International Nuclear Information System (INIS)
Sarkar, Sudipta; Shankaranarayanan, S.; Sriramkumar, L.
2008-01-01
The brick wall model is a semiclassical approach to understand the microscopic origin of black hole entropy. In this approach, the black hole geometry is assumed to be a fixed classical background on which matter fields propagate, and the entropy of black holes supposedly arises due to the canonical entropy of matter fields outside the black hole event horizon, evaluated at the Hawking temperature. Apart from certain lower dimensional cases, the density of states of the matter fields around black holes cannot be evaluated exactly. As a result, often, in the brick wall model, the density of states and the resulting canonical entropy of the matter fields are evaluated at the leading order (in terms of (ℎ/2π)) in the WKB approximation. The success of the approach is reflected by the fact that the Bekenstein-Hawking area law - viz. that the entropy of black holes is equal to one-quarter the area of their event horizon, say, A H - has been recovered using this model in a variety of black hole spacetimes. In this work, we compute the canonical entropy of a quantum scalar field around static and spherically symmetric black holes through the brick wall approach at the higher orders (in fact, up to the sixth order in (ℎ/2π)) in the WKB approximation. We explicitly show that the brick wall model generally predicts corrections to the Bekenstein-Hawking entropy in all spacetime dimensions. In four dimensions, we find that the corrections to the Bekenstein-Hawking entropy are of the form [A H n logA H ], while, in six dimensions, the corrections behave as [A H m +A H n logA H ], where (m,n)<1. We compare our results with the corrections to the Bekenstein-Hawking entropy that have been obtained through the other approaches in the literature, and discuss the implications.
Isolated Horizon, Killing Horizon and Event Horizon
Date, G.
2001-01-01
We consider space-times which in addition to admitting an isolated horizon also admit Killing horizons with or without an event horizon. We show that an isolated horizon is a Killing horizon provided either (1) it admits a stationary neighbourhood or (2) it admits a neighbourhood with two independent, commuting Killing vectors. A Killing horizon is always an isolated horizon. For the case when an event horizon is definable, all conceivable relative locations of isolated horizon and event hori...
Directory of Open Access Journals (Sweden)
Marc-Thorsten Hütt
2012-06-01
Full Text Available Cellular automata (CA are a remarkably efficient tool for exploring general properties of complex systems and spatiotemporal patterns arising from local rules. Totalistic cellular automata, where the update rules depend only on the density of neighboring states, are at the same time a versatile tool for exploring dynamical processes on graphs. Here we briefly review our previous results on cellular automata on graphs, emphasizing some systematic relationships between network architecture and dynamics identified in this way. We then extend the investigation towards graphs obtained in a simulated-evolution procedure, starting from Erdő s–Rényi (ER graphs and selecting for low entropies of the CA dynamics. Our key result is a strong association of low Shannon entropies with a broadening of the graph’s degree distribution.
Hawking radiation as tunneling from the event horizon of NUT-Kerr-Newman de Sitter black hole
International Nuclear Information System (INIS)
Hui-Ling, Li; Shu-Shenh, Yang; Qing-Quan, Jiang; De-Jiang, Qi
2005-01-01
Adopting the method of quantum radiation as tunneling, Hawking radiation as tunneling from the event horizon of NUT-Kerr-Newman de Sitter black hole is studied. The result indicates that the tunneling rate of the particle on the event horizon is related to the change of Bekenstein-Hawking entropy and the real spectrum is not strictly thermal at all
RG flow and thermodynamics of causal horizons in higher-derivative AdS gravity
International Nuclear Information System (INIS)
Banerjee, Shamik; Bhattacharyya, Arpan
2016-01-01
In http://arxiv.org/abs/1508.01343 [hep-th], one of the authors proposed that in AdS/CFT the gravity dual of the boundary c-theorem is the second law of thermodynamics satisfied by causal horizons in AdS and this was verified for Einstein gravity in the bulk. In this paper we verify this for higher derivative theories. We pick up theories for which an entropy expression satisfying the second law exists and show that the entropy density evaluated on the causal horizon in a RG flow geometry is a holographic c-function. We also prove that given a theory of gravity described by a local covariant action in the bulk a sufficient condition to ensure holographic c-theorem is that the second law of causal horizon thermodynamics be satisfied by the theory. This allows us to explicitly construct holographic c-function in a theory where there is curvature coupling between gravity and matter and standard null energy condition cannot be defined although second law is known to hold. Based on the duality between c-theorem and the second law of causal horizon thermodynamics proposed in http://arxiv.org/abs/1508.01343 [hep-th] and the supporting calculations of this paper we conjecture that every Unitary higher derivative theory of gravity in AdS satisfies the second law of causal horizon thermodynamics. If this is not true then c-theorem will be violated in a unitary Lorentz invariant field theory.
3D flat holography: entropy and logarithmic corrections
International Nuclear Information System (INIS)
Bagchi, Arjun; Basu, Rudranil
2014-01-01
We compute the leading corrections to the Bekenstein-Hawking entropy of the Flat Space Cosmological (FSC) solutions in 3D flat spacetimes, which are the flat analogues of the BTZ black holes in AdS 3 . The analysis is done by a computation of density of states in the dual 2D Galilean Conformal Field Theory and the answer obtained by this matches with the limiting value of the expected result for the BTZ inner horizon entropy as well as what is expected for a generic thermodynamic system. Along the way, we also develop other aspects of holography of 3D flat spacetimes
Dynamical noise filter and conditional entropy analysis in chaos synchronization.
Wang, Jiao; Lai, C-H
2006-06-01
It is shown that, in a chaotic synchronization system whose driving signal is exposed to channel noise, the estimation of the drive system states can be greatly improved by applying the dynamical noise filtering to the response system states. If the noise is bounded in a certain range, the estimation errors, i.e., the difference between the filtered responding states and the driving states, can be made arbitrarily small. This property can be used in designing an alternative digital communication scheme. An analysis based on the conditional entropy justifies the application of dynamical noise filtering in generating quality synchronization.
Generalized entropy formalism and a new holographic dark energy model
Sayahian Jahromi, A.; Moosavi, S. A.; Moradpour, H.; Morais Graça, J. P.; Lobo, I. P.; Salako, I. G.; Jawad, A.
2018-05-01
Recently, the Rényi and Tsallis generalized entropies have extensively been used in order to study various cosmological and gravitational setups. Here, using a special type of generalized entropy, a generalization of both the Rényi and Tsallis entropy, together with holographic principle, we build a new model for holographic dark energy. Thereinafter, considering a flat FRW universe, filled by a pressureless component and the new obtained dark energy model, the evolution of cosmos has been investigated showing satisfactory results and behavior. In our model, the Hubble horizon plays the role of IR cutoff, and there is no mutual interaction between the cosmos components. Our results indicate that the generalized entropy formalism may open a new window to become more familiar with the nature of spacetime and its properties.
Noether Current of the Surface Term of Einstein-Hilbert Action, Virasoro Algebra, and Entropy
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Bibhas Ranjan Majhi
2013-01-01
Full Text Available A derivation of Noether current from the surface term of Einstein-Hilbert action is given. We show that the corresponding charge, calculated on the horizon, is related to the Bekenstein-Hawking entropy. Also using the charge, the same entropy is found based on the Virasoro algebra and Cardy formula approach. In this approach, the relevant diffeomorphisms are found by imposing a very simple physical argument: diffeomorphisms keep the horizon structure invariant. This complements similar earlier results (Majhi and Padmanabhan (2012 (arXiv:1204.1422 obtained from York-Gibbons-Hawking surface term. Finally we discuss the technical simplicities and improvements over the earlier attempts and also various important physical implications.
Bekenstein-Hawking Entropy and Strange Metals
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Subir Sachdev
2015-11-01
Full Text Available We examine models of fermions with infinite-range interactions that realize non-Fermi liquids with a continuously variable U(1 charge density Q and a nonzero entropy density S at vanishing temperature. Real-time correlators of operators carrying U(1 charge q at a low temperature T are characterized by a Q-dependent frequency ω_{S}=(qT/ℏ(∂S/∂Q, which determines a spectral asymmetry. We show that the correlators match precisely with those of the two-dimensional anti–de Sitter (AdS_{2} horizons of extremal charged black holes. On the black hole side, the matching employs S as the Bekenstein-Hawking entropy density and the laws of black hole thermodynamics that relate (∂S/∂Q/(2π to the electric field strength in AdS_{2}. The fermion model entropy is computed using the microscopic degrees of freedom of a UV complete theory without supersymmetry.
The concept of entropy. Relation between action and entropy
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J.-P.Badiali
2005-01-01
Full Text Available The Boltzmann expression for entropy represents the traditional link between thermodynamics and statistical mechanics. New theoretical developments like the Unruh effect or the black hole theory suggest a new definition of entropy. In this paper we consider the thermodynamics of black holes as seriously founded and we try to see what we can learn from it in the case of ordinary systems for which a pre-relativistic description is sufficient. We introduce a space-time model and a new definition of entropy considering the thermal equilibrium from a dynamic point of view. Then we show that for black hole and ordinary systems we have the same relation relating a change of entropy to a change of action.
Ahmadi, Samira; Wu, Christine; Sepehri, Nariman; Kantikar, Anuprita; Nankar, Mayur; Szturm, Tony
2018-01-01
Quantized dynamical entropy (QDE) has recently been proposed as a new measure to quantify the complexity of dynamical systems with the purpose of offering a better computational efficiency. This paper further investigates the viability of this method using five different human gait signals. These signals are recorded while normal walking and while performing secondary tasks among two age groups (young and older age groups). The results are compared with the outcomes of previously established sample entropy (SampEn) measure for the same signals. We also study how analyzing segmented and spatially and temporally normalized signal differs from analyzing whole data. Our findings show that human gait signals become more complex as people age and while they are cognitively loaded. Center of pressure (COP) displacement in mediolateral direction is the best signal for showing the gait changes. Moreover, the results suggest that by segmenting data, more information about intrastride dynamical features are obtained. Most importantly, QDE is shown to be a reliable measure for human gait complexity analysis.
What happens at the horizon(s) of an extreme black hole?
International Nuclear Information System (INIS)
Murata, Keiju; Reall, Harvey S; Tanahashi, Norihiro
2013-01-01
A massless scalar field exhibits an instability at the event horizon of an extreme black hole. We study numerically the nonlinear evolution of this instability for spherically symmetric perturbations of an extreme Reissner–Nordstrom (RN) black hole. We find that generically the endpoint of the instability is a non-extreme RN solution. However, there exist fine-tuned initial perturbations for which the instability never decays. In this case, the perturbed spacetime describes a time-dependent extreme black hole. Such solutions settle down to extreme RN outside, but not on, the event horizon. The event horizon remains smooth but certain observers who cross it at late time experience large gradients there. Our results indicate that these dynamical extreme black holes admit a C 1 extension across an inner (Cauchy) horizon. (paper)
Entropy Maximization as a Basis for Information Recovery in Dynamic Economic Behavioral Systems
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George Judge
2015-02-01
Full Text Available As a basis for information recovery in open dynamic microeconomic systems, we emphasize the connection between adaptive intelligent behavior, causal entropy maximization and self-organized equilibrium seeking behavior. This entropy-based causal adaptive behavior framework permits the use of information-theoretic methods as a solution basis for the resulting pure and stochastic inverse economic-econometric problems. We cast the information recovery problem in the form of a binary network and suggest information-theoretic methods to recover estimates of the unknown binary behavioral parameters without explicitly sampling the configuration-arrangement of the sample space.
International Nuclear Information System (INIS)
Myung, Y.S.
2003-01-01
We calculate corrections to the Bekenstein-Hawking entropy formula for the five-dimensional topological AdS (TAdS)-black holes and topological de Sitter (TdS) spaces due to thermal fluctuations. We can derive all thermal properties of the TdS spaces from those of the TAdS black holes by replacing k by -k. Also we obtain the same correction to the Cardy-Verlinde formula for TAdS and TdS cases including the cosmological horizon of the Schwarzschild-de Sitter (SdS) black hole. Finally we discuss the AdS/CFT and dS/CFT correspondences and their dynamic correspondences
Clausius entropy for arbitrary bifurcate null surfaces
International Nuclear Information System (INIS)
Baccetti, Valentina; Visser, Matt
2014-01-01
Jacobson’s thermodynamic derivation of the Einstein equations was originally applied only to local Rindler horizons. But at least some parts of that construction can usefully be extended to give meaningful results for arbitrary bifurcate null surfaces. As presaged in Jacobson’s original article, this more general construction sharply brings into focus the questions: is entropy objectively ‘real’? Or is entropy in some sense subjective and observer-dependent? These innocent questions open a Pandora’s box of often inconclusive debate. A consensus opinion, though certainly not universally held, seems to be that Clausius entropy (thermodynamic entropy, defined via a Clausius relation dS=đQ/T) should be objectively real, but that the ontological status of statistical entropy (Shannon or von Neumann entropy) is much more ambiguous, and much more likely to be observer-dependent. This question is particularly pressing when it comes to understanding Bekenstein entropy (black hole entropy). To perhaps further add to the confusion, we shall argue that even the Clausius entropy can often be observer-dependent. In the current article we shall conclusively demonstrate that one can meaningfully assign a notion of Clausius entropy to arbitrary bifurcate null surfaces—effectively defining a ‘virtual Clausius entropy’ for arbitrary ‘virtual (local) causal horizons’. As an application, we see that we can implement a version of the generalized second law (GSL) for this virtual Clausius entropy. This version of GSL can be related to certain (nonstandard) integral variants of the null energy condition. Because the concepts involved are rather subtle, we take some effort in being careful and explicit in developing our framework. In future work we will apply this construction to generalize Jacobson’s derivation of the Einstein equations. (paper)
International Nuclear Information System (INIS)
Hudetz, T.
1989-01-01
As a 'by-product' of the Connes-Narnhofer-Thirring theory of dynamical entropy for (originally non-Abelian) nuclear C * -algebras, the well-known variational principle for topological entropy is eqivalently reformulated in purly algebraically defined terms for (separable) Abelian C * -algebras. This 'algebraic variational principle' should not only nicely illustrate the 'feed-back' of methods developed for quantum dynamical systems to the classical theory, but it could also be proved directly by 'algebraic' methods and could thus further simplify the original proof of the variational principle (at least 'in principle'). 23 refs. (Author)
Toward explaining black hole entropy quantization in loop quantum gravity
International Nuclear Information System (INIS)
Sahlmann, Hanno
2007-01-01
In a remarkable numerical analysis of the spectrum of states for a spherically symmetric black hole in loop quantum gravity, Corichi, Diaz-Polo and Fernandez-Borja found that the entropy of the black hole horizon increases in what resembles discrete steps as a function of area. In the present article we reformulate the combinatorial problem of counting horizon states in terms of paths through a certain space. This formulation sheds some light on the origins of this steplike behavior of the entropy. In particular, using a few extra assumptions we arrive at a formula that reproduces the observed step length to a few tenths of a percent accuracy. However, in our reformulation the periodicity ultimately arises as a property of some complicated process, the properties of which, in turn, depend on the properties of the area spectrum in loop quantum gravity in a rather opaque way. Thus, in some sense, a deep explanation of the observed periodicity is still lacking
Generalized Einstein’s Equations from Wald Entropy
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Maulik Parikh
2016-03-01
Full Text Available We derive the gravitational equations of motion of general theories of gravity from thermodynamics applied to a local Rindler horizon through any point in spacetime. Specifically, for a given theory of gravity, we substitute the corresponding Wald entropy into the Clausius relation. Our approach works for all diffeomorphism-invariant theories of gravity in which the Lagrangian is a polynomial in the Riemann tensor.
Entanglement interpretation of black hole entropy in string theory
International Nuclear Information System (INIS)
Brustein, Ram; Einhorn, Martin B.; Yarom, Amos
2006-01-01
We show that the entropy resulting from the counting of microstates of non extremal black holes using field theory duals of string theories can be interpreted as arising from entanglement. The conditions for making such an interpretation consistent are discussed. First, we interpret the entropy (and thermodynamics) of spacetimes with non degenerate, bifurcating Killing horizons as arising from entanglement. We use a path integral method to define the Hartle-Hawking vacuum state in such spacetimes and discuss explicitly its entangled nature and its relation to the geometry. If string theory on such spacetimes has a field theory dual, then, in the low-energy, weak coupling limit, the field theory state that is dual to the Hartle-Hawking state is a thermofield double state. This allows the comparison of the entanglement entropy with the entropy of the field theory dual, and thus, with the Bekenstein-Hawking entropy of the black hole. As an example, we discuss in detail the case of the five dimensional anti-de Sitter, black hole spacetime
Renormalized thermodynamic entropy of black holes in higher dimensions
International Nuclear Information System (INIS)
Kim, S.P.; Kim, S.K.; Soh, K.; Yee, J.H.
1997-01-01
We study the ultraviolet divergent structures of the matter (scalar) field in a higher D-dimensional Reissner-Nordstroem black hole and compute the matter field contribution to the Bekenstein-Hawking entropy by using the Pauli-Villars regularization method. We find that the matter field contribution to the black hole entropy does not, in general, yield the correct renormalization of the gravitational coupling constants. In particular, we show that the matter field contribution in odd dimensions does not give the term proportional to the area of the black hole event horizon. copyright 1997 The American Physical Society
Thermodynamic interpretation of the field equation of BTZ charged black hole near the horizon
International Nuclear Information System (INIS)
Larranaga, A.
2008-01-01
As is already known, a spacetime horizon acts like a boundary of a thermal system and we can associate with it notions such as temperature and entropy. Following the work of M. Akbar, in this paper we will show how it is possible to interpret the field equation of a charged BTZ black hole near the horizon as a thermodynamic identity dE=TdS+P r dA+ΦdQ$, where Φ is the electric potential and $Q$ is the electric charge of a BTZ black hole. These results indicate that the field equations for the charged BTZ black hole possess intrinsic thermodynamic properties near the horizon.
Numerical calculation of the entanglement entropy for scalar field in dilaton spacetimes
Huang, Shifeng; Fang, Xiongjun; Jing, Jiliang
2018-06-01
Using coupled harmonic oscillators model, we numerical analyze the entanglement entropy of massless scalar field in Gafinkle-Horowitz-Strominger (GHS) dilaton spacetime and Gibbons-Maeda (GM) dilaton spacetime. By numerical fitting, we find that the entanglement entropy of the dilaton black holes receive contribution from dilaton charge and is proportional to the area of the event horizon. It is interesting to note that the results of numerical fitting are coincide with ones obtained by using brick wall method and Euclidean path integral approach.
Entropy in molecular recognition by proteins.
Caro, José A; Harpole, Kyle W; Kasinath, Vignesh; Lim, Jackwee; Granja, Jeffrey; Valentine, Kathleen G; Sharp, Kim A; Wand, A Joshua
2017-06-20
Molecular recognition by proteins is fundamental to molecular biology. Dissection of the thermodynamic energy terms governing protein-ligand interactions has proven difficult, with determination of entropic contributions being particularly elusive. NMR relaxation measurements have suggested that changes in protein conformational entropy can be quantitatively obtained through a dynamical proxy, but the generality of this relationship has not been shown. Twenty-eight protein-ligand complexes are used to show a quantitative relationship between measures of fast side-chain motion and the underlying conformational entropy. We find that the contribution of conformational entropy can range from favorable to unfavorable, which demonstrates the potential of this thermodynamic variable to modulate protein-ligand interactions. For about one-quarter of these complexes, the absence of conformational entropy would render the resulting affinity biologically meaningless. The dynamical proxy for conformational entropy or "entropy meter" also allows for refinement of the contributions of solvent entropy and the loss in rotational-translational entropy accompanying formation of high-affinity complexes. Furthermore, structure-based application of the approach can also provide insight into long-lived specific water-protein interactions that escape the generic treatments of solvent entropy based simply on changes in accessible surface area. These results provide a comprehensive and unified view of the general role of entropy in high-affinity molecular recognition by proteins.
Black Hole Entropy from Indistinguishable Quantum Geometric Excitations
Directory of Open Access Journals (Sweden)
Abhishek Majhi
2016-01-01
Full Text Available In loop quantum gravity the quantum geometry of a black hole horizon consists of discrete nonperturbative quantum geometric excitations (or punctures labeled by spins, which are responsible for the quantum area of the horizon. If these punctures are compared to a gas of particles, then the spins associated with the punctures can be viewed as single puncture area levels analogous to single particle energy levels. Consequently, if we assume these punctures to be indistinguishable, the microstate count for the horizon resembles that of Bose-Einstein counting formula for gas of particles. For the Bekenstein-Hawking area law to follow from the entropy calculation in the large area limit, the Barbero-Immirzi parameter (γ approximately takes a constant value. As a by-product, we are able to speculate the state counting formula for the SU(2 quantum Chern-Simons theory coupled to indistinguishable sources in the weak coupling limit.
Simple regular black hole with logarithmic entropy correction
Energy Technology Data Exchange (ETDEWEB)
Morales-Duran, Nicolas; Vargas, Andres F.; Hoyos-Restrepo, Paulina; Bargueno, Pedro [Universidad de los Andes, Departamento de Fisica, Bogota, Distrito Capital (Colombia)
2016-10-15
A simple regular black hole solution satisfying the weak energy condition is obtained within Einstein-non-linear electrodynamics theory. We have computed the thermodynamic properties of this black hole by a careful analysis of the horizons and we have found that the usual Bekenstein-Hawking entropy gets corrected by a logarithmic term. Therefore, in this sense our model realises some quantum gravity predictions which add this kind of correction to the black hole entropy. In particular, we have established some similitudes between our model and a quadratic generalised uncertainty principle. This similitude has been confirmed by the existence of a remnant, which prevents complete evaporation, in agreement with the quadratic generalised uncertainty principle case. (orig.)
Directory of Open Access Journals (Sweden)
Beretta, Gian Paolo
2008-02-01
Full Text Available What is the physical significance of entropy? What is the physical origin of irreversibility? Do entropy and irreversibility exist only for complex and macroscopic systems? Most physicists still accept and teach that the rationalization of these fundamental questions is given by Statistical Mechanics. Indeed, for everyday laboratory physics, the mathematical formalism of Statistical Mechanics (canonical and grand-canonical, Boltzmann, Bose-Einstein and Fermi-Dirac distributions allows a successful description of the thermodynamic equilibrium properties of matter, including entropy values. However, as already recognized by Schrodinger in 1936, Statistical Mechanics is impaired by conceptual ambiguities and logical inconsistencies, both in its explanation of the meaning of entropy and in its implications on the concept of state of a system. An alternative theory has been developed by Gyftopoulos, Hatsopoulos and the present author to eliminate these stumbling conceptual blocks while maintaining the mathematical formalism so successful in applications. To resolve both the problem of the meaning of entropy and that of the origin of irreversibility we have built entropy and irreversibility into the laws of microscopic physics. The result is a theory, that we call Quantum Thermodynamics, that has all the necessary features to combine Mechanics and Thermodynamics uniting all the successful results of both theories, eliminating the logical inconsistencies of Statistical Mechanics and the paradoxes on irreversibility, and providing an entirely new perspective on the microscopic origin of irreversibility, nonlinearity (therefore including chaotic behavior and maximal-entropy-generation nonequilibrium dynamics. In this paper we discuss the background and formalism of Quantum Thermodynamics including its nonlinear equation of motion and the main general results. Our objective is to show in a not-too-technical manner that this theory provides indeed a
Area density of localization-entropy I: the case of wedge-localization
International Nuclear Information System (INIS)
Schroer, Bert
2006-04-01
Using an appropriately formulated holographic light front projection, we derive an area law for the localization-entropy caused by vacuum polarization on the horizon of a wedge region. Its area density has a simple kinematic relation to the heat bath entropy of the light front algebra. Apart from a change of parametrization the infinite light like length contribution to the light front volume factor corresponds to the short-distance divergence of the area density of the localization entropy. This correspondence is a consequence of the conformal invariance of the light front holography combined with the well-known fact that in conformality relates short to long distances. In the explicit calculation of the strength factor we use the temperature duality relation of rational chiral theories whose derivation will be briefly reviewed. We comment on the potential relevance for the understanding of Black hole entropy. (author)
Entropy Evolution and Uncertainty Estimation with Dynamical Systems
Directory of Open Access Journals (Sweden)
X. San Liang
2014-06-01
Full Text Available This paper presents a comprehensive introduction and systematic derivation of the evolutionary equations for absolute entropy H and relative entropy D, some of which exist sporadically in the literature in different forms under different subjects, within the framework of dynamical systems. In general, both H and D are dissipated, and the dissipation bears a form reminiscent of the Fisher information; in the absence of stochasticity, dH/dt is connected to the rate of phase space expansion, and D stays invariant, i.e., the separation of two probability density functions is always conserved. These formulas are validated with linear systems, and put to application with the Lorenz system and a large-dimensional stochastic quasi-geostrophic flow problem. In the Lorenz case, H falls at a constant rate with time, implying that H will eventually become negative, a situation beyond the capability of the commonly used computational technique like coarse-graining and bin counting. For the stochastic flow problem, it is first reduced to a computationally tractable low-dimensional system, using a reduced model approach, and then handled through ensemble prediction. Both the Lorenz system and the stochastic flow system are examples of self-organization in the light of uncertainty reduction. The latter particularly shows that, sometimes stochasticity may actually enhance the self-organization process.
Nonlinear optics of fibre event horizons.
Webb, Karen E; Erkintalo, Miro; Xu, Yiqing; Broderick, Neil G R; Dudley, John M; Genty, Goëry; Murdoch, Stuart G
2014-09-17
The nonlinear interaction of light in an optical fibre can mimic the physics at an event horizon. This analogue arises when a weak probe wave is unable to pass through an intense soliton, despite propagating at a different velocity. To date, these dynamics have been described in the time domain in terms of a soliton-induced refractive index barrier that modifies the velocity of the probe. Here we complete the physical description of fibre-optic event horizons by presenting a full frequency-domain description in terms of cascaded four-wave mixing between discrete single-frequency fields, and experimentally demonstrate signature frequency shifts using continuous wave lasers. Our description is confirmed by the remarkable agreement with experiments performed in the continuum limit, reached using ultrafast lasers. We anticipate that clarifying the description of fibre event horizons will significantly impact on the description of horizon dynamics and soliton interactions in photonics and other systems.
Dynamical glucometry: Use of multiscale entropy analysis in diabetes
Costa, Madalena D.; Henriques, Teresa; Munshi, Medha N.; Segal, Alissa R.; Goldberger, Ary L.
2014-09-01
Diabetes mellitus (DM) is one of the world's most prevalent medical conditions. Contemporary management focuses on lowering mean blood glucose values toward a normal range, but largely ignores the dynamics of glucose fluctuations. We probed analyte time series obtained from continuous glucose monitor (CGM) sensors. We show that the fluctuations in CGM values sampled every 5 min are not uncorrelated noise. Next, using multiscale entropy analysis, we quantified the complexity of the temporal structure of the CGM time series from a group of elderly subjects with type 2 DM and age-matched controls. We further probed the structure of these CGM time series using detrended fluctuation analysis. Our findings indicate that the dynamics of glucose fluctuations from control subjects are more complex than those of subjects with type 2 DM over time scales ranging from about 5 min to 5 h. These findings support consideration of a new framework, dynamical glucometry, to guide mechanistic research and to help assess and compare therapeutic interventions, which should enhance complexity of glucose fluctuations and not just lower mean and variance of blood glucose levels.
Black brane entropy and hydrodynamics
Booth, I.; Heller, M.P.; Spaliński, M.
2010-01-01
A generalization of entropy to near-equilibrium phenomena is provided by the notion of a hydrodynamic entropy current. Recent advances in holography have lead to the formulation of fluid-gravity duality, a remarkable connection between the hydrodynamics of certain strongly coupled media and dynamics
Black brane entropy and hydrodynamics
Booth, I.; Heller, M.P.; Spaliński, M.
2011-01-01
A generalization of entropy to near-equilibrium phenomena is provided by the notion of a hydrodynamic entropy current. Recent advances in holography have lead to the formulation of fluid-gravity duality, a remarkable connection between the hydrodynamics of certain strongly coupled media and dynamics
Balasis, G.; Daglis, I. A.; Papadimitriou, C.; Kalimeri, M.; Anastasiadis, A.; Eftaxias, K.
2008-12-01
Dynamical complexity detection for output time series of complex systems is one of the foremost problems in physics, biology, engineering, and economic sciences. Especially in magnetospheric physics, accurate detection of the dissimilarity between normal and abnormal states (e.g. pre-storm activity and magnetic storms) can vastly improve space weather diagnosis and, consequently, the mitigation of space weather hazards. Herein, we examine the fractal spectral properties of the Dst data using a wavelet analysis technique. We show that distinct changes in associated scaling parameters occur (i.e., transition from anti- persistent to persistent behavior) as an intense magnetic storm approaches. We then analyze Dst time series by introducing the non-extensive Tsallis entropy, Sq, as an appropriate complexity measure. The Tsallis entropy sensitively shows the complexity dissimilarity among different "physiological" (normal) and "pathological" states (intense magnetic storms). The Tsallis entropy implies the emergence of two distinct patterns: (i) a pattern associated with the intense magnetic storms, which is characterized by a higher degree of organization, and (ii) a pattern associated with normal periods, which is characterized by a lower degree of organization.
High-Order Entropy Stable Formulations for Computational Fluid Dynamics
Carpenter, Mark H.; Fisher, Travis C.
2013-01-01
A systematic approach is presented for developing entropy stable (SS) formulations of any order for the Navier-Stokes equations. These SS formulations discretely conserve mass, momentum, energy and satisfy a mathematical entropy inequality. They are valid for smooth as well as discontinuous flows provided sufficient dissipation is added at shocks and discontinuities. Entropy stable formulations exist for all diagonal norm, summation-by-parts (SBP) operators, including all centered finite-difference operators, Legendre collocation finite-element operators, and certain finite-volume operators. Examples are presented using various entropy stable formulations that demonstrate the current state-of-the-art of these schemes.
Entropy for gravitational Chern-Simons terms by squashed cone method
International Nuclear Information System (INIS)
Guo, Wu-Zhong; Miao, Rong-Xin
2016-01-01
In this paper we investigate the entropy of gravitational Chern-Simons terms for the horizon with non-vanishing extrinsic curvatures, or the holographic entanglement entropy for arbitrary entangling surface. In 3D there is no anomaly of entropy. But the original squashed cone method can not be used directly to get the correct result. For higher dimensions the anomaly of entropy would appear, still, we can not use the squashed cone method directly. That is becasuse the Chern-Simons action is not gauge invariant. To get a reasonable result we suggest two methods. One is by adding a boundary term to recover the gauge invariance. This boundary term can be derived from the variation of the Chern-Simons action. The other one is by using the Chern-Simons relation dΩ_4_n_−_1=tr(R"2"n). We notice that the entropy of tr(R"2"n) is a total derivative locally, i.e. S=ds_C_S. We propose to identify s_C_S with the entropy of gravitational Chern-Simons terms Ω_4_n_−_1. In the first method we could get the correct result for Wald entropy in arbitrary dimension. In the second approach, in addition to Wald entropy, we can also obtain the anomaly of entropy with non-zero extrinsic curvatures. Our results imply that the entropy of a topological invariant, such as the Pontryagin term tr(R"2"n) and the Euler density, is a topological invariant on the entangling surface.
Watanabe, Shinya
2014-01-01
This chapter presents excavation data from two archaeological sites, El Palacio and Paredones, located in the Department of Cajamarca in the northern sierra of Peru, a geographic area of social dynamism during the Middle Horizon. The presence of the large-scale site of El Palacio — a Wari administrative center — would suggest that the valley came under direct Wari imperial control in a manner similar to that known under the Inca during the Late Horizon. Yet at the same time, there are chullpa...
Generalized second law of thermodynamics for non-canonical scalar field model with corrected-entropy
International Nuclear Information System (INIS)
Das, Sudipta; Mamon, Abdulla Al; Debnath, Ujjal
2015-01-01
In this work, we have considered a non-canonical scalar field dark energy model in the framework of flat FRW background. It has also been assumed that the dark matter sector interacts with the non-canonical dark energy sector through some interaction term. Using the solutions for this interacting non-canonical scalar field dark energy model, we have investigated the validity of generalized second law (GSL) of thermodynamics in various scenarios using first law and area law of thermodynamics. For this purpose, we have assumed two types of horizons viz apparent horizon and event horizon for the universe and using first law of thermodynamics, we have examined the validity of GSL on both apparent and event horizons. Next, we have considered two types of entropy-corrections on apparent and event horizons. Using the modified area law, we have examined the validity of GSL of thermodynamics on apparent and event horizons under some restrictions of model parameters. (orig.)
Dynamic Universe Model Predicts the Trajectory of New Horizons Satellite Going to Pluto.......
Naga Parameswara Gupta, Satyavarapu
2012-07-01
New Horizons is NASA's artificial satellite now going towards to the dwarf planet Pluto. It has crossed Jupiter. It is expected to be the rst spacecraft to go near and study Pluto and its moons, Charon, Nix, and Hydra. These are the predictions for New Horizons (NH) space craft as on A.D. 2009-Aug-09 00:00:00.0000 hrs. The behavior of NH is similar to Pioneer Space craft as NH traveling is alike to Pioneer. NH is supposed to reach Pluto in 2015 AD. There was a gravity assist taken at Jupiter about a year back. As Dynamic universe model explains Pioneer anomaly and the higher gravitational attraction forces experienced towards SUN, It can explain NH also in a similar fashion. I am giving the predictions for NH by Dynamic Universe Model in the following Table 4. Here first two rows give Dynamic Universe Model predictions based on 02-01-2009 00:00 hrs data with Daily time step and hourly time step. Third row gives Ephemeris from Jet propulsion lab.Dynamic Universe Model can predict further to 9-Aug-2009. These Ephemeris data is from their web as on 28th June 2009 Any new data can be calculated..... For finding trajectories of Pioneer satellite (Anomaly), New Horizons satellite going to Pluto, the Calculations of Dynamic Universe model can be successfully applied. No dark matter is assumed within solar system radius. The effect on the masses around SUN shows as though there is extra gravitation pull toward SUN. It solves the Dynamics of Extra-solar planets like Planet X, satellite like Pioneer and NH for 3-Position, 3-velocity 3-acceleration for their masses,considering the complex situation of Multiple planets, Stars, Galaxy parts and Galaxy center and other Galaxies Using simple Newtonian Physics. It already solved problems Missing mass in Galaxies observed by galaxy circular velocity curves successfully. `SITA Simulations' software was developed about 18 years back for Dynamic Universe Model of Cosmology. It is based on Newtonian physics. It is Classical singularity
Gulamsarwar, Syazwani; Salleh, Zabidin
2017-08-01
The purpose of this paper is to generalize the notions of Adler's topological entropy along with their several fundamental properties. A function f : X → Y is said to be R-map if f-1 (V) is regular open in X for every regular open set V in Y. Thus, we initiated a notion of topological nearly entropy for topological R-dynamical systems which is based on nearly compact relative to the space by using R-map.
Variable horizon in a peridynamic medium.
Energy Technology Data Exchange (ETDEWEB)
Silling, Stewart Andrew; Littlewood, David John; Seleson, Pablo
2014-10-01
A notion of material homogeneity is proposed for peridynamic bodies with vari- able horizon but constant bulk properties. A relation is derived that scales the force state according to the position-dependent horizon while keeping the bulk properties un- changed. Using this scaling relation, if the horizon depends on position, artifacts called ghost forces may arise in a body under homogeneous deformation. These artifacts de- pend on the second derivative of horizon and can be reduced by use of a modified equilibrium equation using a new quantity called the partial stress . Bodies with piece- wise constant horizon can be modeled without ghost forces by using a technique called a splice between the regions. As a limiting case of zero horizon, both partial stress and splice techniques can be used to achieve local-nonlocal coupling. Computational examples, including dynamic fracture in a one-dimensional model with local-nonlocal coupling, illustrate the methods.
Vibrational entropies in metallic alloys
Ozolins, Vidvuds; Asta, Mark; Wolverton, Christopher
2000-03-01
Recently, it has been recognized that vibrational entropy can have significant effects on the phase stability of metallic alloys. Using density functional linear response calculations and molecular dynamics simulations we study three representative cases: (i) phase diagram of Al-rich Al-Sc alloys, (ii) stability of precipitate phases in CuAl_2, and (iii) phonon dynamics in bcc Zr. We find large vibrational entropy effects in all cases. In the Al-Sc system, vibrations increase the solid solubility of Sc in Al by decreasing the stability of the L12 (Al_3Sc) phase. This leads to a nearly ten-fold increase in the solid solubility of Sc in Al at T=800 K. In the Cu-Al system, our calculations predict that the tetragonal Laves phase of CuAl2 has 0.35 kB/atom higher vibrational entropy than the cubic CaF_2-type phase (the latter is predicted to be the T=0 K ground state of CuAl_2). This entropy difference causes a structural transformation in CuAl2 precipitates from the fluorite to the tetragonal Laves phase around T=500 K. Finally, we analyze the highly unusual dynamics of anharmonically stabilized bcc Zr, finding large diffuse-scattering intensity streaks between the bcc Bragg peaks.
Valenza, Gaetano; Garcia, Ronald G; Citi, Luca; Scilingo, Enzo P; Tomaz, Carlos A; Barbieri, Riccardo
2015-01-01
Nonlinear digital signal processing methods that address system complexity have provided useful computational tools for helping in the diagnosis and treatment of a wide range of pathologies. More specifically, nonlinear measures have been successful in characterizing patients with mental disorders such as Major Depression (MD). In this study, we propose the use of instantaneous measures of entropy, namely the inhomogeneous point-process approximate entropy (ipApEn) and the inhomogeneous point-process sample entropy (ipSampEn), to describe a novel characterization of MD patients undergoing affective elicitation. Because these measures are built within a nonlinear point-process model, they allow for the assessment of complexity in cardiovascular dynamics at each moment in time. Heartbeat dynamics were characterized from 48 healthy controls and 48 patients with MD while emotionally elicited through either neutral or arousing audiovisual stimuli. Experimental results coming from the arousing tasks show that ipApEn measures are able to instantaneously track heartbeat complexity as well as discern between healthy subjects and MD patients. Conversely, standard heart rate variability (HRV) analysis performed in both time and frequency domains did not show any statistical significance. We conclude that measures of entropy based on nonlinear point-process models might contribute to devising useful computational tools for care in mental health.
Entropy of holographic dark energy and the generalized second law
International Nuclear Information System (INIS)
Praseetha, P; Mathew, Titus K
2014-01-01
In this paper we have considered holographic dark energy and studied its cosmology and thermodynamics. We have analyzed the generalized second law (GSL) of thermodynamics in a flat universe consisting of interacting dark energy and dark matter. We performed the analysis under both thermal equilibrium and nonequilibrium conditions. If the apparent horizon is taken as the boundary of the universe, we have shown that the rate of change of the total entropy of the universe is proportional to (1+q) 2 , which in fact shows that the GSL is valid at the apparent horizon, irrespective of the sign of the deceleration parameter, q. Hence, for any form of dark energy, the apparent horizon can be considered as a perfect thermodynamic boundary of the universe. We confirmed this conclusion by using the holographic dark energy model. When the event horizon is taken as the boundary, we found that the GSL is only partially satisfied. The analysis under nonequilibrium conditions revealed that the GSL is satisfied if the temperature of the dark energy is greater than the temperature of the dark matter. (paper)
Towse, Clare-Louise; Akke, Mikael; Daggett, Valerie
2017-04-27
Molecular dynamics (MD) simulations contain considerable information with regard to the motions and fluctuations of a protein, the magnitude of which can be used to estimate conformational entropy. Here we survey conformational entropy across protein fold space using the Dynameomics database, which represents the largest existing data set of protein MD simulations for representatives of essentially all known protein folds. We provide an overview of MD-derived entropies accounting for all possible degrees of dihedral freedom on an unprecedented scale. Although different side chains might be expected to impose varying restrictions on the conformational space that the backbone can sample, we found that the backbone entropy and side chain size are not strictly coupled. An outcome of these analyses is the Dynameomics Entropy Dictionary, the contents of which have been compared with entropies derived by other theoretical approaches and experiment. As might be expected, the conformational entropies scale linearly with the number of residues, demonstrating that conformational entropy is an extensive property of proteins. The calculated conformational entropies of folding agree well with previous estimates. Detailed analysis of specific cases identifies deviations in conformational entropy from the average values that highlight how conformational entropy varies with sequence, secondary structure, and tertiary fold. Notably, α-helices have lower entropy on average than do β-sheets, and both are lower than coil regions.
Information-theoretical aspects of quantum-mechanical entropy
International Nuclear Information System (INIS)
Wehrl, A.
1990-01-01
Properties of the quantum ( = von Neumann) entropy S(ρ) -k Trρ lnρ, ρ being a compact operator, are proved first, and differences against the classical case, e.g. the Shannon entropy, are worked out. The main result is on the strong subadditivity of this quantum entropy. Then another entropy, a function not of the state but of the dynamics of the system, is considered as a quantum analogue of the classical Kolmogorov-Sinai-entropy. An attempt in defining such a quantity had only recently sucess in a paper of Connes, Narnhofer and Thirring. A definition of this entropy is given. 34 refs
Dynamics of non-stationary processes that follow the maximum of the Rényi entropy principle.
Shalymov, Dmitry S; Fradkov, Alexander L
2016-01-01
We propose dynamics equations which describe the behaviour of non-stationary processes that follow the maximum Rényi entropy principle. The equations are derived on the basis of the speed-gradient principle originated in the control theory. The maximum of the Rényi entropy principle is analysed for discrete and continuous cases, and both a discrete random variable and probability density function (PDF) are used. We consider mass conservation and energy conservation constraints and demonstrate the uniqueness of the limit distribution and asymptotic convergence of the PDF for both cases. The coincidence of the limit distribution of the proposed equations with the Rényi distribution is examined.
Non-analyticity of holographic Rényi entropy in Lovelock gravity
Puletti, V. Giangreco M.; Pourhasan, Razieh
2017-08-01
We compute holographic Rényi entropies for spherical entangling surfaces on the boundary while considering third order Lovelock gravity with negative cosmological constant in the bulk. Our study shows that third order Lovelock black holes with hyperbolic event horizon are unstable, and at low temperatures those with smaller mass are favoured, giving rise to first order phase transitions in the bulk. We determine regions in the Lovelock parameter space in arbitrary dimensions, where bulk phase transitions happen and where boundary causality constraints are met. We show that each of these points corresponds to a dual boundary conformal field theory whose Rényi entropy exhibits a kink at a certain critical index n.
Dynamics of Entropy in Quantum-like Model of Decision Making
Basieva, Irina; Khrennikov, Andrei; Asano, Masanari; Ohya, Masanori; Tanaka, Yoshiharu
2011-03-01
We present a quantum-like model of decision making in games of the Prisoner's Dilemma type. By this model the brain processes information by using representation of mental states in complex Hilbert space. Driven by the master equation the mental state of a player, say Alice, approaches an equilibrium point in the space of density matrices. By using this equilibrium point Alice determines her mixed (i.e., probabilistic) strategy with respect to Bob. Thus our model is a model of thinking through decoherence of initially pure mental state. Decoherence is induced by interaction with memory and external environment. In this paper we study (numerically) dynamics of quantum entropy of Alice's state in the process of decision making. Our analysis demonstrates that this dynamics depends nontrivially on the initial state of Alice's mind on her own actions and her prediction state (for possible actions of Bob.)
Configurational entropy of glueball states
Energy Technology Data Exchange (ETDEWEB)
Bernardini, Alex E., E-mail: alexeb@ufscar.br [Departamento de Física, Universidade Federal de São Carlos, PO Box 676, 13565-905, São Carlos, SP (Brazil); Braga, Nelson R.F., E-mail: braga@if.ufrj.br [Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, RJ 21941-972 (Brazil); Rocha, Roldão da, E-mail: roldao.rocha@ufabc.edu.br [CMCC, Universidade Federal do ABC, UFABC, 09210-580, Santo André (Brazil)
2017-02-10
The configurational entropy of glueball states is calculated using a holographic description. Glueball states are represented by a supergravity dual picture, consisting of a 5-dimensional graviton–dilaton action of a dynamical holographic AdS/QCD model. The configurational entropy is studied as a function of the glueball spin and of the mass, providing information about the stability of the glueball states.
Dualities in D=5, N=2 supergravity, black hole entropy, and AdS central charges
International Nuclear Information System (INIS)
Klemm, D.
2001-01-01
The issue of microstate counting for general black holes in D=5, N=2 supergravity coupled to vector multiplets is discussed from various viewpoints. The statistical entropy is computed for the near-extremal case by using the central charge appearing in the asymptotic symmetry algebra of AdS 2 . Furthermore, we show that the considered supergravity theory enjoys a duality invariance which connects electrically charged black holes and magnetically charged black strings. The near-horizon geometry of the latter turns out to be AdS 3 x S 2 , which allows a microscopic calculation of their entropy using the Brown-Hennaux central charges in Cardy's formula. In both approaches we find perfect agreement between statistical and thermodynamical entropy. (orig.)
Takahashi, Osamu; Nomura, Tetsuo; Tabayashi, Kiyohiko; Yamasaki, Katsuyoshi
2008-07-01
We performed spectral analysis by using the maximum entropy method instead of the traditional Fourier transform technique to investigate the short-time behavior in molecular systems, such as the energy transfer between vibrational modes and chemical reactions. This procedure was applied to direct ab initio molecular dynamics calculations for the decomposition of formic acid. More reactive trajectories of dehydrolation than those of decarboxylation were obtained for Z-formic acid, which was consistent with the prediction of previous theoretical and experimental studies. Short-time maximum entropy method analyses were performed for typical reactive and non-reactive trajectories. Spectrograms of a reactive trajectory were obtained; these clearly showed the reactant, transient, and product regions, especially for the dehydrolation path.
Ehrenfest's Lottery--Time and Entropy Maximization
Ashbaugh, Henry S.
2010-01-01
Successful teaching of the Second Law of Thermodynamics suffers from limited simple examples linking equilibrium to entropy maximization. I describe a thought experiment connecting entropy to a lottery that mixes marbles amongst a collection of urns. This mixing obeys diffusion-like dynamics. Equilibrium is achieved when the marble distribution is…
Topological entropy of continuous functions on topological spaces
International Nuclear Information System (INIS)
Liu Lei; Wang Yangeng; Wei Guo
2009-01-01
Adler, Konheim and McAndrew introduced the concept of topological entropy of a continuous mapping for compact dynamical systems. Bowen generalized the concept to non-compact metric spaces, but Walters indicated that Bowen's entropy is metric-dependent. We propose a new definition of topological entropy for continuous mappings on arbitrary topological spaces (compactness, metrizability, even axioms of separation not necessarily required), investigate fundamental properties of the new entropy, and compare the new entropy with the existing ones. The defined entropy generates that of Adler, Konheim and McAndrew and is metric-independent for metrizable spaces. Yet, it holds various basic properties of Adler, Konheim and McAndrew's entropy, e.g., the entropy of a subsystem is bounded by that of the original system, topologically conjugated systems have a same entropy, the entropy of the induced hyperspace system is larger than or equal to that of the original system, and in particular this new entropy coincides with Adler, Konheim and McAndrew's entropy for compact systems
Shannon versus Kullback-Leibler entropies in nonequilibrium random motion
International Nuclear Information System (INIS)
Garbaczewski, Piotr
2005-01-01
We analyze dynamical properties of the Shannon information entropy of a continuous probability distribution, which is driven by a standard diffusion process. This entropy choice is confronted with another option, employing the conditional Kullback-Leibler entropy. Both entropies discriminate among various probability distributions, either statically or in the time domain. An asymptotic approach towards equilibrium is typically monotonic in terms of the Kullback entropy. The Shannon entropy time rate needs not to be positive and is a sensitive indicator of the power transfer processes (removal/supply) due to an active environment. In the case of Smoluchowski diffusions, the Kullback entropy time rate coincides with the Shannon entropy 'production' rate
Microscopic insights into the NMR relaxation based protein conformational entropy meter
Kasinath, Vignesh; Sharp, Kim A.; Wand, A. Joshua
2013-01-01
Conformational entropy is a potentially important thermodynamic parameter contributing to protein function. Quantitative measures of conformational entropy are necessary for an understanding of its role but have been difficult to obtain. An empirical method that utilizes changes in conformational dynamics as a proxy for changes in conformational entropy has recently been introduced. Here we probe the microscopic origins of the link between conformational dynamics and conformational entropy using molecular dynamics simulations. Simulation of seven pro! teins gave an excellent correlation with measures of side-chain motion derived from NMR relaxation. The simulations show that the motion of methyl-bearing side-chains are sufficiently coupled to that of other side chains to serve as excellent reporters of the overall side-chain conformational entropy. These results tend to validate the use of experimentally accessible measures of methyl motion - the NMR-derived generalized order parameters - as a proxy from which to derive changes in protein conformational entropy. PMID:24007504
Dissecting Protein Configurational Entropy into Conformational and Vibrational Contributions.
Chong, Song-Ho; Ham, Sihyun
2015-10-01
Quantifying how the rugged nature of the underlying free-energy landscape determines the entropic cost a protein must incur upon folding and ligand binding is a challenging problem. Here, we present a novel computational approach that dissects the protein configurational entropy on the basis of the classification of protein dynamics on the landscape into two separate components: short-term vibrational dynamics related to individual free-energy wells and long-term conformational dynamics associated with transitions between wells. We apply this method to separate the configurational entropy of the protein villin headpiece subdomain into its conformational and vibrational components. We find that the change in configurational entropy upon folding is dominated by the conformational entropy despite the fact that the magnitude of the vibrational entropy is the significantly larger component in each of the folded and unfolded states, which is in accord with the previous empirical estimations. The straightforward applicability of our method to unfolded proteins promises a wide range of applications, including those related to intrinsically disordered proteins.
Nonlinear symmetries of black hole entropy in gauged supergravity
Energy Technology Data Exchange (ETDEWEB)
Klemm, Dietmar [Dipartimento di Fisica, Università di Milano,and INFN, Sezione di Milano,Via Celoria 16, I-20133 Milano (Italy); Marrani, Alessio [Museo Storico della Fisica e Centro Studi e Ricerche ‘Enrico Fermi’,Via Panisperna 89A, I-00184 Roma (Italy); Dipartimento di Fisica e Astronomia ‘Galileo Galilei’, Università di Padova,and INFN, Sezione di Padova,Via Marzolo 8, I-35131 Padova (Italy); Petri, Nicolò; Rabbiosi, Marco [Dipartimento di Fisica, Università di Milano,and INFN, Sezione di Milano,Via Celoria 16, I-20133 Milano (Italy)
2017-04-04
Freudenthal duality in N=2, D=4 ungauged supergravity is generated by an anti-involutive operator that acts on the electromagnetic fluxes, and results to be a symmetry of the Bekenstein-Hawking entropy. We show that, with a suitable extension, this duality can be generalized to the abelian gauged case as well, even in presence of hypermultiplets. By defining Freudenthal duality along the scalar flow, one can prove that two configurations of charges and gaugings linked by the Freudenthal operator share the same set of values of the scalar fields at the black hole horizon. Consequently, Freudenthal duality is promoted to a nonlinear symmetry of the black hole entropy. We explicitly show this invariance for the model with prepotential F=−iX{sup 0}X{sup 1} and Fayet-Iliopoulos gauging.
Entropy of self-gravitating radiation
International Nuclear Information System (INIS)
Sorkin, R.D.; Wald, R.M.; Jiu, Z.Z.
1981-01-01
The entropy of self-gravitating radiation confined to a spherical box of radius R is examined in the context of general relativity. It is expected that configurations (i.e., initial data) which extremize total entropy will be spherically symmetric, time symmetric distributions of radiation in local thermodynamic equilibrium. Assuming this is the case, it is proved that extrema of S coincide precisely with static equilibrium configurations of the radiation fluid. Furthermore, dynamically stable equilibrium configurations are shown to coincide with local maxima of S. The equilibrium configurations and their entropies are calculated and their properties are discussed. However, it is shown that entropies higher than these local extrema can be achieved and, indeed, arbitrarily high entropies can be attained by configurations inside of or outside but arbitrarily near their own Schwarzschild radius. However, consideration is limited to configurations which are outside their own Schwarzschild radius by at least one radiation wavelength, then the entropy is bounded and it is found Ssub(max) < is approximately equal to MR, where M is the total mass. This supports the validity for self-gravitating systems of the Bekenstein upper limit on the entropy to energy ratio of material bodies. (author)
Maximum entropy production rate in quantum thermodynamics
Energy Technology Data Exchange (ETDEWEB)
Beretta, Gian Paolo, E-mail: beretta@ing.unibs.i [Universita di Brescia, via Branze 38, 25123 Brescia (Italy)
2010-06-01
In the framework of the recent quest for well-behaved nonlinear extensions of the traditional Schroedinger-von Neumann unitary dynamics that could provide fundamental explanations of recent experimental evidence of loss of quantum coherence at the microscopic level, a recent paper [Gheorghiu-Svirschevski 2001 Phys. Rev. A 63 054102] reproposes the nonlinear equation of motion proposed by the present author [see Beretta G P 1987 Found. Phys. 17 365 and references therein] for quantum (thermo)dynamics of a single isolated indivisible constituent system, such as a single particle, qubit, qudit, spin or atomic system, or a Bose-Einstein or Fermi-Dirac field. As already proved, such nonlinear dynamics entails a fundamental unifying microscopic proof and extension of Onsager's reciprocity and Callen's fluctuation-dissipation relations to all nonequilibrium states, close and far from thermodynamic equilibrium. In this paper we propose a brief but self-contained review of the main results already proved, including the explicit geometrical construction of the equation of motion from the steepest-entropy-ascent ansatz and its exact mathematical and conceptual equivalence with the maximal-entropy-generation variational-principle formulation presented in Gheorghiu-Svirschevski S 2001 Phys. Rev. A 63 022105. Moreover, we show how it can be extended to the case of a composite system to obtain the general form of the equation of motion, consistent with the demanding requirements of strong separability and of compatibility with general thermodynamics principles. The irreversible term in the equation of motion describes the spontaneous attraction of the state operator in the direction of steepest entropy ascent, thus implementing the maximum entropy production principle in quantum theory. The time rate at which the path of steepest entropy ascent is followed has so far been left unspecified. As a step towards the identification of such rate, here we propose a possible
Using heteroclinic orbits to quantify topological entropy in fluid flows
International Nuclear Information System (INIS)
Sattari, Sulimon; Chen, Qianting; Mitchell, Kevin A.
2016-01-01
Topological approaches to mixing are important tools to understand chaotic fluid flows, ranging from oceanic transport to the design of micro-mixers. Typically, topological entropy, the exponential growth rate of material lines, is used to quantify topological mixing. Computing topological entropy from the direct stretching rate is computationally expensive and sheds little light on the source of the mixing. Earlier approaches emphasized that topological entropy could be viewed as generated by the braiding of virtual, or “ghost,” rods stirring the fluid in a periodic manner. Here, we demonstrate that topological entropy can also be viewed as generated by the braiding of ghost rods following heteroclinic orbits instead. We use the machinery of homotopic lobe dynamics, which extracts symbolic dynamics from finite-length pieces of stable and unstable manifolds attached to fixed points of the fluid flow. As an example, we focus on the topological entropy of a bounded, chaotic, two-dimensional, double-vortex cavity flow. Over a certain parameter range, the topological entropy is primarily due to the braiding of a period-three orbit. However, this orbit does not explain the topological entropy for parameter values where it does not exist, nor does it explain the excess of topological entropy for the entire range of its existence. We show that braiding by heteroclinic orbits provides an accurate computation of topological entropy when the period-three orbit does not exist, and that it provides an explanation for some of the excess topological entropy when the period-three orbit does exist. Furthermore, the computation of symbolic dynamics using heteroclinic orbits has been automated and can be used to compute topological entropy for a general 2D fluid flow.
Characterizing time series via complexity-entropy curves
Ribeiro, Haroldo V.; Jauregui, Max; Zunino, Luciano; Lenzi, Ervin K.
2017-06-01
The search for patterns in time series is a very common task when dealing with complex systems. This is usually accomplished by employing a complexity measure such as entropies and fractal dimensions. However, such measures usually only capture a single aspect of the system dynamics. Here, we propose a family of complexity measures for time series based on a generalization of the complexity-entropy causality plane. By replacing the Shannon entropy by a monoparametric entropy (Tsallis q entropy) and after considering the proper generalization of the statistical complexity (q complexity), we build up a parametric curve (the q -complexity-entropy curve) that is used for characterizing and classifying time series. Based on simple exact results and numerical simulations of stochastic processes, we show that these curves can distinguish among different long-range, short-range, and oscillating correlated behaviors. Also, we verify that simulated chaotic and stochastic time series can be distinguished based on whether these curves are open or closed. We further test this technique in experimental scenarios related to chaotic laser intensity, stock price, sunspot, and geomagnetic dynamics, confirming its usefulness. Finally, we prove that these curves enhance the automatic classification of time series with long-range correlations and interbeat intervals of healthy subjects and patients with heart disease.
System Entropy Measurement of Stochastic Partial Differential Systems
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Bor-Sen Chen
2016-03-01
Full Text Available System entropy describes the dispersal of a system’s energy and is an indication of the disorder of a physical system. Several system entropy measurement methods have been developed for dynamic systems. However, most real physical systems are always modeled using stochastic partial differential dynamic equations in the spatio-temporal domain. No efficient method currently exists that can calculate the system entropy of stochastic partial differential systems (SPDSs in consideration of the effects of intrinsic random fluctuation and compartment diffusion. In this study, a novel indirect measurement method is proposed for calculating of system entropy of SPDSs using a Hamilton–Jacobi integral inequality (HJII-constrained optimization method. In other words, we solve a nonlinear HJII-constrained optimization problem for measuring the system entropy of nonlinear stochastic partial differential systems (NSPDSs. To simplify the system entropy measurement of NSPDSs, the global linearization technique and finite difference scheme were employed to approximate the nonlinear stochastic spatial state space system. This allows the nonlinear HJII-constrained optimization problem for the system entropy measurement to be transformed to an equivalent linear matrix inequalities (LMIs-constrained optimization problem, which can be easily solved using the MATLAB LMI-toolbox (MATLAB R2014a, version 8.3. Finally, several examples are presented to illustrate the system entropy measurement of SPDSs.
Entropy Stable Summation-by-Parts Formulations for Compressible Computational Fluid Dynamics
Carpenter, M.H.
2016-11-09
A systematic approach based on a diagonal-norm summation-by-parts (SBP) framework is presented for implementing entropy stable (SS) formulations of any order for the compressible Navier–Stokes equations (NSE). These SS formulations discretely conserve mass, momentum, energy and satisfy a mathematical entropy equality for smooth problems. They are also valid for discontinuous flows provided sufficient dissipation is added at shocks and discontinuities to satisfy an entropy inequality. Admissible SBP operators include all centred diagonal-norm finite-difference (FD) operators and Legendre spectral collocation-finite element methods (LSC-FEM). Entropy stable multiblock FD and FEM operators follows immediately via nonlinear coupling operators that ensure conservation, accuracy and preserve the interior entropy estimates. Nonlinearly stable solid wall boundary conditions are also available. Existing SBP operators that lack a stability proof (e.g. weighted essentially nonoscillatory) may be combined with an entropy stable operator using a comparison technique to guarantee nonlinear stability of the pair. All capabilities extend naturally to a curvilinear form of the NSE provided that the coordinate mappings satisfy a geometric conservation law constraint. Examples are presented that demonstrate the robustness of current state-of-the-art entropy stable SBP formulations.
Receding Horizon H∞ Control for Input-Delayed Systems
Directory of Open Access Journals (Sweden)
Han Woong Yoo
2012-01-01
Full Text Available We propose the receding horizon H∞ control (RHHC for input-delayed systems. A new cost function for a finite horizon dynamic game problem is first introduced, which includes two terminal weighting terms parameterized by a positive definite matrix, called a terminal weighing matrix. Secondly, the RHHC is obtained from the solution to the finite dynamic game problem. Thirdly, we propose an LMI condition under which the saddle point value satisfies the nonincreasing monotonicity. Finally, we show the asymptotic stability and H∞ boundedness of the closed-loop system controlled by the proposed RHHC. The proposed RHHC has a guaranteed H∞ performance bound for nonzero external disturbances and the quadratic cost can be improved by adjusting the prediction horizon length for nonzero initial condition and zero disturbance, which is not the case for existing memoryless state-feedback controllers. It is shown through a numerical example that the proposed RHHC is stabilizing and satisfies the infinite horizon H∞ performance bound. Furthermore, the performance in terms of the quadratic cost is shown to be improved by adjusting the prediction horizon length when there exists no external disturbance with nonzero initial condition.
Microscopic entropy and nonlocality
International Nuclear Information System (INIS)
Karpov, E.; Ordonets, G.; Petroskij, T.; Prigozhin, I.
2003-01-01
We have obtained a microscopic expression for entropy in terms of H function based on nonunitary Λ transformation which leads from the time evolution as a unitary group to a Markovian dynamics and unifies the reversible and irreversible aspects of quantum mechanics. This requires a new representation outside the Hilbert space. In terms of H, we show the entropy production and the entropy flow during the emission and absorption of radiation by an atom. Analyzing the time inversion experiment, we emphasize the importance of pre- and postcollisional correlations, which break the symmetry between incoming and outgoing waves. We consider the angle dependence of the H function in a three-dimensional situation. A model including virtual transitions is discussed in a subsequent paper
Prediction of Protein Configurational Entropy (Popcoen).
Goethe, Martin; Gleixner, Jan; Fita, Ignacio; Rubi, J Miguel
2018-03-13
A knowledge-based method for configurational entropy prediction of proteins is presented; this methodology is extremely fast, compared to previous approaches, because it does not involve any type of configurational sampling. Instead, the configurational entropy of a query fold is estimated by evaluating an artificial neural network, which was trained on molecular-dynamics simulations of ∼1000 proteins. The predicted entropy can be incorporated into a large class of protein software based on cost-function minimization/evaluation, in which configurational entropy is currently neglected for performance reasons. Software of this type is used for all major protein tasks such as structure predictions, proteins design, NMR and X-ray refinement, docking, and mutation effect predictions. Integrating the predicted entropy can yield a significant accuracy increase as we show exemplarily for native-state identification with the prominent protein software FoldX. The method has been termed Popcoen for Prediction of Protein Configurational Entropy. An implementation is freely available at http://fmc.ub.edu/popcoen/ .
Entropy Information of Cardiorespiratory Dynamics in Neonates during Sleep
Directory of Open Access Journals (Sweden)
Maristella Lucchini
2017-05-01
Full Text Available Sleep is a central activity in human adults and characterizes most of the newborn infant life. During sleep, autonomic control acts to modulate heart rate variability (HRV and respiration. Mechanisms underlying cardiorespiratory interactions in different sleep states have been studied but are not yet fully understood. Signal processing approaches have focused on cardiorespiratory analysis to elucidate this co-regulation. This manuscript proposes to analyze heart rate (HR, respiratory variability and their interrelationship in newborn infants to characterize cardiorespiratory interactions in different sleep states (active vs. quiet. We are searching for indices that could detect regulation alteration or malfunction, potentially leading to infant distress. We have analyzed inter-beat (RR interval series and respiration in a population of 151 newborns, and followed up with 33 at 1 month of age. RR interval series were obtained by recognizing peaks of the QRS complex in the electrocardiogram (ECG, corresponding to the ventricles depolarization. Univariate time domain, frequency domain and entropy measures were applied. In addition, Transfer Entropy was considered as a bivariate approach able to quantify the bidirectional information flow from one signal (respiration to another (RR series. Results confirm the validity of the proposed approach. Overall, HRV is higher in active sleep, while high frequency (HF power characterizes more quiet sleep. Entropy analysis provides higher indices for SampEn and Quadratic Sample entropy (QSE in quiet sleep. Transfer Entropy values were higher in quiet sleep and point to a major influence of respiration on the RR series. At 1 month of age, time domain parameters show an increase in HR and a decrease in variability. No entropy differences were found across ages. The parameters employed in this study help to quantify the potential for infants to adapt their cardiorespiratory responses as they mature. Thus, they
Entropy Information of Cardiorespiratory Dynamics in Neonates during Sleep.
Lucchini, Maristella; Pini, Nicolò; Fifer, William P; Burtchen, Nina; Signorini, Maria G
2017-05-01
Sleep is a central activity in human adults and characterizes most of the newborn infant life. During sleep, autonomic control acts to modulate heart rate variability (HRV) and respiration. Mechanisms underlying cardiorespiratory interactions in different sleep states have been studied but are not yet fully understood. Signal processing approaches have focused on cardiorespiratory analysis to elucidate this co-regulation. This manuscript proposes to analyze heart rate (HR), respiratory variability and their interrelationship in newborn infants to characterize cardiorespiratory interactions in different sleep states (active vs. quiet). We are searching for indices that could detect regulation alteration or malfunction, potentially leading to infant distress. We have analyzed inter-beat (RR) interval series and respiration in a population of 151 newborns, and followed up with 33 at 1 month of age. RR interval series were obtained by recognizing peaks of the QRS complex in the electrocardiogram (ECG), corresponding to the ventricles depolarization. Univariate time domain, frequency domain and entropy measures were applied. In addition, Transfer Entropy was considered as a bivariate approach able to quantify the bidirectional information flow from one signal (respiration) to another (RR series). Results confirm the validity of the proposed approach. Overall, HRV is higher in active sleep, while high frequency (HF) power characterizes more quiet sleep. Entropy analysis provides higher indices for SampEn and Quadratic Sample entropy (QSE) in quiet sleep. Transfer Entropy values were higher in quiet sleep and point to a major influence of respiration on the RR series. At 1 month of age, time domain parameters show an increase in HR and a decrease in variability. No entropy differences were found across ages. The parameters employed in this study help to quantify the potential for infants to adapt their cardiorespiratory responses as they mature. Thus, they could be useful
Non-equilibrium Dynamics, Thermalization and Entropy Production
International Nuclear Information System (INIS)
Hinrichsen, Haye; Janotta, Peter; Gogolin, Christian
2011-01-01
This paper addresses fundamental aspects of statistical mechanics such as the motivation of a classical state space with spontaneous transitions, the meaning of non-equilibrium in the context of thermalization, and the justification of these concepts from the quantum-mechanical point of view. After an introductory part we focus on the problem of entropy production in non-equilibrium systems. In particular, the generally accepted formula for entropy production in the environment is analyzed from a critical perspective. It is shown that this formula is only valid in the limit of separated time scales of the system's and the environmental degrees of freedom. Finally, we present an alternative simple proof of the fluctuation theorem.
International Nuclear Information System (INIS)
Csernai, L.P.; Lukacs, B.
1984-04-01
In a fluid-dynamical model the extra entropy production is calculated which arises from a non-equilibrium phase transition from nuclear to quark matter. The dynamics of processes producing extra entropy are treated in linear approximation. It is shown that there is a considerable extra entropy production provided the transition is not too fast. In measuring the entropy at the break-up, an excess entropy might signalize the phase transition to a transient quark-gluon plasma. (D.Gy.)
The Entropy of Co-Compact Open Covers
Directory of Open Access Journals (Sweden)
Steven Bourquin
2013-06-01
Full Text Available Co-compact entropy is introduced as an invariant of topological conjugation for perfect mappings defined on any Hausdorff space (compactness and metrizability are not necessarily required. This is achieved through the consideration of co-compact covers of the space. The advantages of co-compact entropy include: (1 it does not require the space to be compact and, thus, generalizes Adler, Konheim and McAndrew’s topological entropy of continuous mappings on compact dynamical systems; and (2 it is an invariant of topological conjugation, compared to Bowen’s entropy, which is metric-dependent. Other properties of co-compact entropy are investigated, e.g., the co-compact entropy of a subsystem does not exceed that of the whole system. For the linear system, (R; f, defined by f(x = 2x, the co-compact entropy is zero, while Bowen’s entropy for this system is at least log 2. More generally, it is found that co-compact entropy is a lower bound of Bowen’s entropies, and the proof of this result also generates the Lebesgue Covering Theorem to co-compact open covers of non-compact metric spaces.
SpatEntropy: Spatial Entropy Measures in R
Altieri, Linda; Cocchi, Daniela; Roli, Giulia
2018-01-01
This article illustrates how to measure the heterogeneity of spatial data presenting a finite number of categories via computation of spatial entropy. The R package SpatEntropy contains functions for the computation of entropy and spatial entropy measures. The extension to spatial entropy measures is a unique feature of SpatEntropy. In addition to the traditional version of Shannon's entropy, the package includes Batty's spatial entropy, O'Neill's entropy, Li and Reynolds' contagion index, Ka...
Two aspects of black hole entropy in Lanczos-Lovelock models of gravity
Kolekar, Sanved; Kothawala, Dawood; Padmanabhan, T.
2012-03-01
We consider two specific approaches to evaluate the black hole entropy which are known to produce correct results in the case of Einstein’s theory and generalize them to Lanczos-Lovelock models. In the first approach (which could be called extrinsic), we use a procedure motivated by earlier work by Pretorius, Vollick, and Israel, and by Oppenheim, and evaluate the entropy of a configuration of densely packed gravitating shells on the verge of forming a black hole in Lanczos-Lovelock theories of gravity. We find that this matter entropy is not equal to (it is less than) Wald entropy, except in the case of Einstein theory, where they are equal. The matter entropy is proportional to the Wald entropy if we consider a specific mth-order Lanczos-Lovelock model, with the proportionality constant depending on the spacetime dimensions D and the order m of the Lanczos-Lovelock theory as (D-2m)/(D-2). Since the proportionality constant depends on m, the proportionality between matter entropy and Wald entropy breaks down when we consider a sum of Lanczos-Lovelock actions involving different m. In the second approach (which could be called intrinsic), we generalize a procedure, previously introduced by Padmanabhan in the context of general relativity, to study off-shell entropy of a class of metrics with horizon using a path integral method. We consider the Euclidean action of Lanczos-Lovelock models for a class of metrics off shell and interpret it as a partition function. We show that in the case of spherically symmetric metrics, one can interpret the Euclidean action as the free energy and read off both the entropy and energy of a black hole spacetime. Surprisingly enough, this leads to exactly the Wald entropy and the energy of the spacetime in Lanczos-Lovelock models obtained by other methods. We comment on possible implications of the result.
de La Sierra, Ruben Ulises
The present study introduces entropy mapping as a comprehensive method to analyze and describe complex interactive systems; and to assess the effect that entropy has in paradigm changes as described by transition theory. Dynamics of interactions among environmental, economic and demographic conditions affect a number of fast growing locations throughout the world. One of the regions especially affected by accelerated growth in terms of demographic and economic development is the border region between Mexico and the US. As the contrast between these countries provides a significant economic and cultural differential, the dynamics of capital, goods, services and people and the rates at which they interact are rather unique. To illustrate the most fundamental economic and political changes affecting the region, a background addressing the causes for these changes leading to the North America Free Trade Agreement (NAFTA) is presented. Although the concept of thermodynamic entropy was first observed in physical sciences, a relevant homology exists in biological, social and economic sciences as the universal tendency towards disorder, dissipation and equilibrium is present in these disciplines when energy or resources become deficient. Furthermore, information theory is expressed as uncertainty and randomness in terms of efficiency in transmission of information. Although entropy in closed systems is unavoidable, its increase in open systems, can be arrested by a flux of energy, resources and/or information. A critical component of all systems is the boundary. If a boundary is impermeable, it will prevent energy flow from the environment into the system; likewise, if the boundary is too porous, it will not be able to prevent the dissipation of energy and resources into the environment, and will not prevent entropy from entering. Therefore, two expressions of entropy--thermodynamic and information--are identified and related to systems in transition and to spatial
Adjoint entropy vs topological entropy
Giordano Bruno, Anna
2012-01-01
Recently the adjoint algebraic entropy of endomorphisms of abelian groups was introduced and studied. We generalize the notion of adjoint entropy to continuous endomorphisms of topological abelian groups. Indeed, the adjoint algebraic entropy is defined using the family of all finite-index subgroups, while we take only the subfamily of all open finite-index subgroups to define the topological adjoint entropy. This allows us to compare the (topological) adjoint entropy with the known topologic...
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
In this paper the author presents an overview on his own research works. More than ten years ago, we proposed a new fundamental equation of nonequilibrium statistical physics in place of the present Liouville equation. That is the stochastic velocity type’s Langevin equation in 6N dimensional phase space or its equivalent Liouville diffusion equation. This equation is time-reversed asymmetrical. It shows that the form of motion of particles in statistical thermodynamic systems has the drift-diffusion duality, and the law of motion of statistical thermodynamics is expressed by a superposition of both the law of dynamics and the stochastic velocity and possesses both determinism and probability. Hence it is different from the law of motion of particles in dynamical systems. The stochastic diffusion motion of the particles is the microscopic origin of macroscopic irreversibility. Starting from this fundamental equation the BBGKY diffusion equation hierarchy, the Boltzmann collision diffusion equation, the hydrodynamic equations such as the mass drift-diffusion equation, the Navier-Stokes equation and the thermal conductivity equation have been derived and presented here. What is more important, we first constructed a nonlinear evolution equation of nonequilibrium entropy density in 6N, 6 and 3 dimensional phase space, predicted the existence of entropy diffusion. This entropy evolution equation plays a leading role in nonequilibrium entropy theory, it reveals that the time rate of change of nonequilibrium entropy density originates together from its drift, diffusion and production in space. From this evolution equation, we presented a formula for entropy production rate (i.e. the law of entropy increase) in 6N and 6 dimensional phase space, proved that internal attractive force in nonequilibrium system can result in entropy decrease while internal repulsive force leads to another entropy increase, and derived a common expression for this entropy decrease rate or
Directory of Open Access Journals (Sweden)
Fuyuan Liao
2018-02-01
Full Text Available Diabetic foot ulcer (DFU is a common complication of diabetes mellitus, while tissue ischemia caused by impaired vasodilatory response to plantar pressure is thought to be a major factor of the development of DFUs, which has been assessed using various measures of skin blood flow (SBF in the time or frequency domain. These measures, however, are incapable of characterizing nonlinear dynamics of SBF, which is an indicator of pathologic alterations of microcirculation in the diabetic foot. This study recruited 18 type 2 diabetics with peripheral neuropathy and eight healthy controls. SBF at the first metatarsal head in response to locally applied pressure and heating was measured using laser Doppler flowmetry. A multiscale entropy algorithm was utilized to quantify the regularity degree of the SBF responses. The results showed that during reactive hyperemia and thermally induced biphasic response, the regularity degree of SBF in diabetics underwent only small changes compared to baseline and significantly differed from that in controls at multiple scales (p < 0.05. On the other hand, the transition of regularity degree of SBF in diabetics distinctively differed from that in controls (p < 0.05. These findings indicated that multiscale entropy could provide a more comprehensive assessment of impaired microvascular reactivity in the diabetic foot compared to other entropy measures based on only a single scale, which strengthens the use of plantar SBF dynamics to assess the risk for DFU.
Upper entropy axioms and lower entropy axioms
International Nuclear Information System (INIS)
Guo, Jin-Li; Suo, Qi
2015-01-01
The paper suggests the concepts of an upper entropy and a lower entropy. We propose a new axiomatic definition, namely, upper entropy axioms, inspired by axioms of metric spaces, and also formulate lower entropy axioms. We also develop weak upper entropy axioms and weak lower entropy axioms. Their conditions are weaker than those of Shannon–Khinchin axioms and Tsallis axioms, while these conditions are stronger than those of the axiomatics based on the first three Shannon–Khinchin axioms. The subadditivity and strong subadditivity of entropy are obtained in the new axiomatics. Tsallis statistics is a special case of satisfying our axioms. Moreover, different forms of information measures, such as Shannon entropy, Daroczy entropy, Tsallis entropy and other entropies, can be unified under the same axiomatics
International Nuclear Information System (INIS)
Beretta, Gian Paolo
2006-01-01
We discuss a nonlinear model for relaxation by energy redistribution within an isolated, closed system composed of noninteracting identical particles with energy levels e i with i=1,2,...,N. The time-dependent occupation probabilities p i (t) are assumed to obey the nonlinear rate equations τ dp i /dt=-p i ln p i -α(t)p i -β(t)e i p i where α(t) and β(t) are functionals of the p i (t)'s that maintain invariant the mean energy E=Σ i=1 N e i p i (t) and the normalization condition 1=Σ i=1 N p i (t). The entropy S(t)=-k B Σ i=1 N p i (t)ln p i (t) is a nondecreasing function of time until the initially nonzero occupation probabilities reach a Boltzmann-like canonical distribution over the occupied energy eigenstates. Initially zero occupation probabilities, instead, remain zero at all times. The solutions p i (t) of the rate equations are unique and well defined for arbitrary initial conditions p i (0) and for all times. The existence and uniqueness both forward and backward in time allows the reconstruction of the ancestral or primordial lowest entropy state. By casting the rate equations in terms not of the p i 's but of their positive square roots √(p i ), they unfold from the assumption that time evolution is at all times along the local direction of steepest entropy ascent or, equivalently, of maximal entropy generation. These rate equations have the same mathematical structure and basic features as the nonlinear dynamical equation proposed in a series of papers ending with G. P. Beretta, Found. Phys. 17, 365 (1987) and recently rediscovered by S. Gheorghiu-Svirschevski [Phys. Rev. A 63, 022105 (2001);63, 054102 (2001)]. Numerical results illustrate the features of the dynamics and the differences from the rate equations recently considered for the same problem by M. Lemanska and Z. Jaeger [Physica D 170, 72 (2002)]. We also interpret the functionals k B α(t) and k B β(t) as nonequilibrium generalizations of the thermodynamic-equilibrium Massieu
DYNAMIC PARAMETER ESTIMATION BASED ON MINIMUM CROSS-ENTROPY METHOD FOR COMBINING INFORMATION SOURCES
Czech Academy of Sciences Publication Activity Database
Sečkárová, Vladimíra
2015-01-01
Roč. 24, č. 5 (2015), s. 181-188 ISSN 0204-9805. [XVI-th International Summer Conference on Probability and Statistics (ISCPS-2014). Pomorie, 21.6.-29.6.2014] R&D Projects: GA ČR GA13-13502S Grant - others:GA UK(CZ) SVV 260225/2015 Institutional support: RVO:67985556 Keywords : minimum cross- entropy principle * Kullback-Leibler divergence * dynamic diffusion estimation Subject RIV: BB - Applied Statistics, Operational Research http://library.utia.cas.cz/separaty/2015/AS/seckarova-0445817.pdf
Nonsymmetric entropy and maximum nonsymmetric entropy principle
International Nuclear Information System (INIS)
Liu Chengshi
2009-01-01
Under the frame of a statistical model, the concept of nonsymmetric entropy which generalizes the concepts of Boltzmann's entropy and Shannon's entropy, is defined. Maximum nonsymmetric entropy principle is proved. Some important distribution laws such as power law, can be derived from this principle naturally. Especially, nonsymmetric entropy is more convenient than other entropy such as Tsallis's entropy in deriving power laws.
Holographic entanglement entropy for the most general higher derivative gravity
International Nuclear Information System (INIS)
Miao, Rong-Xin; Guo, Wu-zhong
2015-01-01
The holographic entanglement entropy for the most general higher derivative gravity is investigated. We find a new type of Wald entropy, which appears on entangling surface without the rotational symmetry and reduces to usual Wald entropy on Killing horizon. Furthermore, we obtain a formal formula of HEE for the most general higher derivative gravity and work it out exactly for some squashed cones. As an important application, we derive HEE for gravitational action with one derivative of the curvature when the extrinsic curvature vanishes. We also study some toy models with non-zero extrinsic curvature. We prove that our formula yields the correct universal term of entanglement entropy for 4d CFTs. Furthermore, we solve the puzzle raised by Hung, Myers and Smolkin that the logarithmic term of entanglement entropy derived from Weyl anomaly of CFTs does not match the holographic result even if the extrinsic curvature vanishes. We find that such mismatch comes from the ‘anomaly of entropy’ of the derivative of curvature. After considering such contributions carefully, we resolve the puzzle successfully. In general, we need to fix the splitting problem for the conical metrics in order to derive the holographic entanglement entropy. We find that, at least for Einstein gravity, the splitting problem can be fixed by using equations of motion. How to derive the splittings for higher derivative gravity is a non-trivial and open question. For simplicity, we ignore the splitting problem in this paper and find that it does not affect our main results.
Pesin’s entropy formula for stochastic flows of diffeomorphisms
Institute of Scientific and Technical Information of China (English)
刘培东
1996-01-01
Pesin’s entropy formula relating entropy and Lyapunov exponents within the context of random dynamical systems generated by (discrete or continuous) stochastic flows of diffeomorphisms (including solution flows of stochastic differential equations on manifolds) is proved.
International Nuclear Information System (INIS)
Zhang Baocheng; Cai Qingyu; Zhan Mingsheng; You Li
2011-01-01
Research Highlights: → Information is found to be encoded and carried away by Hawking radiations. → Entropy is conserved in Hawking radiation. → We thus conclude no information is lost. → The dynamics of black hole may be unitary. - Abstract: We revisit in detail the paradox of black hole information loss due to Hawking radiation as tunneling. We compute the amount of information encoded in correlations among Hawking radiations for a variety of black holes, including the Schwarzchild black hole, the Reissner-Nordstroem black hole, the Kerr black hole, and the Kerr-Newman black hole. The special case of tunneling through a quantum horizon is also considered. Within a phenomenological treatment based on the accepted emission probability spectrum from a black hole, we find that information is leaked out hidden in the correlations of Hawking radiation. The recovery of this previously unaccounted for information helps to conserve the total entropy of a system composed of a black hole plus its radiations. We thus conclude, irrespective of the microscopic picture for black hole collapsing, the associated radiation process: Hawking radiation as tunneling, is consistent with unitarity as required by quantum mechanics.
Entropy, neutro-entropy and anti-entropy for neutrosophic information
Vasile Patrascu
2017-01-01
This approach presents a multi-valued representation of the neutrosophic information. It highlights the link between the bifuzzy information and neutrosophic one. The constructed deca-valued structure shows the neutrosophic information complexity. This deca-valued structure led to construction of two new concepts for the neutrosophic information: neutro-entropy and anti-entropy. These two concepts are added to the two existing: entropy and non-entropy. Thus, we obtained the following triad: e...
Entanglement entropy and higher spin holography in AdS{sub 3}
Energy Technology Data Exchange (ETDEWEB)
Boer, Jan de; Jottar, Juan I. [Institute for Theoretical Physics, University of Amsterdam,Science Park 904, Postbus 94485, 1090 GL Amsterdam (Netherlands)
2014-04-14
A holographic correspondence has been recently developed between higher spin theories in three-dimensional anti-de Sitter space (AdS{sub 3}) and two-dimensional Conformal Field Theories (CFTs) with extended symmetries. A class of such dualities involves SL(N,R)×SL(N,R) Chern-Simons gauge theories in the (2+1)-dimensional bulk spacetime, and CFTs with W{sub N} symmetry algebras on the (1+1)-dimensional boundary. The topological character of the bulk theory forces one to reconsider standard geometric notions such as black hole horizons and entropy, as well as the usual holographic dictionary. Motivated by this challenge, in this note we present a proposal to compute entanglement entropy in the W{sub N} CFTs via holographic methods. In particular, we introduce a functional constructed from Wilson lines in the bulk Chern-Simons theory that captures the entanglement entropy in the CFTs dual to standard AdS{sub 3} gravity, corresponding to SL(2,R)×SL(2,R) gauge group, and admits an immediate generalization to the higher spin case. We explicitly evaluate this functional for several known solutions of the bulk theory, including charged black holes dual to thermal CFT states carrying higher spin charge, and show that it reproduces expected features of entanglement entropy, study whether it obeys strong subadditivity, and moreover show that it reduces to the thermal entropy in the appropriate limit.
Entropy of the information retrieved from black holes
International Nuclear Information System (INIS)
Mersini-Houghton, Laura
2016-01-01
The retrieval of black hole information was recently presented in two interesting proposals in the ‘Hawking Radiation’ conference: a revised version by Hooft of a proposal he initially suggested 20 years ago and, a new proposal by Hawking. Both proposals address the problem of black hole information loss at the classical level and derive an expression for the scattering matrix. The former uses gravitation back reaction of incoming particles that imprints its information on the outgoing modes. The latter uses supertranslation symmetry of horizons to relate a phase delay of the outgoing wave packet compared to their incoming wave partners. The difficulty in both proposals is that the entropy obtained from them appears to be infinite. By including quantum effects into the Hawking and Hooft’s proposals, I show that a subtlety arising from the inescapable measurement process, the quantum Zeno effect, not only tames divergences but it actually recovers the correct 1/4 of the area Bekenstein–Hawking entropy law of black holes. (note)
Shannon information entropy in heavy-ion collisions
Ma, Chun-Wang; Ma, Yu-Gang
2018-03-01
The general idea of information entropy provided by C.E. Shannon "hangs over everything we do" and can be applied to a great variety of problems once the connection between a distribution and the quantities of interest is found. The Shannon information entropy essentially quantify the information of a quantity with its specific distribution, for which the information entropy based methods have been deeply developed in many scientific areas including physics. The dynamical properties of heavy-ion collisions (HICs) process make it difficult and complex to study the nuclear matter and its evolution, for which Shannon information entropy theory can provide new methods and observables to understand the physical phenomena both theoretically and experimentally. To better understand the processes of HICs, the main characteristics of typical models, including the quantum molecular dynamics models, thermodynamics models, and statistical models, etc., are briefly introduced. The typical applications of Shannon information theory in HICs are collected, which cover the chaotic behavior in branching process of hadron collisions, the liquid-gas phase transition in HICs, and the isobaric difference scaling phenomenon for intermediate mass fragments produced in HICs of neutron-rich systems. Even though the present applications in heavy-ion collision physics are still relatively simple, it would shed light on key questions we are seeking for. It is suggested to further develop the information entropy methods in nuclear reactions models, as well as to develop new analysis methods to study the properties of nuclear matters in HICs, especially the evolution of dynamics system.
Explaining the entropy concept and entropy components
Directory of Open Access Journals (Sweden)
Marko Popovic
2018-04-01
Full Text Available Total entropy of a thermodynamic system consists of two components: thermal entropy due to energy, and residual entropy due to molecular orientation. In this article, a three-step method for explaining entropy is suggested. Step one is to use a classical method to introduce thermal entropy STM as a function of temperature T and heat capacity at constant pressure Cp: STM = ∫(Cp/T dT. Thermal entropy is the entropy due to uncertainty in motion of molecules and vanishes at absolute zero (zero-point energy state. It is also the measure of useless thermal energy that cannot be converted into useful work. The next step is to introduce residual entropy S0 as a function of the number of molecules N and the number of distinct orientations available to them in a crystal m: S0 = N kB ln m, where kB is the Boltzmann constant. Residual entropy quantifies the uncertainty in molecular orientation. Residual entropy, unlike thermal entropy, is independent of temperature and remains present at absolute zero. The third step is to show that thermal entropy and residual entropy add up to the total entropy of a thermodynamic system S: S = S0 + STM. This method of explanation should result in a better comprehension of residual entropy and thermal entropy, as well as of their similarities and differences. The new method was tested in teaching at Faculty of Chemistry University of Belgrade, Serbia. The results of the test show that the new method has a potential to improve the quality of teaching.
Quantum topological entropy: First steps of a 'pedestrian' approach
International Nuclear Information System (INIS)
Hudetz, T.
1991-01-01
We introduce a notion of topological entropy for automorphisms of arbitrary (noncommutative, but unital) nuclear C * -algebras A, generalizing the 'classical' topological entropy for a homeomorphism T: X → X of an arbitrary (possibly connected) compact Hausdorff space X, where the generalization is of course understood in the sense that the latter topological dynamical system (with Z-action) is equivalently viewed as the C * -dynamical system given by the T-induced automorphism of the Abelian C * -algebra A = C(X) of (complex-valued) continuous functions on X. As a simple but basic example, we calculate our quantum topological entropy for shift automorphisms on AF algebras A associated with topological Markov chains (i.e. 'quantum topological' Markov chains); and also a real physical interpretation of our simple 'quantum probabilistic' entropy functionals is discussed (already in the introduction, anticipating the later definitions and results). (author)
Entropy, neutro-entropy and anti-entropy for neutrosophic information
Vasile Patrascu
2017-01-01
This article shows a deca-valued representation of neutrosophic information in which are defined the following features: truth, falsity, weak truth, weak falsity, ignorance, contradiction, saturation, neutrality, ambiguity and hesitation. Using these features, there are constructed computing formulas for entropy, neutro-entropy and anti-entropy.
Maximum Entropy Approach in Dynamic Contrast-Enhanced Magnetic Resonance Imaging.
Farsani, Zahra Amini; Schmid, Volker J
2017-01-01
In the estimation of physiological kinetic parameters from Dynamic Contrast-Enhanced Magnetic Resonance Imaging (DCE-MRI) data, the determination of the arterial input function (AIF) plays a key role. This paper proposes a Bayesian method to estimate the physiological parameters of DCE-MRI along with the AIF in situations, where no measurement of the AIF is available. In the proposed algorithm, the maximum entropy method (MEM) is combined with the maximum a posterior approach (MAP). To this end, MEM is used to specify a prior probability distribution of the unknown AIF. The ability of this method to estimate the AIF is validated using the Kullback-Leibler divergence. Subsequently, the kinetic parameters can be estimated with MAP. The proposed algorithm is evaluated with a data set from a breast cancer MRI study. The application shows that the AIF can reliably be determined from the DCE-MRI data using MEM. Kinetic parameters can be estimated subsequently. The maximum entropy method is a powerful tool to reconstructing images from many types of data. This method is useful for generating the probability distribution based on given information. The proposed method gives an alternative way to assess the input function from the existing data. The proposed method allows a good fit of the data and therefore a better estimation of the kinetic parameters. In the end, this allows for a more reliable use of DCE-MRI. Schattauer GmbH.
Computing black hole entropy in loop quantum gravity from a conformal field theory perspective
International Nuclear Information System (INIS)
Agulló, Iván; Borja, Enrique F.; Díaz-Polo, Jacobo
2009-01-01
Motivated by the analogy proposed by Witten between Chern-Simons and conformal field theories, we explore an alternative way of computing the entropy of a black hole starting from the isolated horizon framework in loop quantum gravity. The consistency of the result opens a window for the interplay between conformal field theory and the description of black holes in loop quantum gravity
Novel Remarks on Point Mass Sources, Firewalls, Null Singularities and Gravitational Entropy
Perelman, Carlos Castro
2016-01-01
A continuous family of static spherically symmetric solutions of Einstein's vacuum field equations with a spatial singularity at the origin r = 0 is found. These solutions are parametrized by a real valued parameter λ (ranging from 0 to 1) and such that the radial horizon's location is displaced continuously towards the singularity ( r = 0 ) as λ increases. In the extreme limit λ = 1, the location of the singularity and horizon merges leading to a null singularity. In this extreme case, any infalling observer hits the null singularity at the very moment he/she crosses the horizon. This fact may have important consequences for the resolution of the fire wall problem and the complementarity controversy in black holes. An heuristic argument is provided how one might avoid the Hawking particle emission process in this extreme case when the singularity and horizon merges. The field equations due to a delta-function point-mass source at r = 0 are solved and the Euclidean gravitational action corresponding to those solutions is evaluated explicitly. It is found that the Euclidean action is precisely equal to the black hole entropy (in Planck area units). This result holds in any dimensions D ≥ 3.
Transfer Entropy as a Log-Likelihood Ratio
Barnett, Lionel; Bossomaier, Terry
2012-09-01
Transfer entropy, an information-theoretic measure of time-directed information transfer between joint processes, has steadily gained popularity in the analysis of complex stochastic dynamics in diverse fields, including the neurosciences, ecology, climatology, and econometrics. We show that for a broad class of predictive models, the log-likelihood ratio test statistic for the null hypothesis of zero transfer entropy is a consistent estimator for the transfer entropy itself. For finite Markov chains, furthermore, no explicit model is required. In the general case, an asymptotic χ2 distribution is established for the transfer entropy estimator. The result generalizes the equivalence in the Gaussian case of transfer entropy and Granger causality, a statistical notion of causal influence based on prediction via vector autoregression, and establishes a fundamental connection between directed information transfer and causality in the Wiener-Granger sense.
Multiscale analysis of heart rate dynamics: entropy and time irreversibility measures.
Costa, Madalena D; Peng, Chung-Kang; Goldberger, Ary L
2008-06-01
Cardiovascular signals are largely analyzed using traditional time and frequency domain measures. However, such measures fail to account for important properties related to multiscale organization and non-equilibrium dynamics. The complementary role of conventional signal analysis methods and emerging multiscale techniques, is, therefore, an important frontier area of investigation. The key finding of this presentation is that two recently developed multiscale computational tools--multiscale entropy and multiscale time irreversibility--are able to extract information from cardiac interbeat interval time series not contained in traditional methods based on mean, variance or Fourier spectrum (two-point correlation) techniques. These new methods, with careful attention to their limitations, may be useful in diagnostics, risk stratification and detection of toxicity of cardiac drugs.
Entropy for theories with indefinite causal structure
International Nuclear Information System (INIS)
Markes, Sonia; Hardy, Lucien
2011-01-01
Any theory with definite causal structure has a defined past and future, be it defined by light cones or an absolute time scale. Entropy is a concept that has traditionally been reliant on a definite notion of causality. However, without a definite notion of causality, the concept of entropy is not all lost. Indefinite causal structure results from combining probabilistic predictions and dynamical space-time. The causaloid framework lays the mathematical groundwork to be able to treat indefinite causal structure. In this paper, we build on the causaloid mathematics and define a causally-unbiased entropy for an indefinite causal structure. In defining a causally-unbiased entropy, there comes about an emergent idea of causality in the form of a measure of causal connectedness, termed the Q factor.
Energy Technology Data Exchange (ETDEWEB)
Gao, Fei; Qin, Si-Xue; Roberts, Craig D.; Rodríguez-Quintero, Jose
2018-02-01
We explore whether a tree-level expression for the gluon two-point function, supposed to express effects of an horizon term introduced to eliminate the Gribov ambiguity, is consistent with the propagator obtained in simulations of lattice-regularised quantum chromodynamics (QCD). In doing so, we insist that the gluon two-point function obey constraints that ensure a minimal level of consistency with parton-like behaviour at ultraviolet momenta. In consequence, we are led to a position which supports a conjecture that the gluon mass and horizon scale are equivalent emergent massscales, each with a value of roughly 0.5 GeV; and wherefrom it appears plausible that the dynamical generation of a running gluon mass may alone be sufficient to remove the Gribov ambiguity.
Gao, Fei; Qin, Si-Xue; Roberts, Craig D.; Rodríguez-Quintero, Jose
2018-02-01
We explore whether a tree-level expression for the gluon two-point function, supposed to express effects of an horizon term introduced to eliminate the Gribov ambiguity, is consistent with the propagator obtained in simulations of lattice-regularized quantum chromodynamics (QCD). In doing so, we insist that the gluon two-point function obey constraints that ensure a minimal level of consistency with parton-like behavior on the ultraviolet domain. In consequence, we are led to a position which supports a conjecture that the gluon mass and horizon scale are equivalent emergent mass-scales, each with a value of roughly 0.5 GeV; and wherefrom it appears plausible that the dynamical generation of a running gluon mass may alone be sufficient to remove the Gribov ambiguity.
Energy Technology Data Exchange (ETDEWEB)
Koss, K. G.; Petrov, O. F.; Myasnikov, M. I., E-mail: miasnikovmi@mail.ru; Statsenko, K. B.; Vasiliev, M. M. [Russian Academy of Sciences, Joint Institute for High Temperatures (Russian Federation)
2016-07-15
The results of experimental and numerical analysis are presented for phase transitions in strongly nonequilibrium small systems of strongly interacting Brownian particles. The dynamic entropy method is applied to analysis of the state of these systems. Experiments are carried out with kinetic heating of the structures of micron-size particles in a laboratory rf discharge plasma. Three phase states of these small systems are observed: crystalline, liquid, and transient. The mechanism of phase transitions in cluster structures of strongly interacting particles is described.
A Cardy-like formula for rotating black holes with planar horizon
Energy Technology Data Exchange (ETDEWEB)
Gaete, Moisés Bravo [Facultad de Ciencias Básicas, Universidad Católica del Maule,Casilla 617, Talca (Chile); Guajardo, Luis; Hassaïne, Mokhtar [Instituto de Matemática y Fisica, Universidad de Talca,Casilla 747, Talca (Chile)
2017-04-18
We show that the semiclassical entropy of D−dimensional rotating (an)isotropic black holes with planar horizon can be successfully computed according to a Cardy-like formula. This formula does not refer to any central charges but instead involves the vacuum energy which is identified with a gravitational bulk soliton. The soliton is obtained from the non-rotating black hole solution by means of a double analytic continuation. The robustness of the Cardy-like formula is tested with numerous and varied examples, including AdS, Lifshitz and hyperscaling violation planar black holes.
Entropy Rate of Time-Varying Wireless Networks
DEFF Research Database (Denmark)
Cika, Arta; Badiu, Mihai Alin; Coon, Justin P.
2018-01-01
In this paper, we present a detailed framework to analyze the evolution of the random topology of a time-varying wireless network via the information theoretic notion of entropy rate. We consider a propagation channel varying over time with random node positions in a closed space and Rayleigh...... fading affecting the connections between nodes. The existence of an edge between two nodes at given locations is modeled by a Markov chain, enabling memory effects in network dynamics. We then derive a lower and an upper bound on the entropy rate of the spatiotemporal network. The entropy rate measures...
Parameters Tuning of Model Free Adaptive Control Based on Minimum Entropy
Institute of Scientific and Technical Information of China (English)
Chao Ji; Jing Wang; Liulin Cao; Qibing Jin
2014-01-01
Dynamic linearization based model free adaptive control(MFAC) algorithm has been widely used in practical systems, in which some parameters should be tuned before it is successfully applied to process industries. Considering the random noise existing in real processes, a parameter tuning method based on minimum entropy optimization is proposed,and the feature of entropy is used to accurately describe the system uncertainty. For cases of Gaussian stochastic noise and non-Gaussian stochastic noise, an entropy recursive optimization algorithm is derived based on approximate model or identified model. The extensive simulation results show the effectiveness of the minimum entropy optimization for the partial form dynamic linearization based MFAC. The parameters tuned by the minimum entropy optimization index shows stronger stability and more robustness than these tuned by other traditional index,such as integral of the squared error(ISE) or integral of timeweighted absolute error(ITAE), when the system stochastic noise exists.
Near horizon geometry of rotating black holes in five dimensions
International Nuclear Information System (INIS)
Cvetic, M.; Larsen, F.
1998-01-01
We interpret the general rotating black holes in five dimensions as rotating black strings in six dimensions. In the near-horizon limit the geometry is locally AdS 3 x S 3 , as in the non-rotating case. However, the global structure couples the AdS 3 and the S 3 , giving angular velocity to the S 3 . The asymptotic geometry is exploited to count the microstates and recover the precise value of the Bekenstein-Hawking entropy, with rotation taken properly into account. We discuss the perturbation spectrum of the rotating black hole, and its relation to the underlying conformal field theory. (orig.)
Secondary structural entropy in RNA switch (Riboswitch) identification.
Manzourolajdad, Amirhossein; Arnold, Jonathan
2015-04-28
RNA regulatory elements play a significant role in gene regulation. Riboswitches, a widespread group of regulatory RNAs, are vital components of many bacterial genomes. These regulatory elements generally function by forming a ligand-induced alternative fold that controls access to ribosome binding sites or other regulatory sites in RNA. Riboswitch-mediated mechanisms are ubiquitous across bacterial genomes. A typical class of riboswitch has its own unique structural and biological complexity, making de novo riboswitch identification a formidable task. Traditionally, riboswitches have been identified through comparative genomics based on sequence and structural homology. The limitations of structural-homology-based approaches, coupled with the assumption that there is a great diversity of undiscovered riboswitches, suggests the need for alternative methods for riboswitch identification, possibly based on features intrinsic to their structure. As of yet, no such reliable method has been proposed. We used structural entropy of riboswitch sequences as a measure of their secondary structural dynamics. Entropy values of a diverse set of riboswitches were compared to that of their mutants, their dinucleotide shuffles, and their reverse complement sequences under different stochastic context-free grammar folding models. Significance of our results was evaluated by comparison to other approaches, such as the base-pairing entropy and energy landscapes dynamics. Classifiers based on structural entropy optimized via sequence and structural features were devised as riboswitch identifiers and tested on Bacillus subtilis, Escherichia coli, and Synechococcus elongatus as an exploration of structural entropy based approaches. The unusually long untranslated region of the cotH in Bacillus subtilis, as well as upstream regions of certain genes, such as the sucC genes were associated with significant structural entropy values in genome-wide examinations. Various tests show that there
Do massive compact objects without event horizon exist in infinite derivative gravity?
Koshelev, Alexey S.; Mazumdar, Anupam
2017-10-01
Einstein's general theory of relativity is plagued by cosmological and black-hole type singularities Recently, it has been shown that infinite derivative, ghost free, gravity can yield nonsingular cosmological and mini-black hole solutions. In particular, the theory possesses a mass-gap determined by the scale of new physics. This paper provides a plausible argument, not a no-go theorem, based on the Area-law of gravitational entropy that within infinite derivative, ghost free, gravity nonsingular compact objects in the static limit need not have horizons.
International Nuclear Information System (INIS)
Ojima, Izumi
1989-01-01
With aid of the so-called dilation method, a concise formula is obtained for the entropy production in the algebraic formulation of quantum dynamical systems. In this framework, the initial ergodic state of an external force system plays a pivotal role in generating dissipativity as a conditional expectation. The physical meaning of van Hove limit is clarified through the scale-changing transformation to control transitions between microscopic and macroscopic levels. It plays a crucial role in realizing the macroscopic stationary in the presence of microscopic fluctuations as well as in the transition from non-Markovian (groupoid) dynamics to Markovian dissipative processes of state changes. The extension of the formalism to cases with spatial and internal inhomogeneity is indicated in the light of the groupoid dynamical systems and noncommutative integration theory
Thermodynamic studies of different black holes with modifications of entropy
Haldar, Amritendu; Biswas, Ritabrata
2018-02-01
In recent years, the thermodynamic properties of black holes are topics of interests. We investigate the thermodynamic properties like surface gravity and Hawking temperature on event horizon of regular black holes viz. Hayward Class and asymptotically AdS (Anti-de Sitter) black holes. We also analyze the thermodynamic volume and naive geometric volume of asymptotically AdS black holes and show that the entropy of these black holes is simply the ratio of the naive geometric volume to thermodynamic volume. We plot the different graphs and interpret them physically. We derive the `cosmic-Censorship-Inequality' for both type of black holes. Moreover, we calculate the thermal heat capacity of aforesaid black holes and study their stabilities in different regimes. Finally, we compute the logarithmic correction to the entropy for both the black holes considering the quantum fluctuations around the thermal equilibrium and study the corresponding thermodynamics.
Dynamic statistical information theory
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In recent years we extended Shannon static statistical information theory to dynamic processes and established a Shannon dynamic statistical information theory, whose core is the evolution law of dynamic entropy and dynamic information. We also proposed a corresponding Boltzmman dynamic statistical information theory. Based on the fact that the state variable evolution equation of respective dynamic systems, i.e. Fokker-Planck equation and Liouville diffusion equation can be regarded as their information symbol evolution equation, we derived the nonlinear evolution equations of Shannon dynamic entropy density and dynamic information density and the nonlinear evolution equations of Boltzmann dynamic entropy density and dynamic information density, that describe respectively the evolution law of dynamic entropy and dynamic information. The evolution equations of these two kinds of dynamic entropies and dynamic informations show in unison that the time rate of change of dynamic entropy densities is caused by their drift, diffusion and production in state variable space inside the systems and coordinate space in the transmission processes; and that the time rate of change of dynamic information densities originates from their drift, diffusion and dissipation in state variable space inside the systems and coordinate space in the transmission processes. Entropy and information have been combined with the state and its law of motion of the systems. Furthermore we presented the formulas of two kinds of entropy production rates and information dissipation rates, the expressions of two kinds of drift information flows and diffusion information flows. We proved that two kinds of information dissipation rates (or the decrease rates of the total information) were equal to their corresponding entropy production rates (or the increase rates of the total entropy) in the same dynamic system. We obtained the formulas of two kinds of dynamic mutual informations and dynamic channel
Foreign exchange rate entropy evolution during financial crises
Stosic, Darko; Stosic, Dusan; Ludermir, Teresa; de Oliveira, Wilson; Stosic, Tatijana
2016-05-01
This paper examines the effects of financial crises on foreign exchange (FX) markets, where entropy evolution is measured for different exchange rates, using the time-dependent block entropy method. Empirical results suggest that financial crises are associated with significant increase of exchange rate entropy, reflecting instability in FX market dynamics. In accordance with phenomenological expectations, it is found that FX markets with large liquidity and large trading volume are more inert - they recover quicker from a crisis than markets with small liquidity and small trading volume. Moreover, our numerical analysis shows that periods of economic uncertainty are preceded by periods of low entropy values, which may serve as a tool for anticipating the onset of financial crises.
Fast Slip Velocity in a High-Entropy Alloy
Rizzardi, Q.; Sparks, G.; Maaß, R.
2018-04-01
Due to fluctuations in nearest-neighbor distances and chemistry within the unit cell, high-entropy alloys are believed to have a much higher resistance to dislocation motion than pure crystals. Here, we investigate the coarse-grained dynamics of a number of dislocations being active during a slip event. We found that the time-resolved dynamics of slip is practically identical in Au and an Al0.3CoCrFeNi high-entropy alloy, but much faster than in Nb. Differences between the FCC-crystals are seen in the spatiotemporal velocity profile, with faster acceleration and slower velocity relaxation in the high-entropy alloy. Assessing distributions that characterize the intermittently evolving plastic flow reveals material-dependent scaling exponents for size, duration, and velocity-size distributions. The results are discussed in view of the underlying dislocation mobility.
Towards an Entropy Stable Spectral Element Framework for Computational Fluid Dynamics
Carpenter, Mark H.
2016-01-04
Nonlinearly stable finite element methods of arbitrary type and order, are currently unavailable for discretizations of the compressible Navier-Stokes equations. Summation-by-parts (SBP) entropy stability analysis provides a means of constructing nonlinearly stable discrete operators of arbitrary order, but is currently limited to simple element types. Herein, recent progress is reported, on developing entropy-stable (SS) discontinuous spectral collocation formulations for hexahedral elements. Two complementary efforts are discussed. The first effort generalizes previous SS spectral collocation work to extend the applicable set of points from tensor product, Legendre-Gauss-Lobatto (LGL) to tensor product Legendre-Gauss (LG) points. The LG and LGL point formulations are compared on a series of test problems. Both the LGL and LG operators are of comparable efficiency and robustness, as is demonstrated using test problems for which conventional FEM techniques suffer instability. The second effort extends previous work on entropy stability to include p-refinement at nonconforming interfaces. A generalization of existing entropy stability theory is required to accommodate the nuances of fully multidimensional SBP operators. The entropy stability of the compressible Euler equations on nonconforming interfaces is demonstrated using the newly developed LG operators and multidimensional interface interpolation operators. Preliminary studies suggest design order accuracy at nonconforming interfaces.
Black-hole horizons in modified spacetime structures arising from canonical quantum gravity
International Nuclear Information System (INIS)
Bojowald, Martin; Paily, George M; Reyes, Juan D; Tibrewala, Rakesh
2011-01-01
Several properties of canonical quantum gravity modify spacetime structures, sometimes to the degree that no effective line elements exist to describe the geometry. An analysis of solutions, for instance in the context of black holes, then requires new insights. In this paper, standard definitions of horizons in spherical symmetry are first reformulated canonically, and then evaluated for solutions of equations and constraints modified by inverse-triad corrections of loop quantum gravity. When possible, a spacetime analysis is performed which reveals a mass threshold for black holes and small changes to Hawking radiation. For more general conclusions, canonical perturbation theory is developed to second order to include back-reaction from matter. The results shed light on the questions of whether renormalization of Newton's constant or other modifications of horizon conditions should be taken into account in computations of black-hole entropy in loop quantum gravity.
Finite entanglement entropy and spectral dimension in quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Arzano, Michele [Rome Univ. (Italy). Dipt. di Fisica; INFN, Rome (Italy); Calcagni, Gianluca [CSIC, Madrid (Spain). Inst. de Estructura de la Materia
2017-12-15
What are the conditions on a field theoretic model leading to a finite entanglement entropy density? We prove two very general results: (1) Ultraviolet finiteness of a theory does not guarantee finiteness of the entropy density; (2) If the spectral dimension of the spatial boundary across which the entropy is calculated is non-negative at all scales, then the entanglement entropy cannot be finite. These conclusions, which we verify in several examples, negatively affect all quantum-gravity models, since their spectral dimension is always positive. Possible ways out are considered, including abandoning the definition of the entanglement entropy in terms of the boundary return probability or admitting an analytic continuation (not a regularization) of the usual definition. In the second case, one can get a finite entanglement entropy density in multi-fractional theories and causal dynamical triangulations. (orig.)
Finite entanglement entropy and spectral dimension in quantum gravity
Arzano, Michele; Calcagni, Gianluca
2017-12-01
What are the conditions on a field theoretic model leading to a finite entanglement entropy density? We prove two very general results: (1) Ultraviolet finiteness of a theory does not guarantee finiteness of the entropy density; (2) If the spectral dimension of the spatial boundary across which the entropy is calculated is non-negative at all scales, then the entanglement entropy cannot be finite. These conclusions, which we verify in several examples, negatively affect all quantum-gravity models, since their spectral dimension is always positive. Possible ways out are considered, including abandoning the definition of the entanglement entropy in terms of the boundary return probability or admitting an analytic continuation (not a regularization) of the usual definition. In the second case, one can get a finite entanglement entropy density in multi-fractional theories and causal dynamical triangulations.
Finite entanglement entropy and spectral dimension in quantum gravity
International Nuclear Information System (INIS)
Arzano, Michele; Calcagni, Gianluca
2017-01-01
What are the conditions on a field theoretic model leading to a finite entanglement entropy density? We prove two very general results: (1) Ultraviolet finiteness of a theory does not guarantee finiteness of the entropy density; (2) If the spectral dimension of the spatial boundary across which the entropy is calculated is non-negative at all scales, then the entanglement entropy cannot be finite. These conclusions, which we verify in several examples, negatively affect all quantum-gravity models, since their spectral dimension is always positive. Possible ways out are considered, including abandoning the definition of the entanglement entropy in terms of the boundary return probability or admitting an analytic continuation (not a regularization) of the usual definition. In the second case, one can get a finite entanglement entropy density in multi-fractional theories and causal dynamical triangulations. (orig.)
Dynamical Formation of Horizons in Recoiling D Branes
Ellis, Jonathan Richard; Nanopoulos, Dimitri V; Ellis, John
2000-01-01
A toy calculation of string/D-particle interactions within a world-sheet approach indicates that quantum recoil effects - reflecting the gravitational back-reaction on space-time foam due to the propagation of energetic particles - induces the appearance of a microscopic event horizon, or `bubble', inside which stable matter can exist. The scattering event causes this horizon to expand, but we expect quantum effects to cause it to contract again, in a `bounce' solution. Within such `bubbles', massless matter propagates with an effective velocity that is less than the velocity of light in vacuo, which may lead to observable violations of Lorentz symmetry that may be tested experimentally. The conformal invariance conditions in the interior geometry of the bubbles select preferentially three for the number of the spatial dimensions, corresponding to a consistent formulation of the interaction of D3 branes with recoiling D particles, which are allowed to fluctuate independently only on the D3-brane hypersurface.
Zan, Hao; Li, Haowei; Jiang, Yuguang; Wu, Meng; Zhou, Weixing; Bao, Wen
2018-06-01
As part of our efforts to find ways and means to further improve the regenerative cooling technology in scramjet, the experiments of thermo-acoustic instability dynamic characteristics of hydrocarbon fuel flowing have been conducted in horizontal circular tubes at different conditions. The experimental results indicate that there is a developing process from thermo-acoustic stability to instability. In order to have a deep understanding on the developing process of thermo-acoustic instability, the method of Multi-scale Shannon Wavelet Entropy (MSWE) based on Wavelet Transform Correlation Filter (WTCF) and Multi-Scale Shannon Entropy (MSE) is adopted in this paper. The results demonstrate that the developing process of thermo-acoustic instability from noise and weak signals is well detected by MSWE method and the differences among the stability, the developing process and the instability can be identified. These properties render the method particularly powerful for warning thermo-acoustic instability of hydrocarbon fuel flowing in scramjet cooling channels. The mass flow rate and the inlet pressure will make an influence on the developing process of the thermo-acoustic instability. The investigation on thermo-acoustic instability dynamic characteristics at supercritical pressure based on wavelet entropy method offers guidance on the control of scramjet fuel supply, which can secure stable fuel flowing in regenerative cooling system.
Entropie analysis of floating car data systems
Directory of Open Access Journals (Sweden)
F. Gössel
2004-01-01
Full Text Available The knowledge of the actual traffic state is a basic prerequisite of modern traffic telematic systems. Floating Car Data (FCD systems are becoming more and more important for the provision of actual and reliable traffic data. In these systems the vehicle velocity is the original variable for the evaluation of the current traffic condition. As real FCDsystems are operating under conditions of limited transmission and processing capacity the analysis of the original variable vehicle speed is of special interest. Entropy considerations are especially useful for the deduction of fundamental restrictions and limitations. The paper analyses velocity-time profiles by means of information entropy. It emphasises in quantification of the information content of velocity-time profiles and the discussion of entropy dynamic in velocity-time profiles. Investigations are based on empirical data derived during field trials. The analysis of entropy dynamic is carried out in two different ways. On one hand velocity differences within a certain interval of time are used, on the other hand the transinformation between velocities in certain time distances was evaluated. One important result is an optimal sample-rate for the detection of velocity data in FCD-systems. The influence of spatial segmentation and of different states of traffic was discussed.
Entropy, energy and negativity in Fermi-resonance coupled states of substituted methanes
International Nuclear Information System (INIS)
Hou Xiwen; Wan Mingfang; Ma Zhongqi
2010-01-01
Several measures of entanglement have attracted considerable interest in the relationship of a measure of entanglement with other quantities. The dynamics of entropy, energy and negativity is studied for Fermi-resonance coupled vibrations in substituted methanes with three kinds of initial mixed states, which are the mixed density matrices of binomial states, thermal states and squeezed states on two vibrational modes, respectively. It is demonstrated that for mixed binomial states and mixed thermal states with small magnitudes the entropies of the stretch and the bend are anti-correlated in the same oscillatory frequency, so do the energies for each kind of state with small magnitudes, whereas the entropies exhibit positive correlations with the corresponding energies. Furthermore, for small magnitudes quantum mutual entropy is positively correlated with the interacting energy. Analytic forms of entropies and energies are provided with initial conditions in which they are stationary, and the agreement between analytic and numerical simulations is satisfactory. The dynamical entanglement measured by negativity is examined for those states and conditions. It is shown that negativity displays a sudden death for mixed binomial states and mixed thermal states with small magnitudes, and the time-averaged negativity has the minimal value under the conditions of stationary entropies and energies. Moreover, negativity is positively correlated with the mutual entropy and the interacting energy just for mixed squeezed states with small magnitudes. Those are useful for molecular quantum information processing and dynamical entanglement.
Emergent Geometry from Entropy and Causality
Engelhardt, Netta
In this thesis, we investigate the connections between the geometry of spacetime and aspects of quantum field theory such as entanglement entropy and causality. This work is motivated by the idea that spacetime geometry is an emergent phenomenon in quantum gravity, and that the physics responsible for this emergence is fundamental to quantum field theory. Part I of this thesis is focused on the interplay between spacetime and entropy, with a special emphasis on entropy due to entanglement. In general spacetimes, there exist locally-defined surfaces sensitive to the geometry that may act as local black hole boundaries or cosmological horizons; these surfaces, known as holographic screens, are argued to have a connection with the second law of thermodynamics. Holographic screens obey an area law, suggestive of an association with entropy; they are also distinguished surfaces from the perspective of the covariant entropy bound, a bound on the total entropy of a slice of the spacetime. This construction is shown to be quite general, and is formulated in both classical and perturbatively quantum theories of gravity. The remainder of Part I uses the Anti-de Sitter/ Conformal Field Theory (AdS/CFT) correspondence to both expand and constrain the connection between entanglement entropy and geometry. The AdS/CFT correspondence posits an equivalence between string theory in the "bulk" with AdS boundary conditions and certain quantum field theories. In the limit where the string theory is simply classical General Relativity, the Ryu-Takayanagi and more generally, the Hubeny-Rangamani-Takayanagi (HRT) formulae provide a way of relating the geometry of surfaces to entanglement entropy. A first-order bulk quantum correction to HRT was derived by Faulkner, Lewkowycz and Maldacena. This formula is generalized to include perturbative quantum corrections in the bulk at any (finite) order. Hurdles to spacetime emergence from entanglement entropy as described by HRT and its quantum
Revisit emission spectrum and entropy quantum of the Reissner-Nordstroem black hole
International Nuclear Information System (INIS)
Jiang, Qing-Quan
2012-01-01
Banerjee and Majhi's recent work shows that black hole's emission spectrum could be fully reproduced in the tunneling picture, where, as an intriguing technique, the Kruskal extension was introduced to connect the left and right modes inside and outside the horizon. Some attempt, as an extension, was focused on producing the Hawking emission spectrum of the (charged) Reissner-Nordstroem black hole in the Banerjee-Majhi treatment. Unfortunately, the Kruskal extension in their observation was so badly defined that the ingoing mode was classically forbidden traveling towards the center of black hole, but could quantum tunnel across the horizon with the probability Γ=e -πω 0 /κ + . This tunneling picture is unphysical. With this point as a central motivation, in this paper we first introduce such a suitable Kruskal extension for the (charged) Reissner-Nordstroem black hole that a perfect tunneling picture can be provided during the charged particle's emission. Then, under the new Kruskal extension, we revisit the Hawking emission spectrum and entropy spectroscopy as tunneling from the charged black hole. The result shows that the tunneling method is so universally robust that the Hawking blackbody emission spectrum from a charged black hole can be well reproduced in the tunneling mechanism, and its induced entropy quantum is a much better approximation for the forthcoming quantum gravity theory. (orig.)
Shortening a loop can increase protein native state entropy.
Gavrilov, Yulian; Dagan, Shlomi; Levy, Yaakov
2015-12-01
Protein loops are essential structural elements that influence not only function but also protein stability and folding rates. It was recently reported that shortening a loop in the AcP protein may increase its native state conformational entropy. This effect on the entropy of the folded state can be much larger than the lower entropic penalty of ordering a shorter loop upon folding, and can therefore result in a more pronounced stabilization than predicted by polymer model for loop closure entropy. In this study, which aims at generalizing the effect of loop length shortening on native state dynamics, we use all-atom molecular dynamics simulations to study how gradual shortening a very long or solvent-exposed loop region in four different proteins can affect their stability. For two proteins, AcP and Ubc7, we show an increase in native state entropy in addition to the known effect of the loop length on the unfolded state entropy. However, for two permutants of SH3 domain, shortening a loop results only with the expected change in the entropy of the unfolded state, which nicely reproduces the observed experimental stabilization. Here, we show that an increase in the native state entropy following loop shortening is not unique to the AcP protein, yet nor is it a general rule that applies to all proteins following the truncation of any loop. This modification of the loop length on the folded state and on the unfolded state may result with a greater effect on protein stability. © 2015 Wiley Periodicals, Inc.
The spatial relation between the event horizon and trapping horizon
International Nuclear Information System (INIS)
Nielsen, Alex B
2010-01-01
The relation between event horizons and trapping horizons is investigated in a number of different situations with emphasis on their role in thermodynamics. A notion of constant change is introduced that in certain situations allows the location of the event horizon to be found locally. When the black hole is accreting matter the difference in area between the two different horizons can be many orders of magnitude larger than the Planck area. When the black hole is evaporating, the difference is small on the Planck scale. A model is introduced that shows how trapping horizons can be expected to appear outside the event horizon before the black hole starts to evaporate. Finally, a modified definition is introduced to invariantly define the location of the trapping horizon under a conformal transformation. In this case the trapping horizon is not always a marginally outer trapped surface.
Solomentsev, Gleb; Diehl, Carl; Akke, Mikael
2018-03-06
FKBP12 (FK506 binding protein 12 kDa) is an important drug target. Nuclear magnetic resonance (NMR) order parameters, describing amplitudes of motion on the pico- to nanosecond time scale, can provide estimates of changes in conformational entropy upon ligand binding. Here we report backbone and methyl-axis order parameters of the apo and FK506-bound forms of FKBP12, based on 15 N and 2 H NMR relaxation. Binding of FK506 to FKBP12 results in localized changes in order parameters, notably for the backbone of residues E54 and I56 and the side chains of I56, I90, and I91, all positioned in the binding site. The order parameters increase slightly upon FK506 binding, indicating an unfavorable entropic contribution to binding of TΔ S = -18 ± 2 kJ/mol at 293 K. Molecular dynamics simulations indicate a change in conformational entropy, associated with all dihedral angles, of TΔ S = -26 ± 9 kJ/mol. Both these values are significant compared to the total entropy of binding determined by isothermal titration calorimetry and referenced to a reactant concentration of 1 mM ( TΔ S = -29 ± 1 kJ/mol). Our results reveal subtle differences in the response to ligand binding compared to that of the previously studied rapamycin-FKBP12 complex, despite the high degree of structural homology between the two complexes and their nearly identical ligand-FKBP12 interactions. These results highlight the delicate dependence of protein dynamics on drug interactions, which goes beyond the view provided by static structures, and reinforce the notion that protein conformational entropy can make important contributions to the free energy of ligand binding.
Entropy Coherent and Entropy Convex Measures of Risk
Laeven, R.J.A.; Stadje, M.A.
2011-01-01
We introduce two subclasses of convex measures of risk, referred to as entropy coherent and entropy convex measures of risk. We prove that convex, entropy convex and entropy coherent measures of risk emerge as certainty equivalents under variational, homothetic and multiple priors preferences,
Spatial-dependence recurrence sample entropy
Pham, Tuan D.; Yan, Hong
2018-03-01
Measuring complexity in terms of the predictability of time series is a major area of research in science and engineering, and its applications are spreading throughout many scientific disciplines, where the analysis of physiological signals is perhaps the most widely reported in literature. Sample entropy is a popular measure for quantifying signal irregularity. However, the sample entropy does not take sequential information, which is inherently useful, into its calculation of sample similarity. Here, we develop a method that is based on the mathematical principle of the sample entropy and enables the capture of sequential information of a time series in the context of spatial dependence provided by the binary-level co-occurrence matrix of a recurrence plot. Experimental results on time-series data of the Lorenz system, physiological signals of gait maturation in healthy children, and gait dynamics in Huntington's disease show the potential of the proposed method.
Entropy coherent and entropy convex measures of risk
Laeven, Roger; Stadje, M.A.
2010-01-01
We introduce entropy coherent and entropy convex measures of risk and prove a collection of axiomatic characterization and duality results. We show in particular that entropy coherent and entropy convex measures of risk emerge as negative certainty equivalents in (the regular and a generalized
Kadanoff, Leo P.
2017-05-01
The science of thermodynamics was put together in the Nineteenth Century to describe large systems in equilibrium. One part of thermodynamics defines entropy for equilibrium systems and demands an ever-increasing entropy for non-equilibrium ones. Since thermodynamics does not define entropy out of equilibrium, pure thermodynamics cannot follow the details of how this increase occurs. However, starting with the work of Ludwig Boltzmann in 1872, and continuing to the present day, various models of non-equilibrium behavior have been put together with the specific aim of generalizing the concept of entropy to non-equilibrium situations. This kind of entropy has been termed kinetic entropy to distinguish it from the thermodynamic variety. Knowledge of kinetic entropy started from Boltzmann's insight about his equation for the time dependence of gaseous systems. In this paper, his result is stated as a definition of kinetic entropy in terms of a local equation for the entropy density. This definition is then applied to Landau's theory of the Fermi liquid thereby giving the kinetic entropy within that theory. The dynamics of many condensed matter systems including Fermi liquids, low temperature superfluids, and ordinary metals lend themselves to the definition of kinetic entropy. In fact, entropy has been defined and used for a wide variety of situations in which a condensed matter system has been allowed to relax for a sufficient period so that the very most rapid fluctuations have been ironed out. One of the broadest applications of non-equilibrium analysis considers quantum degenerate systems using Martin-Schwinger Green's functions (Phys Rev 115:1342-1373, 1959) as generalized Wigner functions, g^({p},ω ,{R},T). This paper describes once again how the quantum kinetic equations for these functions give locally defined conservation laws for mass momentum and energy. In local thermodynamic equilibrium, this kinetic theory enables a reasonable definition of the density
Near horizon structure of extremal vanishing horizon black holes
Directory of Open Access Journals (Sweden)
S. Sadeghian
2015-11-01
Full Text Available We study the near horizon structure of Extremal Vanishing Horizon (EVH black holes, extremal black holes with vanishing horizon area with a vanishing one-cycle on the horizon. We construct the most general near horizon EVH and near-EVH ansatz for the metric and other fields, like dilaton and gauge fields which may be present in the theory. We prove that (1 the near horizon EVH geometry for generic gravity theory in generic dimension has a three dimensional maximally symmetric subspace; (2 if the matter fields of the theory satisfy strong energy condition either this 3d part is AdS3, or the solution is a direct product of a locally 3d flat space and a d−3 dimensional part; (3 these results extend to the near horizon geometry of near-EVH black holes, for which the AdS3 part is replaced with BTZ geometry. We present some specific near horizon EVH geometries in 3, 4 and 5 dimensions for which there is a classification. We also briefly discuss implications of these generic results for generic (gauged supergravity theories and also for the thermodynamics of near-EVH black holes and the EVH/CFT proposal.
Entropy localization and extensivity in the semiclassical black hole evaporation
International Nuclear Information System (INIS)
Casini, H.
2009-01-01
I aim to quantify the distribution of information in the Hawking radiation and inside the black hole in the semiclassical evaporation process. The structure of relativistic quantum field theory does not allow one to define a localized entropy unambiguously, but rather forces one to consider the shared information (mutual information) between two different regions of space-time. Using this tool, I first show that the entropy of a thermal gas at the Unruh temperature underestimates the actual amount of (shared) information present in a region of the Rindler space. Then, I analyze the mutual information between the black hole and the late time radiation region. A well-known property of the entropy implies that this is monotonically increasing with time. This means that in the semiclassical picture it is not possible to recover the eventual purity of the initial state in the final Hawking radiation through subtle correlations established during the whole evaporation period, no matter the interactions present in the theory. I find extensivity of the entropy as a consequence of a reduction to a two dimensional conformal problem in a simple approximation. However, the extensivity of information in the radiation region in a full four dimensional calculation seems not to be guaranteed on general grounds. I also analyze the localization of shared information inside the black hole finding that a large amount of it is contained in a small, approximately flat region of space-time near the point where the horizon begins. This gives place to large violations of the entropy bounds. I show that this problem is not eased by backscattering effects and argue that a breaking of conformal invariance is necessary to delocalize the entropy. Finally, I indicate that the mutual information could lead to a way to understand the Bekenstein-Hawking black hole entropy which does not require a drastic reduction in degrees of freedom in order to regulate the entanglement entropy. On the contrary
Entropy coherent and entropy convex measures of risk
Laeven, R.J.A.; Stadje, M.
2013-01-01
We introduce two subclasses of convex measures of risk, referred to as entropy coherent and entropy convex measures of risk. Entropy coherent and entropy convex measures of risk are special cases of φ-coherent and φ-convex measures of risk. Contrary to the classical use of coherent and convex
Zucker, M. H.
temperature and thus, by itself; reverse entropy. The vast encompassing gravitational forces that the universe has at its disposal, forces that dominate the phase of contraction, provide the compacting, compressive mechanism that regenerates heat in an expanded, cooled universe and decreases entropy. And this phenomenon takes place without diminishing or depleting the finite amount of mass/energy with which the universe began. The fact that the universe can reverse the entropic process leads to possibilities previously ignored when assessing which of the three models (open, closed, of flat) most probably represents the future of the universe. After analyzing the models, the conclusion reached here is that the open model is only an expanded version of the closed model and therefore is not open, and the closed model will never collapse to a big crunch and, therefore, is not closed. Which leaves a modified model, oscillating forever between limited phases of expansion and contraction (a universe in "dynamic equilibrium") as the only feasible choice.
Infinite-horizon optimal control problems in economics
International Nuclear Information System (INIS)
Aseev, Sergei M; Besov, Konstantin O; Kryazhimskii, Arkadii V
2012-01-01
This paper extends optimal control theory to a class of infinite-horizon problems that arise in studying models of optimal dynamic allocation of economic resources. In a typical problem of this sort the initial state is fixed, no constraints are imposed on the behaviour of the admissible trajectories at large times, and the objective functional is given by a discounted improper integral. We develop the method of finite-horizon approximations in a broad context and use it to derive complete versions of the Pontryagin maximum principle for such problems. We provide sufficient conditions for the normality of infinite-horizon optimal control problems and for the validity of the 'standard' limit transversality conditions with time going to infinity. As a meaningful example, we consider a new two-sector model of optimal economic growth subject to a random jump in prices. Bibliography: 53 titles.
Dynamical regimes due to technological change in a microeconomical model of production
Hamacher, K.
2012-09-01
We develop a microeconomical model to investigate the impact of technological change onto production decisions of suppliers—modeling an effective feedback mechanism of the market. An important property—the time horizon of production planning—is related to the Kolmogorov entropy of the one-dimensional maps describing price dynamics. We simulate this price dynamics in an ensemble representing the whole macroeconomy. We show how this model can be used to support ongoing research in economic growth and incorporate the obtained microeconomic findings into the discussion about appropriate macroeconomic quantities such as the production function—thus effectively underpinning macroeconomics with microeconomical dynamics. From there we can show that the model exhibits different dynamical regimes (suggesting "phase transitions") with respect to an order parameter. The non-linear feedback under technological change was found to be the crucial mechanism. The implications of the obtained regimes are finally discussed.
The first law of black hole mechanics for fields with internal gauge freedom
International Nuclear Information System (INIS)
Prabhu, Kartik
2017-01-01
We derive the first law of black hole mechanics for physical theories based on a local, covariant and gauge-invariant Lagrangian where the dynamical fields transform non-trivially under the action of some internal gauge transformations. The theories of interest include General Relativity formulated in terms of tetrads, Einstein–Yang–Mills theory and Einstein–Dirac theory. Since the dynamical fields of these theories have some internal gauge freedom, we argue that there is no natural group action of diffeomorphisms of spacetime on such dynamical fields. In general, such fields cannot even be represented as smooth, globally well-defined tensor fields on spacetime. Consequently the derivation of the first law by Iyer and Wald cannot be used directly. Nevertheless, we show how such theories can be formulated on a principal bundle and that there is a natural action of automorphisms of the bundle on the fields. These bundle automorphisms encode both spacetime diffeomorphisms and internal gauge transformations. Using this reformulation we define the Noether charge associated to an infinitesimal automorphism and the corresponding notion of stationarity and axisymmetry of the dynamical fields. We first show that we can define certain potentials and charges at the horizon of a black hole so that the potentials are constant on the bifurcate Killing horizon, giving a generalised zeroth law for bifurcate Killing horizons. We further identify the gravitational potential and perturbed charge as the temperature and perturbed entropy of the black hole which gives an explicit formula for the perturbed entropy analogous to the Wald entropy formula. We then obtain a general first law of black hole mechanics for such theories. The first law relates the perturbed Hamiltonians at spatial infinity and the horizon, and the horizon contributions take the form of a ‘potential times perturbed charge’ term. We also comment on the ambiguities in defining a prescription for the total
International Nuclear Information System (INIS)
Diehl, Carl; Genheden, Samuel; Modig, Kristofer; Ryde, Ulf; Akke, Mikael
2009-01-01
The conformational entropy of proteins can make significant contributions to the free energy of ligand binding. NMR spin relaxation enables site-specific investigation of conformational entropy, via order parameters that parameterize local reorientational fluctuations of rank-2 tensors. Here we have probed the conformational entropy of lactose binding to the carbohydrate recognition domain of galectin-3 (Gal3), a protein that plays an important role in cell growth, cell differentiation, cell cycle regulation, and apoptosis, making it a potential target for therapeutic intervention in inflammation and cancer. We used 15 N spin relaxation experiments and molecular dynamics simulations to monitor the backbone amides and secondary amines of the tryptophan and arginine side chains in the ligand-free and lactose-bound states of Gal3. Overall, we observe good agreement between the experimental and computed order parameters of the ligand-free and lactose-bound states. Thus, the 15 N spin relaxation data indicate that the molecular dynamics simulations provide reliable information on the conformational entropy of the binding process. The molecular dynamics simulations reveal a correlation between the simulated order parameters and residue-specific backbone entropy, re-emphasizing that order parameters provide useful estimates of local conformational entropy. The present results show that the protein backbone exhibits an increase in conformational entropy upon binding lactose, without any accompanying structural changes
Generalized Entanglement Entropies of Quantum Designs
Liu, Zi-Wen; Lloyd, Seth; Zhu, Elton Yechao; Zhu, Huangjun
2018-03-01
The entanglement properties of random quantum states or dynamics are important to the study of a broad spectrum of disciplines of physics, ranging from quantum information to high energy and many-body physics. This Letter investigates the interplay between the degrees of entanglement and randomness in pure states and unitary channels. We reveal strong connections between designs (distributions of states or unitaries that match certain moments of the uniform Haar measure) and generalized entropies (entropic functions that depend on certain powers of the density operator), by showing that Rényi entanglement entropies averaged over designs of the same order are almost maximal. This strengthens the celebrated Page's theorem. Moreover, we find that designs of an order that is logarithmic in the dimension maximize all Rényi entanglement entropies and so are completely random in terms of the entanglement spectrum. Our results relate the behaviors of Rényi entanglement entropies to the complexity of scrambling and quantum chaos in terms of the degree of randomness, and suggest a generalization of the fast scrambling conjecture.
Three theorems on near horizon extremal vanishing horizon geometries
Directory of Open Access Journals (Sweden)
S. Sadeghian
2016-02-01
Full Text Available EVH black holes are Extremal black holes with Vanishing Horizon area, where vanishing of horizon area is a result of having a vanishing one-cycle on the horizon. We prove three theorems regarding near horizon geometry of EVH black hole solutions to generic Einstein gravity theories in diverse dimensions. These generic gravity theories are Einstein–Maxwell-dilaton-Λ theories, and gauged or ungauged supergravity theories with U(1 Maxwell fields. Our three theorems are: (1 The near horizon geometry of any EVH black hole has a three dimensional maximally symmetric subspace. (2 If the energy momentum tensor of the theory satisfies strong energy condition either this 3d part is an AdS3, or the solution is a direct product of a locally 3d flat space and a d−3 dimensional part. (3 These results extend to the near horizon geometry of near-EVH black holes, for which the AdS3 part is replaced with BTZ geometry.
International Nuclear Information System (INIS)
Gupta, Rajesh Kumar; Ito, Yuto; Jeon, Imtak
2015-01-01
We use the techniques of supersymmetric localization to compute the BPS black hole entropy in N=2 supergravity. We focus on the n_v+1 vector multiplets on the black hole near horizon background which is AdS_2× S"2 space. We find the localizing saddle point of the vector multiplets by solving the localization equations, and compute the exact one-loop partition function on the saddle point. Furthermore, we propose the appropriate functional integration measure. Through this measure, the one-loop determinant is written in terms of the radius of the physical metric, which depends on the localizing saddle point value of the vector multiplets. The result for the one-loop determinant is consistent with the logarithmic corrections to the BPS black hole entropy from vector multiplets.
Using Link Disconnection Entropy Disorder to Detect Fast Moving Nodes in MANETs.
Alvarez, Carlos F; Palafox, Luis E; Aguilar, Leocundo; Sanchez, Mauricio A; Martinez, Luis G
2016-01-01
Mobile ad-hoc networks (MANETs) are dynamic by nature; this dynamism comes from node mobility, traffic congestion, and other transmission conditions. Metrics to evaluate the effects of those conditions shine a light on node's behavior in an ad-hoc network, helping to identify the node or nodes with better conditions of connection. In this paper, we propose a relative index to evaluate a single node reliability, based on the link disconnection entropy disorder using neighboring nodes as reference. Link disconnection entropy disorder is best used to identify fast moving nodes or nodes with unstable communications, this without the need of specialized sensors such as GPS. Several scenarios were studied to verify the index, measuring the effects of Speed and traffic density on the link disconnection entropy disorder. Packet delivery ratio is associated to the metric detecting a strong relationship, enabling the use of the link disconnection entropy disorder to evaluate the stability of a node to communicate with other nodes. To expand the utilization of the link entropy disorder, we identified nodes with higher speeds in network simulations just by using the link entropy disorder.
Thermodynamics in modified Brans-Dicke gravity with entropy corrections
Energy Technology Data Exchange (ETDEWEB)
Rani, Shamaila; Jawad, Abdul; Nawaz, Tanzeela [COMSATS Institute of Information Technology, Department of Mathematics, Lahore (Pakistan); Manzoor, Rubab [University of Management and Technology, Department of Mathematics, Lahore (Pakistan)
2018-01-15
In this paper, we investigate the thermodynamics in the frame-work of recently proposed theory called modified Brans-Dicke gravity (Kofinas et al. in Class Quantum Gravity 33:15, 2016). For this purpose, we develop the generalized second law of thermodynamics by assuming usual entropy as well as its corrected forms (logarithmic and power law corrected) on the apparent and event horizons. In order to analyzed the clear view of thermodynamic law, the power law forms of scalar field and scale factor is being assumed. We evaluate the results graphically and found that generalized second law of thermodynamics holds in most of the cases. (orig.)
Thermodynamics in modified Brans-Dicke gravity with entropy corrections
International Nuclear Information System (INIS)
Rani, Shamaila; Jawad, Abdul; Nawaz, Tanzeela; Manzoor, Rubab
2018-01-01
In this paper, we investigate the thermodynamics in the frame-work of recently proposed theory called modified Brans-Dicke gravity (Kofinas et al. in Class Quantum Gravity 33:15, 2016). For this purpose, we develop the generalized second law of thermodynamics by assuming usual entropy as well as its corrected forms (logarithmic and power law corrected) on the apparent and event horizons. In order to analyzed the clear view of thermodynamic law, the power law forms of scalar field and scale factor is being assumed. We evaluate the results graphically and found that generalized second law of thermodynamics holds in most of the cases. (orig.)
Valenza, Gaetano; Faes, Luca; Citi, Luca; Orini, Michele; Barbieri, Riccardo
2018-05-01
Measures of transfer entropy (TE) quantify the direction and strength of coupling between two complex systems. Standard approaches assume stationarity of the observations, and therefore are unable to track time-varying changes in nonlinear information transfer with high temporal resolution. In this study, we aim to define and validate novel instantaneous measures of TE to provide an improved assessment of complex nonstationary cardiorespiratory interactions. We here propose a novel instantaneous point-process TE (ipTE) and validate its assessment as applied to cardiovascular and cardiorespiratory dynamics. In particular, heartbeat and respiratory dynamics are characterized through discrete time series, and modeled with probability density functions predicting the time of the next physiological event as a function of the past history. Likewise, nonstationary interactions between heartbeat and blood pressure dynamics are characterized as well. Furthermore, we propose a new measure of information transfer, the instantaneous point-process information transfer (ipInfTr), which is directly derived from point-process-based definitions of the Kolmogorov-Smirnov distance. Analysis on synthetic data, as well as on experimental data gathered from healthy subjects undergoing postural changes confirms that ipTE, as well as ipInfTr measures are able to dynamically track changes in physiological systems coupling. This novel approach opens new avenues in the study of hidden, transient, nonstationary physiological states involving multivariate autonomic dynamics in cardiovascular health and disease. The proposed method can also be tailored for the study of complex multisystem physiology (e.g., brain-heart or, more in general, brain-body interactions).
The two event horizons - an apparent contribution of vacuum to gravitation
International Nuclear Information System (INIS)
Dinculescu, A.
1994-01-01
Our possibilities of investigation are limited by two horizons: a local one - the black hole horizon R 0 , and the global one - the cosmic horizon R u . Till now, only the first horizon has been taken into consideration as a measure of the curvature of space near a massive body. It is argued that in order to satisfy Mach's principle when characterizing matter in a point relative to a center of mass, one has to take into consideration both event horizons. Accordingly, a local cosmological term Λ * =(R 0 R u ) -1 is defined as a combination of the above horizons in a given point. The corresponding non-dimensional coefficient ξ=Λ * R 2 is an indicator of the position of a mass point between the two event horizons. When taking into account as a contribution of vacuum energy to the gravitational field it restores the low of conservation of energy in an expanding universe, and explains the dynamics of galaxies and clusters of galaxies without resorting to the 'dark matter' hypothesis. (Author) 3 Tabs., 38 Refs
Perturbation of Fractional Multi-Agent Systems in Cloud Entropy Computing
Directory of Open Access Journals (Sweden)
Rabha W. Ibrahim
2016-01-01
Full Text Available A perturbed multi-agent system is a scheme self-possessed of multiple networking agents within a location. This scheme can be used to discuss problems that are impossible or difficult for a specific agent to solve. Intelligence cloud entropy management systems involve functions, methods, procedural approaches, and algorithms. In this study, we introduce a new perturbed algorithm based on the fractional Poisson process. The discrete dynamics are suggested by using fractional entropy and fractional type Tsallis entropy. Moreover, we study the algorithm stability.
ENTROPY FUNCTIONAL FOR CONTINUOUS SYSTEMS OF FINITE ENTROPY
Institute of Scientific and Technical Information of China (English)
M. Rahimi A. Riazi
2012-01-01
In this article,we introduce the concept of entropy functional for continuous systems on compact metric spaces,and prove some of its properties.We also extract the Kolmogorov entropy from the entropy functional.
International Nuclear Information System (INIS)
Gutierrez, Rafael M.; Useche, Gina M.; Buitrago, Elias
2007-01-01
We present a procedure developed to detect stochastic and deterministic information contained in empirical time series, useful to characterize and make models of different aspects of complex phenomena represented by such data. This procedure is applied to a seismological time series to obtain new information to study and understand geological phenomena. We use concepts and methods from nonlinear dynamics and maximum entropy. The mentioned method allows an optimal analysis of the available information
Entropy of the Mixture of Sources and Entropy Dimension
Smieja, Marek; Tabor, Jacek
2011-01-01
We investigate the problem of the entropy of the mixture of sources. There is given an estimation of the entropy and entropy dimension of convex combination of measures. The proof is based on our alternative definition of the entropy based on measures instead of partitions.
Infinite-horizon optimal control problems in economics
Energy Technology Data Exchange (ETDEWEB)
Aseev, Sergei M; Besov, Konstantin O; Kryazhimskii, Arkadii V
2012-04-30
This paper extends optimal control theory to a class of infinite-horizon problems that arise in studying models of optimal dynamic allocation of economic resources. In a typical problem of this sort the initial state is fixed, no constraints are imposed on the behaviour of the admissible trajectories at large times, and the objective functional is given by a discounted improper integral. We develop the method of finite-horizon approximations in a broad context and use it to derive complete versions of the Pontryagin maximum principle for such problems. We provide sufficient conditions for the normality of infinite-horizon optimal control problems and for the validity of the 'standard' limit transversality conditions with time going to infinity. As a meaningful example, we consider a new two-sector model of optimal economic growth subject to a random jump in prices. Bibliography: 53 titles.
The Shannon entropy as a measure of diffusion in multidimensional dynamical systems
Giordano, C. M.; Cincotta, P. M.
2018-05-01
In the present work, we introduce two new estimators of chaotic diffusion based on the Shannon entropy. Using theoretical, heuristic and numerical arguments, we show that the entropy, S, provides a measure of the diffusion extent of a given small initial ensemble of orbits, while an indicator related with the time derivative of the entropy, S', estimates the diffusion rate. We show that in the limiting case of near ergodicity, after an appropriate normalization, S' coincides with the standard homogeneous diffusion coefficient. The very first application of this formulation to a 4D symplectic map and to the Arnold Hamiltonian reveals very successful and encouraging results.
Short-horizon regulation for long-term investors
Shi, Z.; Werker, B.J.M.
2012-01-01
We study the effects of imposing repeated short-horizon regulatory constraints on long-term investors. We show that Value-at-Risk and Expected Shortfall constraints, when imposed dynamically, lead to similar optimal portfolios and wealth distributions. We also show that, in utility terms, the costs
Entropy generation and inflation in collision induced pre-big-bang cosmology
Feinstein, A.; Kunze, K.E.; Vazquez-Mozo, M.A.
2000-01-01
We study inflation and entropy generation in a recently proposed pre-big-bang model universe produced in a collision of gravitational and dilaton waves. It is shown that enough inflation occurs provided the incoming waves are sufficiently weak. We also find that entropy in this model is dynamically
Von Neumann entropy in a Rashba-Dresselhaus nanodot; dynamical electronic spin-orbit entanglement
Safaiee, Rosa; Golshan, Mohammad Mehdi
2017-06-01
The main purpose of the present article is to report the characteristics of von Neumann entropy, thereby, the electronic hybrid entanglement, in the heterojunction of two semiconductors, with due attention to the Rashba and Dresselhaus spin-orbit interactions. To this end, we cast the von Neumann entropy in terms of spin polarization and compute its time evolution; with a vast span of applications. It is assumed that gate potentials are applied to the heterojunction, providing a two dimensional parabolic confining potential (forming an isotropic nanodot at the junction), as well as means of controlling the spin-orbit couplings. The spin degeneracy is also removed, even at electronic zero momentum, by the presence of an external magnetic field which, in turn, leads to the appearance of Landau states. We then proceed by computing the time evolution of the corresponding von Neumann entropy from a separable (spin-polarized) initial state. The von Neumann entropy, as we show, indicates that electronic hybrid entanglement does occur between spin and two-dimensional Landau levels. Our results also show that von Neumann entropy, as well as the degree of spin-orbit entanglement, periodically collapses and revives. The characteristics of such behavior; period, amplitude, etc., are shown to be determined from the controllable external agents. Moreover, it is demonstrated that the phenomenon of collapse-revivals' in the behavior of von Neumann entropy, equivalently, electronic hybrid entanglement, is accompanied by plateaus (of great importance in quantum computation schemes) whose durations are, again, controlled by the external elements. Along these lines, we also make a comparison between effects of the two spin-orbit couplings on the entanglement (von Neumann entropy) characteristics. The finer details of the electronic hybrid entanglement, which may be easily verified through spin polarization measurements, are also accreted and discussed. The novel results of the present
Entropies from Markov Models as Complexity Measures of Embedded Attractors
Directory of Open Access Journals (Sweden)
Julián D. Arias-Londoño
2015-06-01
Full Text Available This paper addresses the problem of measuring complexity from embedded attractors as a way to characterize changes in the dynamical behavior of different types of systems with a quasi-periodic behavior by observing their outputs. With the aim of measuring the stability of the trajectories of the attractor along time, this paper proposes three new estimations of entropy that are derived from a Markov model of the embedded attractor. The proposed estimators are compared with traditional nonparametric entropy measures, such as approximate entropy, sample entropy and fuzzy entropy, which only take into account the spatial dimension of the trajectory. The method proposes the use of an unsupervised algorithm to find the principal curve, which is considered as the “profile trajectory”, that will serve to adjust the Markov model. The new entropy measures are evaluated using three synthetic experiments and three datasets of physiological signals. In terms of consistency and discrimination capabilities, the results show that the proposed measures perform better than the other entropy measures used for comparison purposes.
Entanglement entropy and differential entropy for massive flavors
International Nuclear Information System (INIS)
Jones, Peter A.R.; Taylor, Marika
2015-01-01
In this paper we compute the holographic entanglement entropy for massive flavors in the D3-D7 system, for arbitrary mass and various entangling region geometries. We show that the universal terms in the entanglement entropy exactly match those computed in the dual theory using conformal perturbation theory. We derive holographically the universal terms in the entanglement entropy for a CFT perturbed by a relevant operator, up to second order in the coupling; our results are valid for any entangling region geometry. We present a new method for computing the entanglement entropy of any top-down brane probe system using Kaluza-Klein holography and illustrate our results with massive flavors at finite density. Finally we discuss the differential entropy for brane probe systems, emphasising that the differential entropy captures only the effective lower-dimensional Einstein metric rather than the ten-dimensional geometry.
Black holes or firewalls: A theory of horizons
Nomura, Yasunori; Varela, Jaime; Weinberg, Sean J.
2013-10-01
We present a quantum theory of black hole (and other) horizons, in which the standard assumptions of complementarity are preserved without contradicting information theoretic considerations. After the scrambling time, the quantum mechanical structure of a black hole becomes that of an eternal black hole at the microscopic level. In particular, the stretched horizon degrees of freedom and the states entangled with them can be mapped into the near-horizon modes in the two exterior regions of an eternal black hole, whose mass is taken to be that of the evolving black hole at each moment. Salient features arising from this picture include (i) the number of degrees of freedom needed to describe a black hole is eA/2lP2, where A is the area of the horizon; (ii) black hole states having smooth horizons, however, span only an eA/4lP2-dimensional subspace of the relevant eA/2lP2-dimensional Hilbert space; (iii) internal dynamics of the horizon is such that an infalling observer finds a smooth horizon with a probability of 1 if a state stays in this subspace. We identify the structure of local operators responsible for describing semiclassical physics in the exterior and interior spacetime regions and show that this structure avoids the arguments for firewalls—the horizon can keep being smooth throughout the evolution. We discuss the fate of infalling observers under various circumstances, especially when the observers manipulate degrees of freedom before entering the horizon, and we find that an observer can never see a firewall by making a measurement on early Hawking radiation. We also consider the presented framework from the viewpoint of an infalling reference frame and argue that Minkowski-like vacua are not unique. In particular, the number of true Minkowski vacua is infinite, although the label discriminating these vacua cannot be accessed in usual nongravitational quantum field theory. An application of the framework to de Sitter horizons is also discussed.
Multi-scale symbolic transfer entropy analysis of EEG
Yao, Wenpo; Wang, Jun
2017-10-01
From both global and local perspectives, we symbolize two kinds of EEG and analyze their dynamic and asymmetrical information using multi-scale transfer entropy. Multi-scale process with scale factor from 1 to 199 and step size of 2 is applied to EEG of healthy people and epileptic patients, and then the permutation with embedding dimension of 3 and global approach are used to symbolize the sequences. The forward and reverse symbol sequences are taken as the inputs of transfer entropy. Scale factor intervals of permutation and global way are (37, 57) and (65, 85) where the two kinds of EEG have satisfied entropy distinctions. When scale factor is 67, transfer entropy of the healthy and epileptic subjects of permutation, 0.1137 and 0.1028, have biggest difference. And the corresponding values of the global symbolization is 0.0641 and 0.0601 which lies in the scale factor of 165. Research results show that permutation which takes contribution of local information has better distinction and is more effectively applied to our multi-scale transfer entropy analysis of EEG.
Connecting diffusion and entropy of bulk water at the single particle ...
Indian Academy of Sciences (India)
The relation between the dynamic (e.g., diffusion) and thermodynamic (e.g., entropy) properties of water and water-like liquids has been an active area of research for a long time. Although several studies have investigated the diffusivity and entropy for different systems, these studies have probed either the configurational ...
Bubble Entropy: An Entropy Almost Free of Parameters.
Manis, George; Aktaruzzaman, Md; Sassi, Roberto
2017-11-01
Objective : A critical point in any definition of entropy is the selection of the parameters employed to obtain an estimate in practice. We propose a new definition of entropy aiming to reduce the significance of this selection. Methods: We call the new definition Bubble Entropy . Bubble Entropy is based on permutation entropy, where the vectors in the embedding space are ranked. We use the bubble sort algorithm for the ordering procedure and count instead the number of swaps performed for each vector. Doing so, we create a more coarse-grained distribution and then compute the entropy of this distribution. Results: Experimental results with both real and synthetic HRV signals showed that bubble entropy presents remarkable stability and exhibits increased descriptive and discriminating power compared to all other definitions, including the most popular ones. Conclusion: The definition proposed is almost free of parameters. The most common ones are the scale factor r and the embedding dimension m . In our definition, the scale factor is totally eliminated and the importance of m is significantly reduced. The proposed method presents increased stability and discriminating power. Significance: After the extensive use of some entropy measures in physiological signals, typical values for their parameters have been suggested, or at least, widely used. However, the parameters are still there, application and dataset dependent, influencing the computed value and affecting the descriptive power. Reducing their significance or eliminating them alleviates the problem, decoupling the method from the data and the application, and eliminating subjective factors. Objective : A critical point in any definition of entropy is the selection of the parameters employed to obtain an estimate in practice. We propose a new definition of entropy aiming to reduce the significance of this selection. Methods: We call the new definition Bubble Entropy . Bubble Entropy is based on permutation
Weakly Isolated horizons: first order actions and gauge symmetries
Corichi, Alejandro; Reyes, Juan D.; Vukašinac, Tatjana
2017-04-01
The notion of Isolated Horizons has played an important role in gravitational physics, being useful from the characterization of the endpoint of black hole mergers to (quantum) black hole entropy. With an eye towards a canonical formulation we consider general relativity in terms of connection and vierbein variables and their corresponding first order actions. We focus on two main issues: (i) The role of the internal gauge freedom that exists, in the consistent formulations of the action principle, and (ii) the role that a 3 + 1 canonical decomposition has in the allowed internal gauge freedom. More concretely, we clarify in detail how the requirement of having well posed variational principles compatible with general weakly isolated horizons (WIHs) as internal boundaries does lead to a partial gauge fixing in the first order descriptions used previously in the literature. We consider the standard Hilbert-Palatini action together with the Holst extension (needed for a consistent 3 + 1 decomposition), with and without boundary terms at the horizon. We show in detail that, for the complete configuration space—with no gauge fixing—, while the Palatini action is differentiable without additional surface terms at the inner WIH boundary, the more general Holst action is not. The introduction of a surface term at the horizon—that renders the action for asymptotically flat configurations differentiable—does make the Holst action differentiable, but only if one restricts the configuration space and partially reduces the internal Lorentz gauge. For the second issue at hand, we show that upon performing a 3 + 1 decomposition and imposing the time gauge, there is a further gauge reduction of the Hamiltonian theory in terms of Ashtekar-Barbero variables to a U(1)-gauge theory on the horizon. We also extend our analysis to the more restricted boundary conditions of (strongly) isolated horizons as inner boundary. We show that even when the
Weakly Isolated horizons: first order actions and gauge symmetries
International Nuclear Information System (INIS)
Corichi, Alejandro; Reyes, Juan D; Vukašinac, Tatjana
2017-01-01
The notion of Isolated Horizons has played an important role in gravitational physics, being useful from the characterization of the endpoint of black hole mergers to (quantum) black hole entropy. With an eye towards a canonical formulation we consider general relativity in terms of connection and vierbein variables and their corresponding first order actions. We focus on two main issues: (i) The role of the internal gauge freedom that exists, in the consistent formulations of the action principle, and (ii) the role that a 3 + 1 canonical decomposition has in the allowed internal gauge freedom. More concretely, we clarify in detail how the requirement of having well posed variational principles compatible with general weakly isolated horizons (WIHs) as internal boundaries does lead to a partial gauge fixing in the first order descriptions used previously in the literature. We consider the standard Hilbert–Palatini action together with the Holst extension (needed for a consistent 3 + 1 decomposition), with and without boundary terms at the horizon. We show in detail that, for the complete configuration space—with no gauge fixing—, while the Palatini action is differentiable without additional surface terms at the inner WIH boundary, the more general Holst action is not. The introduction of a surface term at the horizon—that renders the action for asymptotically flat configurations differentiable—does make the Holst action differentiable, but only if one restricts the configuration space and partially reduces the internal Lorentz gauge. For the second issue at hand, we show that upon performing a 3 + 1 decomposition and imposing the time gauge, there is a further gauge reduction of the Hamiltonian theory in terms of Ashtekar–Barbero variables to a U (1)-gauge theory on the horizon. We also extend our analysis to the more restricted boundary conditions of (strongly) isolated horizons as inner boundary. We show that even when
Energy Technology Data Exchange (ETDEWEB)
Schroer, Bert [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)]|[Institut fuer Theoretische Physik, Berlin (Germany); E-mail schroer@cbpf.br
2003-02-01
Modular theory of operator algebras and the associated K MS property are used to obtain a unified description for the thermal aspects of the standard heat bath situation and those caused by quantum vacuum fluctuations from localization. An algebraic variant of light front holography reveals that the vacuum polarization on wedge horizons is compressed into the light ray direction. Their absence in the transverse direction is the prerequisite to an area (generalized Banknotes-) behavior of entropy-like measures which reveal the loss of purity due to restrictions to wedges and their horizons. Besides the well-known fact that localization-induced (generalized Hawking-) temperature is fixed by the geometric aspects, this area behavior (versus the standard volume dependence) constitutes the main difference between localization-caused and standard thermal behavior. (author)
International Nuclear Information System (INIS)
De Nicola, Sergio; Fedele, Renato; Man'ko, Margarita A; Man'ko, Vladimir I
2007-01-01
The tomographic-probability description of quantum states is reviewed. The symplectic tomography of quantum states with continuous variables is studied. The symplectic entropy of the states with continuous variables is discussed and its relation to Shannon entropy and information is elucidated. The known entropic uncertainty relations of the probability distribution in position and momentum of a particle are extended and new uncertainty relations for symplectic entropy are obtained. The partial case of symplectic entropy, which is optical entropy of quantum states, is considered. The entropy associated to optical tomogram is shown to satisfy the new entropic uncertainty relation. The example of Gaussian states of harmonic oscillator is studied and the entropic uncertainty relations for optical tomograms of the Gaussian state are shown to minimize the uncertainty relation
Resonance transport and kinetic entropy
International Nuclear Information System (INIS)
Ivanov, Yu.B.; Knoll, J.; Voskresensky, D.N.
2000-01-01
We continue the description of the dynamics of unstable particles within the real-time formulation of nonequilibrium field theory initiated in a previous paper . There we suggest to use Baym's PHI-functional method in order to achieve approximation schemes with 'built in' consistency with respect to conservation laws and thermodynamics even in the case of particles with finite damping width. Starting from Kadanoff-Baym equations we discuss a consistent first order gradient approach to transport which preserves the PHI-derivable properties. The validity conditions for the resulting quantum four-phase-space kinetic theory are discussed under the perspective to treat particles with broad damping widths. This non-equilibrium dynamics naturally includes all those quantum features already inherent in the corresponding equilibrium limit (e.g. Matsubara formalism) at the same level of PHI-derivable approximation. Various collision-term diagrams are discussed including those of higher order which lead to memory effects. As an important novel part we derive a generalized nonequilibrium expression for the kinetic entropy flow, which includes contributions from fluctuations and mass-width effects. In special cases an H-theorem is derived implying that the entropy can only increase with time. Memory effects in the kinetic terms provide contributions to the kinetic entropy flow that in the equilibrium limit recover the famous bosonic type T 3 lnT correction to the specific heat in the case of Fermi liquids like Helium-3
The Elusive Nature of Entropy and Its Physical Meaning
Directory of Open Access Journals (Sweden)
Milivoje M. Kostic
2014-02-01
Full Text Available Entropy is the most used and often abused concept in science, but also in philosophy and society. Further confusions are produced by some attempts to generalize entropy with similar but not the same concepts in other disciplines. The physical meaning of phenomenological, thermodynamic entropy is reasoned and elaborated by generalizing Clausius definition with inclusion of generated heat, since it is irrelevant if entropy is changed due to reversible heat transfer or irreversible heat generation. Irreversible, caloric heat transfer is introduced as complementing reversible heat transfer. It is also reasoned and thus proven why entropy cannot be destroyed but is always generated (and thus over-all increased locally and globally, at every space and time scales, without any exception. It is concluded that entropy is a thermal displacement (dynamic thermal-volume of thermal energy due to absolute temperature as a thermal potential (dQ = TdS, and thus associated with thermal heat and absolute temperature, i.e., distribution of thermal energy within thermal micro-particles in space. Entropy is an integral measure of (random thermal energy redistribution (due to heat transfer and/or irreversible heat generation within a material system structure in space, per absolute temperature level: dS = dQSys/T = mCSysdT/T, thus logarithmic integral function, with J/K unit. It may be also expressed as a measure of “thermal disorder”, being related to logarithm of number of all thermal, dynamic microstates W (their position and momenta, S = kBlnW, or to the sum of their logarithmic probabilities S = −kB∑pilnpi, that correspond to, or are consistent with the given thermodynamic macro-state. The number of thermal microstates W, is correlated with macro-properties temperature T and volume V for ideal gases. A system form and/or functional order or disorder are not (thermal energy order/disorder and the former is not related to Thermodynamic entropy. Expanding
Turnpike phenomenon and infinite horizon optimal control
Zaslavski, Alexander J
2014-01-01
This book is devoted to the study of the turnpike phenomenon and describes the existence of solutions for a large variety of infinite horizon optimal control classes of problems. Chapter 1 provides introductory material on turnpike properties. Chapter 2 studies the turnpike phenomenon for discrete-time optimal control problems. The turnpike properties of autonomous problems with extended-value intergrands are studied in Chapter 3. Chapter 4 focuses on large classes of infinite horizon optimal control problems without convexity (concavity) assumptions. In Chapter 5, the turnpike results for a class of dynamic discrete-time two-player zero-sum game are proven. This thorough exposition will be very useful for mathematicians working in the fields of optimal control, the calculus of variations, applied functional analysis, and infinite horizon optimization. It may also be used as a primary text in a graduate course in optimal control or as supplementary text for a variety of courses in other disciplines. Resea...
Siino, Masaru
1997-01-01
The topologies of event horizons are investigated. Considering the existence of the endpoint of the event horizon, it cannot be differentiable. Then there are the new possibilities of the topology of the event horizon though they are excluded in smooth event horizons. The relation between the topology of the event horizon and the endpoint of it is revealed. A torus event horizon is caused by two-dimensional endpoints. One-dimensional endpoints provide the coalescence of spherical event horizo...
Zhang, Eugene
2016-11-28
In this paper we seek to answer the following question: where do contour lines and visible contour lines (silhouette) tend to occur in a 3D surface. Our study leads to two novel shape descriptors, the horizon measure and the visible horizon measure, which we apply to the visualization of 3D shapes including archeological artifacts. In addition to introducing the shape descriptors, we also provide a closed-form formula for the horizon measure based on classical spherical geometry. To compute the visible horizon measure, which depends on the exact computation of the surface visibility function, we instead of provide an image-based approach which can process a model with high complexity within a few minutes.
International Nuclear Information System (INIS)
Monthus, Cécile
2011-01-01
Filyokov and Karpov (1967 Inzh.-Fiz. Zh. 13 624) have proposed a theory of non-equilibrium steady states in direct analogy with the theory of equilibrium states: the principle is to maximize the Shannon entropy associated with the probability distribution of dynamical trajectories in the presence of constraints, including the macroscopic current of interest, via the method of Lagrange multipliers. This maximization leads directly to the generalized Gibbs distribution for the probability distribution of dynamical trajectories, and to some fluctuation relation of the integrated current. The simplest stochastic dynamics where these ideas can be applied are discrete-time Markov chains, defined by transition probabilities W i→j between configurations i and j: instead of choosing the dynamical rules W i→j a priori, one determines the transition probabilities and the associate stationary state that maximize the entropy of dynamical trajectories with the other physical constraints that one wishes to impose. We give a self-contained and unified presentation of this type of approach, both for discrete-time Markov chains and for continuous-time master equations. The obtained results are in full agreement with the Bayesian approach introduced by Evans (2004 Phys. Rev. Lett. 92 150601) under the name 'Non-equilibrium Counterpart to detailed balance', and with the 'invariant quantities' derived by Baule and Evans (2008 Phys. Rev. Lett. 101 240601), but provide a slightly different perspective via the formulation in terms of an eigenvalue problem
Wider horizons, wiser choices: horizon scanning for public health protection and improvement.
Urquhart, Graham J; Saunders, Patrick
2017-06-01
Systematic continuous thinking about the future helps organizations, professions and communities to both prepare for, and shape, the future. This becomes ever more critical given the accelerating rate at which new data emerge, and in some cases uncertainties around their reliability and interpretation. Businesses with the capability to filter and analyse vast volumes of data to create knowledge and insights requiring action have a competitive advantage. Similarly Government and the public sector, including public health can be more effective and efficient through the early identification of emerging issues (both threats and opportunities). Horizon scanning approaches, and the use of resulting intelligence related to health protection and improvement were reviewed. Public health horizon scanning systems have to date focussed on health technologies and infectious diseases. While these have been successful there is a major gap in terms of non-infectious hazards and health improvement. Any system to meet this need must recognize the changed environment for delivering front line public health services and the critical role of local authorities and the local democratic process. This presents opportunities and challenges and this paper explores those dynamics describing an existing environment and health horizon scanning system which could readily and rapidly be re-engineered to provide a national service. © The Author 2016. Published by Oxford University Press on behalf of Faculty of Public Health. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.
Black Hole Entropy from Conformal Field Theory in Any Dimension
International Nuclear Information System (INIS)
Carlip, S.
1999-01-01
Restricted to a black hole horizon, the open-quotes gaugeclose quotes algebra of surface deformations in general relativity contains a Virasoro subalgebra with a calculable central charge. The fields in any quantum theory of gravity must transform accordingly, i.e., they must admit a conformal field theory description. Applying Cardy close-quote s formula for the asymptotic density of states, I use this result to derive the Bekenstein-Hawking entropy. This method is universal it holds for any black hole, and requires no details of quantum gravity but it is also explicitly statistical mechanical, based on counting microscopic states. copyright 1999 The American Physical Society
Photoinduced entropy of InGaN/GaN p-i-n double-heterostructure nanowires
Alfaraj, Nasir; Mitra, Somak; Wu, Feng; Ajia, Idris A.; Janjua, Bilal; Prabaswara, Aditya; Aljefri, Renad A.; Sun, Haiding; Ng, Tien Khee; Ooi, Boon S.; Roqan, Iman S.; Li, Xiaohang
2017-01-01
The photoinduced entropy of InGaN/GaN p-i-n nanowires was investigated using temperature-dependent (6–290 K) photoluminescence. We also analyzed the photocarrier dynamics in the InGaN active regions using time-resolved photoluminescence. An increasing trend in the amount of generated photoinduced entropy of the system above 250 K was observed, while we observed an oscillatory trend in the generated entropy of the system below 250 K that stabilizes between 200 and 250 K. Strong exciton localization in indium-rich clusters, carrier trapping by surface defect states, and thermodynamic entropy effects were examined and related to the photocarrier dynamics. We conjecture that the amount of generated photoinduced entropy of the system increases as more non-radiative channels become activated and more shallowly localized carriers settle into deeply localized states; thereby, additional degrees of uncertainty related to the energy of states involved in thermionic transitions are attained.
Photoinduced entropy of InGaN/GaN p-i-n double-heterostructure nanowires
Alfaraj, Nasir
2017-04-17
The photoinduced entropy of InGaN/GaN p-i-n nanowires was investigated using temperature-dependent (6–290 K) photoluminescence. We also analyzed the photocarrier dynamics in the InGaN active regions using time-resolved photoluminescence. An increasing trend in the amount of generated photoinduced entropy of the system above 250 K was observed, while we observed an oscillatory trend in the generated entropy of the system below 250 K that stabilizes between 200 and 250 K. Strong exciton localization in indium-rich clusters, carrier trapping by surface defect states, and thermodynamic entropy effects were examined and related to the photocarrier dynamics. We conjecture that the amount of generated photoinduced entropy of the system increases as more non-radiative channels become activated and more shallowly localized carriers settle into deeply localized states; thereby, additional degrees of uncertainty related to the energy of states involved in thermionic transitions are attained.
DEFF Research Database (Denmark)
Escudero, Javier; Evrim, Acar Ataman; Fernández, Alberto
2015-01-01
dynamics. We consider the "refined composite multiscale entropy" (rcMSE), which computes entropy "profiles" showing levels of physiological complexity over temporal scales for individual signals. We compute the rcMSE of resting-state magnetoencephalogram (MEG) recordings from 36 patients with Alzheimer...
Remarks on entanglement entropy in string theory
Balasubramanian, Vijay; Parrikar, Onkar
2018-03-01
Entanglement entropy for spatial subregions is difficult to define in string theory because of the extended nature of strings. Here we propose a definition for bosonic open strings using the framework of string field theory. The key difference (compared to ordinary quantum field theory) is that the subregion is chosen inside a Cauchy surface in the "space of open string configurations." We first present a simple calculation of this entanglement entropy in free light-cone string field theory, ignoring subtleties related to the factorization of the Hilbert space. We reproduce the answer expected from an effective field theory point of view, namely a sum over the one-loop entanglement entropies corresponding to all the particle-excitations of the string, and further show that the full string theory regulates ultraviolet divergences in the entanglement entropy. We then revisit the question of factorization of the Hilbert space by analyzing the covariant phase-space associated with a subregion in Witten's covariant string field theory. We show that the pure gauge (i.e., BRST exact) modes in the string field become dynamical at the entanglement cut. Thus, a proper definition of the entropy must involve an extended Hilbert space, with new stringy edge modes localized at the entanglement cut.
On the Entropy Based Associative Memory Model with Higher-Order Correlations
Directory of Open Access Journals (Sweden)
Masahiro Nakagawa
2010-01-01
Full Text Available In this paper, an entropy based associative memory model will be proposed and applied to memory retrievals with an orthogonal learning model so as to compare with the conventional model based on the quadratic Lyapunov functional to be minimized during the retrieval process. In the present approach, the updating dynamics will be constructed on the basis of the entropy minimization strategy which may be reduced asymptotically to the above-mentioned conventional dynamics as a special case ignoring the higher-order correlations. According to the introduction of the entropy functional, one may involve higer-order correlation effects between neurons in a self-contained manner without any heuristic coupling coefficients as in the conventional manner. In fact we shall show such higher order coupling tensors are to be uniquely determined in the framework of the entropy based approach. From numerical results, it will be found that the presently proposed novel approach realizes much larger memory capacity than that of the quadratic Lyapunov functional approach, e.g., associatron.
Nonuniform Sparse Data Clustering Cascade Algorithm Based on Dynamic Cumulative Entropy
Directory of Open Access Journals (Sweden)
Ning Li
2016-01-01
Full Text Available A small amount of prior knowledge and randomly chosen initial cluster centers have a direct impact on the accuracy of the performance of iterative clustering algorithm. In this paper we propose a new algorithm to compute initial cluster centers for k-means clustering and the best number of the clusters with little prior knowledge and optimize clustering result. It constructs the Euclidean distance control factor based on aggregation density sparse degree to select the initial cluster center of nonuniform sparse data and obtains initial data clusters by multidimensional diffusion density distribution. Multiobjective clustering approach based on dynamic cumulative entropy is adopted to optimize the initial data clusters and the best number of the clusters. The experimental results show that the newly proposed algorithm has good performance to obtain the initial cluster centers for the k-means algorithm and it effectively improves the clustering accuracy of nonuniform sparse data by about 5%.
Generation of skeletal mechanism by means of projected entropy participation indices
Paolucci, Samuel; Valorani, Mauro; Ciottoli, Pietro Paolo; Galassi, Riccardo Malpica
2017-11-01
When the dynamics of reactive systems develop very-slow and very-fast time scales separated by a range of active time scales, with gaps in the fast/active and slow/active time scales, then it is possible to achieve multi-scale adaptive model reduction along-with the integration of the ODEs using the G-Scheme. The scheme assumes that the dynamics is decomposed into active, slow, fast, and invariant subspaces. We derive expressions that establish a direct link between time scales and entropy production by using estimates provided by the G-Scheme. To calculate the contribution to entropy production, we resort to a standard model of a constant pressure, adiabatic, batch reactor, where the mixture temperature of the reactants is initially set above the auto-ignition temperature. Numerical experiments show that the contribution to entropy production of the fast subspace is of the same magnitude as the error threshold chosen for the identification of the decomposition of the tangent space, and the contribution of the slow subspace is generally much smaller than that of the active subspace. The information on entropy production associated with reactions within each subspace is used to define an entropy participation index that is subsequently utilized for model reduction.
Entropy favours open colloidal lattices
Mao, Xiaoming; Chen, Qian; Granick, Steve
2013-03-01
Burgeoning experimental and simulation activity seeks to understand the existence of self-assembled colloidal structures that are not close-packed. Here we describe an analytical theory based on lattice dynamics and supported by experiments that reveals the fundamental role entropy can play in stabilizing open lattices. The entropy we consider is associated with the rotational and vibrational modes unique to colloids interacting through extended attractive patches. The theory makes predictions of the implied temperature, pressure and patch-size dependence of the phase diagram of open and close-packed structures. More generally, it provides guidance for the conditions at which targeted patchy colloidal assemblies in two and three dimensions are stable, thus overcoming the difficulty in exploring by experiment or simulation the full range of conceivable parameters.
The improvement of Clausius entropy and its application in entropy analysis
Institute of Scientific and Technical Information of China (English)
WU Jing; GUO ZengYuan
2008-01-01
The defects of Cleusius entropy which Include s premise of reversible process and a process quantlty of heat in Its definition are discussed in this paper. Moreover, the heat temperature quotient under reversible conditions, i.e. (δQ/T)rev, is essentially a process quantity although it is numerically equal to the entropy change. The sum of internal energy temperature quotient and work temperature quotient is defined as the improved form of Clausius entropy and it can be further proved to be a state funcllon. Unlike Clausius entropy, the improved deflnltion consists of system properties wlthout premise just like other state functions, for example, pressure p and enthalpy h, etc. it is unnecessary to invent reversible paths when calculating entropy change for irreversible processes based on the improved form of entropy since it is independent of process. Furthermore, entropy balance equations for internally and externally irreversible processes are deduced respectively based on the concepts of thermal reservoir entropy transfer and system entropy transfer. Finally, some examples are presented to show that the improved deflnitlon of Clausius entropy provides a clear concept as well as a convenient method for en-tropy change calculation.
Entropy, complexity, and Markov diagrams for random walk cancer models.
Newton, Paul K; Mason, Jeremy; Hurt, Brian; Bethel, Kelly; Bazhenova, Lyudmila; Nieva, Jorge; Kuhn, Peter
2014-12-19
The notion of entropy is used to compare the complexity associated with 12 common cancers based on metastatic tumor distribution autopsy data. We characterize power-law distributions, entropy, and Kullback-Liebler divergence associated with each primary cancer as compared with data for all cancer types aggregated. We then correlate entropy values with other measures of complexity associated with Markov chain dynamical systems models of progression. The Markov transition matrix associated with each cancer is associated with a directed graph model where nodes are anatomical locations where a metastatic tumor could develop, and edge weightings are transition probabilities of progression from site to site. The steady-state distribution corresponds to the autopsy data distribution. Entropy correlates well with the overall complexity of the reduced directed graph structure for each cancer and with a measure of systemic interconnectedness of the graph, called graph conductance. The models suggest that grouping cancers according to their entropy values, with skin, breast, kidney, and lung cancers being prototypical high entropy cancers, stomach, uterine, pancreatic and ovarian being mid-level entropy cancers, and colorectal, cervical, bladder, and prostate cancers being prototypical low entropy cancers, provides a potentially useful framework for viewing metastatic cancer in terms of predictability, complexity, and metastatic potential.
Entropy-reducing dynamics of a double demon
Ford, Ian J.; Maitland, Michael
2016-01-01
We study the reduction in total entropy, and associated conversion of environmental heat into work, arising from the coupling and decoupling of two systems followed by processing determined by suitable mutual feedback. The scheme is based on the actions of Maxwell's demon, namely the performance of a measurement on a system followed by an exploitation of the outcome to extract work. When this is carried out in a symmetric fashion, with each system informing the exploitation of the other (and ...
Application of different entropy formalisms in a neural network for novel word learning
Khordad, R.; Rastegar Sedehi, H. R.
2015-12-01
In this paper novel word learning in adults is studied. For this goal, four entropy formalisms are employed to include some degree of non-locality in a neural network. The entropy formalisms are Tsallis, Landsberg-Vedral, Kaniadakis, and Abe entropies. First, we have analytically obtained non-extensive cost functions for the all entropies. Then, we have used a generalization of the gradient descent dynamics as a learning rule in a simple perceptron. The Langevin equations are numerically solved and the error function (learning curve) is obtained versus time for different values of the parameters. The influence of index q and number of neuron N on learning is investigated for the all entropies. It is found that learning is a decreasing function of time for the all entropies. The rate of learning for the Landsberg-Vedral entropy is slower than other entropies. The variation of learning with time for the Landsberg-Vedral entropy is not appreciable when the number of neurons increases. It is said that entropy formalism can be used as a means for studying the learning.
Upper Estimates on the Higher-dimensional Multifractal Spectrum of Local Entropy%局部熵高维重分形谱的上界估计
Institute of Scientific and Technical Information of China (English)
严珍珍; 陈二才
2008-01-01
We discuss the problem of higher-dimensional multifractal spectrum of lo-cal entropy for arbitrary invariant measures. By utilizing characteristics of a dynam-ical system, namely, higher-dimensional entropy capacities and higher-dimensional correlation entropies, we obtain three upper estimates on the higher-dimensional mul-tifractal spectrum of local entropies. We also study the domain of higher-dimensional multifractal spetrum of entropies.
Namazi, Hamidreza; Akrami, Amin; Nazeri, Sina; Kulish, Vladimir V
2016-01-01
An important challenge in brain research is to make out the relation between the features of olfactory stimuli and the electroencephalogram (EEG) signal. Yet, no one has discovered any relation between the structures of olfactory stimuli and the EEG signal. This study investigates the relation between the structures of EEG signal and the olfactory stimulus (odorant). We show that the complexity of the EEG signal is coupled with the molecular complexity of the odorant, where more structurally complex odorant causes less fractal EEG signal. Also, odorant having higher entropy causes the EEG signal to have lower approximate entropy. The method discussed here can be applied and investigated in case of patients with brain diseases as the rehabilitation purpose.
Volkenstein, Mikhail V
2009-01-01
The book "Entropy and Information" deals with the thermodynamical concept of entropy and its relationship to information theory. It is successful in explaining the universality of the term "Entropy" not only as a physical phenomenon, but reveals its existence also in other domains. E.g., Volkenstein discusses the "meaning" of entropy in a biological context and shows how entropy is related to artistic activities. Written by the renowned Russian bio-physicist Mikhail V. Volkenstein, this book on "Entropy and Information" surely serves as a timely introduction to understand entropy from a thermodynamic perspective and is definitely an inspiring and thought-provoking book that should be read by every physicist, information-theorist, biologist, and even artist.
Parametric Bayesian Estimation of Differential Entropy and Relative Entropy
Gupta; Srivastava
2010-01-01
Given iid samples drawn from a distribution with known parametric form, we propose the minimization of expected Bregman divergence to form Bayesian estimates of differential entropy and relative entropy, and derive such estimators for the uniform, Gaussian, Wishart, and inverse Wishart distributions. Additionally, formulas are given for a log gamma Bregman divergence and the differential entropy and relative entropy for the Wishart and inverse Wishart. The results, as always with Bayesian est...
Entropy fluxes, endoreversibility, and solar energy conversion
de Vos, A.; Landsberg, P. T.; Baruch, P.; Parrott, J. E.
1993-09-01
A formalism illustrating the conversion of radiation energy into work can be obtained in terms of energy and entropy fluxes. Whereas the Landsberg equality was derived for photothermal conversion with zero bandgap, a generalized inequality for photothermal/photovoltaic conversion with a single, but arbitrary, bandgap was deduced. This result was derived for a direct energy and entropy balance. The formalism of endoreversible dynamics was adopted in order to show the correlation with the latter approach. It was a surprising fact that the generalized Landsberg inequality was derived by optimizing some quantity W(sup *), which obtains it maximum value under short-circuit condition.
International Nuclear Information System (INIS)
Zhang Min-Min; Mei Dong-Cheng; Wang Can-Jun
2011-01-01
The effects of the time delay on the upper bound of the time derivative of information entropy are investigated in a time-delayed dynamical system driven by correlated noise. Using the Markov approximation of the stochastic delay differential equations and the Schwartz inequality principle, we obtain an analytical expression for the upper bound U B (t) of the time derivative of the information entropy. The results show that there is a critical value of τ (delay time), and U B (t) presents opposite behaviours on difference sides of the critical value. For the case of the weak additive noise, τ can induce a reentrance transition. Delay time τ also causes a reversal behaviour in U B (t)-λ plot, where λ denotes the degree of the correlation between the two noises. (general)
Hydrodynamic Relaxation of an Electron Plasma to a Near-Maximum Entropy State
International Nuclear Information System (INIS)
Rodgers, D. J.; Servidio, S.; Matthaeus, W. H.; Mitchell, T. B.; Aziz, T.; Montgomery, D. C.
2009-01-01
Dynamical relaxation of a pure electron plasma in a Malmberg-Penning trap is studied, comparing experiments, numerical simulations and statistical theories of weakly dissipative two-dimensional (2D) turbulence. Simulations confirm that the dynamics are approximated well by a 2D hydrodynamic model. Statistical analysis favors a theoretical picture of relaxation to a near-maximum entropy state with constrained energy, circulation, and angular momentum. This provides evidence that 2D electron fluid relaxation in a turbulent regime is governed by principles of maximum entropy.
The improvement of Clausius entropy and its application in entropy analysis
Institute of Scientific and Technical Information of China (English)
2008-01-01
The defects of Clausius entropy which include a premise of reversible process and a process quantity of heat in its definition are discussed in this paper. Moreover, the heat temperature quotient under reversible conditions, i.e. (δQ/T)rev, is essentially a process quantity although it is numerically equal to the entropy change. The sum of internal energy temperature quotient and work temperature quotient is defined as the improved form of Clausius entropy and it can be further proved to be a state function. Unlike Clausius entropy, the improved definition consists of system properties without premise just like other state functions, for example, pressure p and enthalpy h, etc. It is unnecessary to invent reversible paths when calculating entropy change for irreversible processes based on the improved form of entropy since it is independent of process. Furthermore, entropy balance equations for internally and externally irreversible processes are deduced respectively based on the concepts of thermal reservoir entropy transfer and system entropy transfer. Finally, some examples are presented to show that the improved definition of Clausius entropy provides a clear concept as well as a convenient method for en- tropy change calculation.
Summary and status of the Horizons ephemeris system
Giorgini, J.
2011-10-01
Since 1996, the Horizons system has provided searchable access to JPL ephemerides for all known solar system bodies, several dozen spacecraft, planetary system barycenters, and some libration points. Responding to 18 400 000 requests from 300 000 unique addresses, the system has recently averaged 420 000 ephemeris requests per month. Horizons is accessed and automated using three interfaces: interactive telnet, web-browser form, and e-mail command-file. Asteroid and comet ephemerides are numerically integrated from JPL's database of initial conditions. This small-body database is updated hourly by a separate process as new measurements and discoveries are reported by the Minor Planet Center and automatically incorporated into new JPL orbit solutions. Ephemerides for other objects are derived by interpolating previously developed solutions whose trajectories have been represented in a file. For asteroids and comets, such files may be dynamically created and transferred to users, effectively recording integrator output. These small-body SPK files may then be interpolated by user software to reproduce the trajectory without duplicating the numerically integrated n-body dynamical model or PPN equations of motion. Other Horizons output is numerical and in the form of plain-text observer, vector, osculating element, or close-approach tables, typically expected be read by other software as input. About one hundred quantities can be requested in various time-scales and coordinate systems. For JPL small-body solutions, this includes statistical uncertainties derived from measurement covariance and state transition matrices. With the exception of some natural satellites, Horizons is consistent with DE405/DE406, the IAU 1976 constants, ITRF93, and IAU2009 rotational models.
Statistical Mechanics and Black Hole Thermodynamics
Carlip, Steven
1997-01-01
Black holes are thermodynamic objects, but despite recent progress, the ultimate statistical mechanical origin of black hole temperature and entropy remains mysterious. Here I summarize an approach in which the entropy is viewed as arising from ``would-be pure gauge'' degrees of freedom that become dynamical at the horizon. For the (2+1)-dimensional black hole, these degrees of freedom can be counted, and yield the correct Bekenstein-Hawking entropy; the corresponding problem in 3+1 dimension...
Damping behavior of AlxCoCrFeNi high-entropy alloys by a dynamic mechanical analyzer
International Nuclear Information System (INIS)
Ma, S.G.; Liaw, P.K.; Gao, M.C.; Qiao, J.W.; Wang, Z.H.; Zhang, Y.
2014-01-01
Highlights: • The Al content is related with structural relaxation and damping capability. • Dynamic modulus is insensitive to the frequency especially for storage modulus. • Several internal-friction peaks are observed in the Al-free or Al-lean alloys. • The damping behavior is proposed to be strongly relied on the level of ordering. - Abstract: For the first time, the damping behavior of high-entropy alloys was studied using the dynamic-mechanical analyzer, over a continuous heating temperature from room temperature to 773 K, at a given frequency range from 1 to 16 Hz in model alloys Al x CoCrFeNi (x = 0, 0.25, 0.5, 0.75, and 1). The experimental results reveal that the Al-rich alloys have a much smaller elastic storage-modulus amplitude over the temperature and thus a larger resistance to structural relaxation, while the Al-free and Al-lean alloys exhibit a much higher loss tangent and thus a much higher damping capability. Overall the elastic storage modulus decreases while the loss tangent increases with increasing the temperature, but little dependence was observed for the frequency. Several visible internal-friction peaks were presented in the face-centered cubic alloys, whose positions and heights are independent of the frequency. The damping capability of these alloys can be comparable to or even overwhelm the conventional Fe–Al alloys. The damping behavior above was proposed to be agreeable with the level of ordering (η) of alloys characterized by two proposed parameters (the relative-entropy effect, Ω, and the atomic-size difference, δ)
Financial time series analysis based on effective phase transfer entropy
Yang, Pengbo; Shang, Pengjian; Lin, Aijing
2017-02-01
Transfer entropy is a powerful technique which is able to quantify the impact of one dynamic system on another system. In this paper, we propose the effective phase transfer entropy method based on the transfer entropy method. We use simulated data to test the performance of this method, and the experimental results confirm that the proposed approach is capable of detecting the information transfer between the systems. We also explore the relationship between effective phase transfer entropy and some variables, such as data size, coupling strength and noise. The effective phase transfer entropy is positively correlated with the data size and the coupling strength. Even in the presence of a large amount of noise, it can detect the information transfer between systems, and it is very robust to noise. Moreover, this measure is indeed able to accurately estimate the information flow between systems compared with phase transfer entropy. In order to reflect the application of this method in practice, we apply this method to financial time series and gain new insight into the interactions between systems. It is demonstrated that the effective phase transfer entropy can be used to detect some economic fluctuations in the financial market. To summarize, the effective phase transfer entropy method is a very efficient tool to estimate the information flow between systems.
Information Entropy Measures for Stand Structural Diversity:Joint Entropy
Institute of Scientific and Technical Information of China (English)
Lei Xiangdong; Lu Yuanchang
2004-01-01
Structural diversity is the key attribute of a stand. A set of biodiversity measures in ecology was introduced in forest management for describing stand structure, of which Shannon information entropy (Shannon index) has been the most widely used measure of species diversity. It is generally thought that tree size diversity could serve as a good proxy for height diversity. However, tree size diversity and height diversity for stand structure is not completely consistent. Stand diameter cannot reflect height information completely. Either tree size diversity or height diversity is one-dimensional information entropy measure. This paper discussed the method of multiple-dimensional information entropy measure with the concept of joint entropy. It is suggested that joint entropy is a good measure for describing overall stand structural diversity.
Quantum chaos: entropy signatures
International Nuclear Information System (INIS)
Miller, P.A.; Sarkar, S.; Zarum, R.
1998-01-01
A definition of quantum chaos is given in terms of entropy production rates for a quantum system coupled weakly to a reservoir. This allows the treatment of classical and quantum chaos on the same footing. In the quantum theory the entropy considered is the von Neumann entropy and in classical systems it is the Gibbs entropy. The rate of change of the coarse-grained Gibbs entropy of the classical system with time is given by the Kolmogorov-Sinai (KS) entropy. The relation between KS entropy and the rate of change of von Neumann entropy is investigated for the kicked rotator. For a system which is classically chaotic there is a linear relationship between these two entropies. Moreover it is possible to construct contour plots for the local KS entropy and compare it with the corresponding plots for the rate of change of von Neumann entropy. The quantitative and qualitative similarities of these plots are discussed for the standard map (kicked rotor) and the generalised cat maps. (author)
Effective horizons, junction conditions and large-scale magnetism
Energy Technology Data Exchange (ETDEWEB)
Giovannini, Massimo [CERN, Department of Physics, Theory Division, Geneva (Switzerland); INFN, Milan (Italy)
2017-08-15
The quantum mechanical generation of hypermagnetic and hyperelectric fields in four-dimensional conformally flat background geometries rests on the simultaneous continuity of the effective horizon and of the extrinsic curvature across the inflationary boundary. The junction conditions for the gauge fields are derived in general terms and corroborated by explicit examples with particular attention to the limit of a sudden (but nonetheless continuous) transition of the effective horizon. After reducing the dynamics to a pair of integral equations related by duality transformations, we compute the power spectra and deduce a novel class of logarithmic corrections which turn out to be, however, numerically insignificant and overwhelmed by the conductivity effects once the gauge modes reenter the effective horizon. In this perspective the magnetogenesis requirements and the role of the postinflationary conductivity are clarified and reappraised. As long as the total duration of the inflationary phase is nearly minimal, quasi-flat hypermagnetic power spectra are comparatively more common than in the case of vacuum initial data. (orig.)
Does the black hole shadow probe the event horizon geometry?
Cunha, Pedro V. P.; Herdeiro, Carlos A. R.; Rodriguez, Maria J.
2018-04-01
There is an exciting prospect of obtaining the shadow of astrophysical black holes (BHs) in the near future with the Event Horizon Telescope. As a matter of principle, this justifies asking how much one can learn about the BH horizon itself from such a measurement. Since the shadow is determined by a set of special photon orbits, rather than horizon properties, it is possible that different horizon geometries yield similar shadows. One may then ask how sensitive is the shadow to details of the horizon geometry? As a case study, we consider the double Schwarzschild BH and analyze the impact on the lensing and shadows of the conical singularity that holds the two BHs in equilibrium—herein taken to be a strut along the symmetry axis in between the two BHs. Whereas the conical singularity induces a discontinuity of the scattering angle of photons, clearly visible in the lensing patterns along the direction of the strut's location, it produces no observable effect on the shadows, whose edges remain everywhere smooth. The latter feature is illustrated by examples including both equal and unequal mass BHs. This smoothness contrasts with the intrinsic geometry of the (spatial sections of the) horizon of these BHs, which is not smooth, and provides a sharp example on how BH shadows are insensitive to some horizon geometry details. This observation, moreover, suggests that for the study of their shadows, this static double BH system may be an informative proxy for a dynamical binary.
Free Energy, Enthalpy and Entropy from Implicit Solvent End-Point Simulations.
Fogolari, Federico; Corazza, Alessandra; Esposito, Gennaro
2018-01-01
Free energy is the key quantity to describe the thermodynamics of biological systems. In this perspective we consider the calculation of free energy, enthalpy and entropy from end-point molecular dynamics simulations. Since the enthalpy may be calculated as the ensemble average over equilibrated simulation snapshots the difficulties related to free energy calculation are ultimately related to the calculation of the entropy of the system and in particular of the solvent entropy. In the last two decades implicit solvent models have been used to circumvent the problem and to take into account solvent entropy implicitly in the solvation terms. More recently outstanding advancement in both implicit solvent models and in entropy calculations are making the goal of free energy estimation from end-point simulations more feasible than ever before. We review briefly the basic theory and discuss the advancements in light of practical applications.
Free Energy, Enthalpy and Entropy from Implicit Solvent End-Point Simulations
Directory of Open Access Journals (Sweden)
Federico Fogolari
2018-02-01
Full Text Available Free energy is the key quantity to describe the thermodynamics of biological systems. In this perspective we consider the calculation of free energy, enthalpy and entropy from end-point molecular dynamics simulations. Since the enthalpy may be calculated as the ensemble average over equilibrated simulation snapshots the difficulties related to free energy calculation are ultimately related to the calculation of the entropy of the system and in particular of the solvent entropy. In the last two decades implicit solvent models have been used to circumvent the problem and to take into account solvent entropy implicitly in the solvation terms. More recently outstanding advancement in both implicit solvent models and in entropy calculations are making the goal of free energy estimation from end-point simulations more feasible than ever before. We review briefly the basic theory and discuss the advancements in light of practical applications.
An understanding of human dynamics in urban subway traffic from the Maximum Entropy Principle
Yong, Nuo; Ni, Shunjiang; Shen, Shifei; Ji, Xuewei
2016-08-01
We studied the distribution of entry time interval in Beijing subway traffic by analyzing the smart card transaction data, and then deduced the probability distribution function of entry time interval based on the Maximum Entropy Principle. Both theoretical derivation and data statistics indicated that the entry time interval obeys power-law distribution with an exponential cutoff. In addition, we pointed out the constraint conditions for the distribution form and discussed how the constraints affect the distribution function. It is speculated that for bursts and heavy tails in human dynamics, when the fitted power exponent is less than 1.0, it cannot be a pure power-law distribution, but with an exponential cutoff, which may be ignored in the previous studies.
Directory of Open Access Journals (Sweden)
ChunPing Ren
2017-01-01
Full Text Available We propose a novel mathematical algorithm to offer a solution for the inverse random dynamic force identification in practical engineering. Dealing with the random dynamic force identification problem using the proposed algorithm, an improved maximum entropy (IME regularization technique is transformed into an unconstrained optimization problem, and a novel conjugate gradient (NCG method was applied to solve the objective function, which was abbreviated as IME-NCG algorithm. The result of IME-NCG algorithm is compared with that of ME, ME-CG, ME-NCG, and IME-CG algorithm; it is found that IME-NCG algorithm is available for identifying the random dynamic force due to smaller root mean-square-error (RMSE, lower restoration time, and fewer iterative steps. Example of engineering application shows that L-curve method is introduced which is better than Generalized Cross Validation (GCV method and is applied to select regularization parameter; thus the proposed algorithm can be helpful to alleviate the ill-conditioned problem in identification of dynamic force and to acquire an optimal solution of inverse problem in practical engineering.
Directory of Open Access Journals (Sweden)
Jeroen Schoenmaker
2014-08-01
Full Text Available We performed an in depth analysis of the subjects of entropy and the second law of thermodynamics and how they are treated in astrophysical systems. These subjects are retraced historically from the early works on thermodynamics to the modern statistical mechanical approach and analyzed in view of specific practices within the field of astrophysics. As often happens in discussions regarding cosmology, the implications of this analysis range from physics to philosophy of science. We argue that the difficult question regarding entropy and the second law in the scope of cosmology is a consequence of the dominating paradigm. We further demonstrate this point by assuming an alternative paradigm, not related to thermodynamics of horizons, and successfully describing entropic behavior of astrophysical systems.
Configurational entropy change of netropsin and distamycin upon DNA minor-groove binding.
Dolenc, Jozica; Baron, Riccardo; Oostenbrink, Chris; Koller, Joze; van Gunsteren, Wilfred F
2006-08-15
Binding of a small molecule to a macromolecular target reduces its conformational freedom, resulting in a negative entropy change that opposes the binding. The goal of this study is to estimate the configurational entropy change of two minor-groove-binding ligands, netropsin and distamycin, upon binding to the DNA duplex d(CGCGAAAAACGCG).d(CGCGTTTTTCGCG). Configurational entropy upper bounds based on 10-ns molecular dynamics simulations of netropsin and distamycin in solution and in complex with DNA in solution were estimated using the covariance matrix of atom-positional fluctuations. The results suggest that netropsin and distamycin lose a significant amount of configurational entropy upon binding to the DNA minor groove. The estimated changes in configurational entropy for netropsin and distamycin are -127 J K(-1) mol(-1) and -104 J K(-1) mol(-1), respectively. Estimates of the configurational entropy contributions of parts of the ligands are presented, showing that the loss of configurational entropy is comparatively more pronounced for the flexible tails than for the relatively rigid central body.
Value at risk estimation with entropy-based wavelet analysis in exchange markets
He, Kaijian; Wang, Lijun; Zou, Yingchao; Lai, Kin Keung
2014-08-01
In recent years, exchange markets are increasingly integrated together. Fluctuations and risks across different exchange markets exhibit co-moving and complex dynamics. In this paper we propose the entropy-based multivariate wavelet based approaches to analyze the multiscale characteristic in the multidimensional domain and improve further the Value at Risk estimation reliability. Wavelet analysis has been introduced to construct the entropy-based Multiscale Portfolio Value at Risk estimation algorithm to account for the multiscale dynamic correlation. The entropy measure has been proposed as the more effective measure with the error minimization principle to select the best basis when determining the wavelet families and the decomposition level to use. The empirical studies conducted in this paper have provided positive evidence as to the superior performance of the proposed approach, using the closely related Chinese Renminbi and European Euro exchange market.
Thermal Expansion Anomaly Regulated by Entropy
Liu, Zi-Kui; Wang, Yi; Shang, Shunli
2014-11-01
Thermal expansion, defined as the temperature dependence of volume under constant pressure, is a common phenomenon in nature and originates from anharmonic lattice dynamics. However, it has been poorly understood how thermal expansion can show anomalies such as colossal positive, zero, or negative thermal expansion (CPTE, ZTE, or NTE), especially in quantitative terms. Here we show that changes in configurational entropy due to metastable micro(scopic)states can lead to quantitative prediction of these anomalies. We integrate the Maxwell relation, statistic mechanics, and first-principles calculations to demonstrate that when the entropy is increased by pressure, NTE occurs such as in Invar alloy (Fe3Pt, for example), silicon, ice, and water, and when the entropy is decreased dramatically by pressure, CPTE is expected such as in anti-Invar cerium, ice and water. Our findings provide a theoretic framework to understand and predict a broad range of anomalies in nature in addition to thermal expansion, which may include gigantic electrocaloric and electromechanical responses, anomalously reduced thermal conductivity, and spin distributions.
Towards an Entropy Stable Spectral Element Framework for Computational Fluid Dynamics
Carpenter, Mark H.; Parsani, Matteo; Fisher, Travis C.; Nielsen, Eric J.
2016-01-01
Entropy stable (SS) discontinuous spectral collocation formulations of any order are developed for the compressible Navier-Stokes equations on hexahedral elements. Recent progress on two complementary efforts is presented. The first effort is a generalization of previous SS spectral collocation work to extend the applicable set of points from tensor product, Legendre-Gauss-Lobatto (LGL) to tensor product Legendre-Gauss (LG) points. The LG and LGL point formulations are compared on a series of test problems. Although being more costly to implement, it is shown that the LG operators are significantly more accurate on comparable grids. Both the LGL and LG operators are of comparable efficiency and robustness, as is demonstrated using test problems for which conventional FEM techniques suffer instability. The second effort generalizes previous SS work to include the possibility of p-refinement at non-conforming interfaces. A generalization of existing entropy stability machinery is developed to accommodate the nuances of fully multi-dimensional summation-by-parts (SBP) operators. The entropy stability of the compressible Euler equations on non-conforming interfaces is demonstrated using the newly developed LG operators and multi-dimensional interface interpolation operators.
Mechanics of apparent horizons
International Nuclear Information System (INIS)
Collins, W.
1992-01-01
An equation for the variation in the surface area of an apparent horizon is derived which has the same form as the thermodynamic relation TdS=dQ. For a stationary vacuum black hole, the expression corresponding to a temperature equals the temperature of the event horizon. Also, if the black hole is perturbed infinitesimally by weak matter and gravitational fields, the area variation of the apparent horizon asymptotically approaches the Hartle-Hawking result for the event horizon. These results support the idea that a local version of black-hole thermodynamics in nonstationary systems can be constructed for apparent horizons
Quantum key distribution with finite resources: Smooth Min entropy vs. Smooth Renyi entropy
Energy Technology Data Exchange (ETDEWEB)
Mertz, Markus; Abruzzo, Silvestre; Bratzik, Sylvia; Kampermann, Hermann; Bruss, Dagmar [Institut fuer Theoretische Physik III, Duesseldorf (Germany)
2010-07-01
We consider different entropy measures that play an important role in the analysis of the security of QKD with finite resources. The smooth min entropy leads to an optimal bound for the length of a secure key. Another bound on the secure key length was derived by using Renyi entropies. Unfortunately, it is very hard or even impossible to calculate these entropies for realistic QKD scenarios. To estimate the security rate it becomes important to find computable bounds on these entropies. Here, we compare a lower bound for the smooth min entropy with a bound using Renyi entropies. We compare these entropies for the six-state protocol with symmetric attacks.
Correlations of multiscale entropy in the FX market
Stosic, Darko; Stosic, Dusan; Ludermir, Teresa; Stosic, Tatijana
2016-09-01
The regularity of price fluctuations in exchange rates plays a crucial role in FX market dynamics. Distinct variations in regularity arise from economic, social and political events, such as interday trading and financial crisis. This paper applies a multiscale time-dependent entropy method on thirty-three exchange rates to analyze price fluctuations in the FX. Correlation matrices of entropy values, termed entropic correlations, are in turn used to describe global behavior of the market. Empirical results suggest a weakly correlated market with pronounced collective behavior at bi-weekly trends. Correlations arise from cycles of low and high regularity in long-term trends. Eigenvalues of the correlation matrix also indicate a dominant European market, followed by shifting American, Asian, African, and Pacific influences. As a result, we find that entropy is a powerful tool for extracting important information from the FX market.
Topological entropy of autonomous flows
Energy Technology Data Exchange (ETDEWEB)
Badii, R. [Paul Scherrer Inst. (PSI), Villigen (Switzerland)
1997-06-01
When studying fluid dynamics, especially in a turbulent regime, it is crucial to estimate the number of active degrees of freedom or of localized structures in the system. The topological entropy quantifies the exponential growth of the number of `distinct` orbits in a dynamical system as a function of their length, in the infinite spatial resolution limit. Here, I illustrate a novel method for its evaluation, which extends beyond maps and is applicable to any system, including autonomous flows: these are characterized by lack of a definite absolute time scale for the orbit lengths. (author) 8 refs.
Local conditional entropy in measure for covers with respect to a fixed partition
Romagnoli, Pierre-Paul
2018-05-01
In this paper we introduce two measure theoretical notions of conditional entropy for finite measurable covers conditioned to a finite measurable partition and prove that they are equal. Using this we state a local variational principle with respect to the notion of conditional entropy defined by Misiurewicz (1976 Stud. Math. 55 176–200) for the case of open covers. This in particular extends the work done in Romagnoli (2003 Ergod. Theor. Dynam. Syst. 23 1601–10), Glasner and Weiss (2006 Handbook of Dynamical Systems vol 1B (Amsterdam: Elsevier)) and Huang et al (2006 Ergod. Theor. Dynam. Syst. 26 219–45).
Residual and Past Entropy for Concomitants of Ordered Random Variables of Morgenstern Family
Directory of Open Access Journals (Sweden)
M. M. Mohie EL-Din
2015-01-01
Full Text Available For a system, which is observed at time t, the residual and past entropies measure the uncertainty about the remaining and the past life of the distribution, respectively. In this paper, we have presented the residual and past entropy of Morgenstern family based on the concomitants of the different types of generalized order statistics (gos and give the linear transformation of such model. Characterization results for these dynamic entropies for concomitants of ordered random variables have been considered.
Brehme, Marc; Koschmieder, Steffen; Montazeri, Maryam; Copland, Mhairi; Oehler, Vivian G.; Radich, Jerald P.; Brümmendorf, Tim H.; Schuppert, Andreas
2016-04-01
Modelling the parameters of multistep carcinogenesis is key for a better understanding of cancer progression, biomarker identification and the design of individualized therapies. Using chronic myeloid leukemia (CML) as a paradigm for hierarchical disease evolution we show that combined population dynamic modelling and CML patient biopsy genomic analysis enables patient stratification at unprecedented resolution. Linking CD34+ similarity as a disease progression marker to patient-derived gene expression entropy separated established CML progression stages and uncovered additional heterogeneity within disease stages. Importantly, our patient data informed model enables quantitative approximation of individual patients’ disease history within chronic phase (CP) and significantly separates “early” from “late” CP. Our findings provide a novel rationale for personalized and genome-informed disease progression risk assessment that is independent and complementary to conventional measures of CML disease burden and prognosis.
Analysis of the anomalous mean-field like properties of Gaussian core model in terms of entropy
Nandi, Manoj Kumar; Maitra Bhattacharyya, Sarika
2018-01-01
Studies of the Gaussian core model (GCM) have shown that it behaves like a mean-field model and the properties are quite different from standard glass former. In this work, we investigate the entropies, namely, the excess entropy (Sex) and the configurational entropy (Sc) and their different components to address these anomalies. Our study corroborates most of the earlier observations and also sheds new light on the high and low temperature dynamics. We find that unlike in standard glass former where high temperature dynamics is dominated by two-body correlation and low temperature by many-body correlations, in the GCM both high and low temperature dynamics are dominated by many-body correlations. We also find that the many-body entropy which is usually positive at low temperatures and is associated with activated dynamics is negative in the GCM suggesting suppression of activation. Interestingly despite the suppression of activation, the Adam-Gibbs (AG) relation that describes activated dynamics holds in the GCM, thus suggesting a non-activated contribution in AG relation. We also find an overlap between the AG relation and mode coupling power law regime leading to a power law behavior of Sc. From our analysis of this power law behavior, we predict that in the GCM the high temperature dynamics will disappear at dynamical transition temperature and below that there will be a transition to the activated regime. Our study further reveals that the activated regime in the GCM is quite narrow.
Stabilizing unstable fixed points of chaotic maps via minimum entropy control
Energy Technology Data Exchange (ETDEWEB)
Salarieh, Hassan [Center of Excellence in Design, Robotics and Automation, Department of Mechanical Engineering, Sharif University of Technology, P.O. Box 11365-9567, Tehran (Iran, Islamic Republic of)], E-mail: salarieh@mech.sharif.edu; Alasty, Aria [Center of Excellence in Design, Robotics and Automation, Department of Mechanical Engineering, Sharif University of Technology, P.O. Box 11365-9567, Tehran (Iran, Islamic Republic of)
2008-08-15
In this paper the problem of chaos control in nonlinear maps using minimization of entropy function is investigated. Invariant probability measure of a chaotic dynamics can be used to produce an entropy function in the sense of Shannon. In this paper it is shown that how the entropy control technique is utilized for chaos elimination. Using only the measured states of a chaotic map the probability measure of the system is numerically estimated and this estimated measure is used to obtain an estimation for the entropy of the chaotic map. The control variable of the chaotic system is determined in such a way that the entropy function descends until the chaotic trajectory of the map is replaced with a regular one. The proposed idea is applied for stabilizing the fixed points of the logistic and the Henon maps as some cases of study. Simulation results show the effectiveness of the method in chaos rejection when only the statistical information is available from the under-study systems.
TIME HORIZON AND UNCOVERED INTEREST PARITY IN EMERGING ECONOMIES
Directory of Open Access Journals (Sweden)
Norlida Hanim Mohd Salleh
2011-07-01
Full Text Available The aim of this study is to re-examine the well-known empirical puzzle of uncovered interest parity (UIP for emerging market economies with different prediction time horizons. The empirical results obtained using dynamic panel and time series techniques for monthly data from January 1995 to December 2009 eventually show that the panel data estimates are more powerful than those obtained by applying individual time series estimations and the significant contribution of the exchange rate prediction horizons in determining the status of UIP. This finding reveals that at the longer time horizon, the model has better econometric specification and thus more predictive power for exchange rate movements compared to the shorter time period. The findings can also be a signalling of well-integrated currency markets and a reliable guide to international investors as well as for the orderly conduct of monetary authorities.
Directory of Open Access Journals (Sweden)
Jacques Demongeot
2018-01-01
Full Text Available Networks used in biological applications at different scales (molecule, cell and population are of different types: neuronal, genetic, and social, but they share the same dynamical concepts, in their continuous differential versions (e.g., non-linear Wilson-Cowan system as well as in their discrete Boolean versions (e.g., non-linear Hopfield system; in both cases, the notion of interaction graph G(J associated to its Jacobian matrix J, and also the concepts of frustrated nodes, positive or negative circuits of G(J, kinetic energy, entropy, attractors, structural stability, etc., are relevant and useful for studying the dynamics and the robustness of these systems. We will give some general results available for both continuous and discrete biological networks, and then study some specific applications of three new notions of entropy: (i attractor entropy, (ii isochronal entropy and (iii entropy centrality; in three domains: a neural network involved in the memory evocation, a genetic network responsible of the iron control and a social network accounting for the obesity spread in high school environment.
Statistical properties of quantum entanglement and information entropy
International Nuclear Information System (INIS)
Abdel-Aty, M.M.A.
2007-03-01
Key words: entropy, entanglement, atom-field interaction, trapped ions, cold atoms, information entropy. Objects of research: Pure state entanglement, entropy squeezing mazer. The aim of the work: Study of the new entanglement features and new measures for both pure-state and mixed state of particle-field interaction. Also, the impact of the information entropy on the quantum information theory. Method of investigation: Methods of theoretical physics and applied mathematics (statistical physics, quantum optics) are used. Results obtained and their novelty are: All the results of the dissertation are new and many new features have been discovered. Particularly: the most general case of the pure state entanglement has been introduced. Although various special aspects of the quantum entropy have been investigated previously, the general features of the dynamics, when a multi-level system and a common environment are considered, have not been treated before and our work therefore, field a gap in the literature. Specifically: 1) A new entanglement measure due to quantum mutual entropy (mixed-state entanglement) we called it DEM, has been introduced, 2) A new treatment of the atomic information entropy in higher level systems has been presented. The problem has been completely solved in the case of three-level system, 3) A new solution of the interaction between the ultra cold atoms and cavity field has been discovered, 4) Some new models of the atom-field interaction have been adopted. Practical value: The subject carries out theoretic character. Application region: Results can be used in quantum computer developments. Also, the presented results can be used for further developments of the quantum information and quantum communications. (author)
Parametric Bayesian Estimation of Differential Entropy and Relative Entropy
Directory of Open Access Journals (Sweden)
Maya Gupta
2010-04-01
Full Text Available Given iid samples drawn from a distribution with known parametric form, we propose the minimization of expected Bregman divergence to form Bayesian estimates of differential entropy and relative entropy, and derive such estimators for the uniform, Gaussian, Wishart, and inverse Wishart distributions. Additionally, formulas are given for a log gamma Bregman divergence and the differential entropy and relative entropy for the Wishart and inverse Wishart. The results, as always with Bayesian estimates, depend on the accuracy of the prior parameters, but example simulations show that the performance can be substantially improved compared to maximum likelihood or state-of-the-art nonparametric estimators.
New horizons in biomagnetics and bioimaging
International Nuclear Information System (INIS)
Ueno, Shogo; Sekino, Masaki
2006-01-01
This paper reviews recently developed techniques in biomagnetics and bioimaging such as transcranial magnetic stimulation (TMS), magnetic resonance imaging (MRI), and cancer therapy based on magnetic stimulation. The technique of localized and vectorial TMS has made it possible to obtain non-invasive functional mapping of the human brain, and the development of new bioimaging technologies such as current distribution MRI and conductivity MRI may make it possible to understand the dynamics of brain functions, which include millisecond-level changes in functional regions and dynamic relations between brain neuronal networks. These techniques are leading medicine and biology toward new horizons through novel applications of magnetism. (author)
EEG entropy measures in anesthesia
Liang, Zhenhu; Wang, Yinghua; Sun, Xue; Li, Duan; Voss, Logan J.; Sleigh, Jamie W.; Hagihira, Satoshi; Li, Xiaoli
2015-01-01
Highlights: ► Twelve entropy indices were systematically compared in monitoring depth of anesthesia and detecting burst suppression.► Renyi permutation entropy performed best in tracking EEG changes associated with different anesthesia states.► Approximate Entropy and Sample Entropy performed best in detecting burst suppression. Objective: Entropy algorithms have been widely used in analyzing EEG signals during anesthesia. However, a systematic comparison of these entropy algorithms in assessing anesthesia drugs' effect is lacking. In this study, we compare the capability of 12 entropy indices for monitoring depth of anesthesia (DoA) and detecting the burst suppression pattern (BSP), in anesthesia induced by GABAergic agents. Methods: Twelve indices were investigated, namely Response Entropy (RE) and State entropy (SE), three wavelet entropy (WE) measures [Shannon WE (SWE), Tsallis WE (TWE), and Renyi WE (RWE)], Hilbert-Huang spectral entropy (HHSE), approximate entropy (ApEn), sample entropy (SampEn), Fuzzy entropy, and three permutation entropy (PE) measures [Shannon PE (SPE), Tsallis PE (TPE) and Renyi PE (RPE)]. Two EEG data sets from sevoflurane-induced and isoflurane-induced anesthesia respectively were selected to assess the capability of each entropy index in DoA monitoring and BSP detection. To validate the effectiveness of these entropy algorithms, pharmacokinetic/pharmacodynamic (PK/PD) modeling and prediction probability (Pk) analysis were applied. The multifractal detrended fluctuation analysis (MDFA) as a non-entropy measure was compared. Results: All the entropy and MDFA indices could track the changes in EEG pattern during different anesthesia states. Three PE measures outperformed the other entropy indices, with less baseline variability, higher coefficient of determination (R2) and prediction probability, and RPE performed best; ApEn and SampEn discriminated BSP best. Additionally, these entropy measures showed an advantage in computation
International Nuclear Information System (INIS)
Baccetti, Valentina; Visser, Matt
2013-01-01
Even if a probability distribution is properly normalizable, its associated Shannon (or von Neumann) entropy can easily be infinite. We carefully analyze conditions under which this phenomenon can occur. Roughly speaking, this happens when arbitrarily small amounts of probability are dispersed into an infinite number of states; we shall quantify this observation and make it precise. We develop several particularly simple, elementary, and useful bounds, and also provide some asymptotic estimates, leading to necessary and sufficient conditions for the occurrence of infinite Shannon entropy. We go to some effort to keep technical computations as simple and conceptually clear as possible. In particular, we shall see that large entropies cannot be localized in state space; large entropies can only be supported on an exponentially large number of states. We are for the time being interested in single-channel Shannon entropy in the information theoretic sense, not entropy in a stochastic field theory or quantum field theory defined over some configuration space, on the grounds that this simple problem is a necessary precursor to understanding infinite entropy in a field theoretic context. (paper)
Relation Entropy and Transferable Entropy Think of Aggregation on Group Decision Making
Institute of Scientific and Technical Information of China (English)
CHENG Qi-yue; QIU Wan-hua; LIU Xiao-feng
2002-01-01
In this paper, aggregation question based on group decision making and a single decision making is studied. The theory of entropy is applied to the sets pair analysis. The system of relation entropy and the transferable entropy notion are put. The character is studied. An potential by the relation entropy and transferable entropy are defined. It is the consistency measure on the group between a single decision making. We gained a new aggregation effective definition on the group misjudge.
RNA Thermodynamic Structural Entropy.
Directory of Open Access Journals (Sweden)
Juan Antonio Garcia-Martin
Full Text Available Conformational entropy for atomic-level, three dimensional biomolecules is known experimentally to play an important role in protein-ligand discrimination, yet reliable computation of entropy remains a difficult problem. Here we describe the first two accurate and efficient algorithms to compute the conformational entropy for RNA secondary structures, with respect to the Turner energy model, where free energy parameters are determined from UV absorption experiments. An algorithm to compute the derivational entropy for RNA secondary structures had previously been introduced, using stochastic context free grammars (SCFGs. However, the numerical value of derivational entropy depends heavily on the chosen context free grammar and on the training set used to estimate rule probabilities. Using data from the Rfam database, we determine that both of our thermodynamic methods, which agree in numerical value, are substantially faster than the SCFG method. Thermodynamic structural entropy is much smaller than derivational entropy, and the correlation between length-normalized thermodynamic entropy and derivational entropy is moderately weak to poor. In applications, we plot the structural entropy as a function of temperature for known thermoswitches, such as the repression of heat shock gene expression (ROSE element, we determine that the correlation between hammerhead ribozyme cleavage activity and total free energy is improved by including an additional free energy term arising from conformational entropy, and we plot the structural entropy of windows of the HIV-1 genome. Our software RNAentropy can compute structural entropy for any user-specified temperature, and supports both the Turner'99 and Turner'04 energy parameters. It follows that RNAentropy is state-of-the-art software to compute RNA secondary structure conformational entropy. Source code is available at https://github.com/clotelab/RNAentropy/; a full web server is available at http
RNA Thermodynamic Structural Entropy.
Garcia-Martin, Juan Antonio; Clote, Peter
2015-01-01
Conformational entropy for atomic-level, three dimensional biomolecules is known experimentally to play an important role in protein-ligand discrimination, yet reliable computation of entropy remains a difficult problem. Here we describe the first two accurate and efficient algorithms to compute the conformational entropy for RNA secondary structures, with respect to the Turner energy model, where free energy parameters are determined from UV absorption experiments. An algorithm to compute the derivational entropy for RNA secondary structures had previously been introduced, using stochastic context free grammars (SCFGs). However, the numerical value of derivational entropy depends heavily on the chosen context free grammar and on the training set used to estimate rule probabilities. Using data from the Rfam database, we determine that both of our thermodynamic methods, which agree in numerical value, are substantially faster than the SCFG method. Thermodynamic structural entropy is much smaller than derivational entropy, and the correlation between length-normalized thermodynamic entropy and derivational entropy is moderately weak to poor. In applications, we plot the structural entropy as a function of temperature for known thermoswitches, such as the repression of heat shock gene expression (ROSE) element, we determine that the correlation between hammerhead ribozyme cleavage activity and total free energy is improved by including an additional free energy term arising from conformational entropy, and we plot the structural entropy of windows of the HIV-1 genome. Our software RNAentropy can compute structural entropy for any user-specified temperature, and supports both the Turner'99 and Turner'04 energy parameters. It follows that RNAentropy is state-of-the-art software to compute RNA secondary structure conformational entropy. Source code is available at https://github.com/clotelab/RNAentropy/; a full web server is available at http
Institute of Scientific and Technical Information of China (English)
S.Abdel-Khalek; M.M.A.Ahmed; A-S F.Obada
2011-01-01
We present an effective two-level system in interaction through two-photon processes with a single mode quantized electromagnetic field,initially prepared in a coherent state.Field entropy squeezing as an indicator of the entanglement in a mixed state system is suggested.The temporal evolution of the negativity,Wehrl entropy,Wehrl phase distribution and field entropy squeezing are investigated.The results highlight the important roles played by both the Stark shift parameters and the mixed state setting in the dynamics of the Wehrl entropy,Wehrl phase distribution and field entropy squeezing.%We present an effective two-level system in interaction through two-photon processes with a single mode quantized electromagnetic Reid, initially prepared in a coherent state. Field entropy squeezing as an indicator of the entanglement in a mixed state system is suggested. The temporal evolution of the negativity, Wehrl entropy, Wehrl phase distribution and field entropy squeezing are investigated. The results highlight the important roles played by both the Stark shift parameters and the mixed state setting in the dynamics of the Wehrl entropy, Wehrl phase distribution and field entropy squeezing.
New constraints for holographic entropy from maximin: A no-go theorem
Rota, Massimiliano; Weinberg, Sean J.
2018-04-01
The Ryu-Takayanagi (RT) formula for static spacetimes arising in the AdS/CFT correspondence satisfies inequalities that are not yet proven in the case of the Rangamani-Hubeny-Takayanagi (HRT) formula, which applies to general dynamical spacetimes. Wall's maximin construction is the only known technique for extending inequalities of holographic entanglement entropy from the static to dynamical case. We show that this method currently has no further utility when dealing with inequalities for five or fewer regions. Despite this negative result, we propose the validity of one new inequality for covariant holographic entanglement entropy for five regions. This inequality, while not maximin provable, is much weaker than many of the inequalities satisfied by the RT formula and should therefore be easier to prove. If it is valid, then there is strong evidence that holographic entanglement entropy plays a role in general spacetimes including those that arise in cosmology. Our new inequality is obtained by the assumption that the HRT formula satisfies every known balanced inequality obeyed by the Shannon entropies of classical probability distributions. This is a property that the RT formula has been shown to possess and which has been previously conjectured to hold for quantum mechanics in general.
Chaos control in an economic model via minimum entropy strategy
Energy Technology Data Exchange (ETDEWEB)
Salarieh, Hassan [Center of Excellence in Design, Robotics and Automation, Department of Mechanical Engineering, Sharif University of Technology, P.O. Box 11365-9567, Tehran (Iran, Islamic Republic of)], E-mail: salarieh@mech.sharif.edu; Alasty, Aria [Center of Excellence in Design, Robotics and Automation, Department of Mechanical Engineering, Sharif University of Technology, P.O. Box 11365-9567, Tehran (Iran, Islamic Republic of); National Research Institute for Science Policy (NRISP), Soheil Street, Shirazi Avenue, Tehran (Iran, Islamic Republic of)], E-mail: aalasti@sharif.edu
2009-04-30
In this paper, minimum entropy algorithm for controlling chaos, is applied to a Cournot duopoly with different constant marginal costs, as a discrete-time dynamical system which shows chaotic behavior. The ME control is implemented through delayed feedback. It is assumed that the equations of the dynamical system are not known, so the feedback gain cannot be obtained analytically from the system equations. In the ME method the feedback gain is obtained adaptively in such a way that the entropy of the system converges to zero, hence a fixed point of the system will be stabilized. Application of the proposed method with different economic control strategies is numerically investigated. Simulation results show the effectiveness of the ME method for controlling chaos in economic systems with unknown equations.
Well posedness and maximum entropy approximation for the dynamics of quantitative traits
Boďová , Katarí na; Haskovec, Jan; Markowich, Peter A.
2017-01-01
We study the Fokker–Planck equation derived in the large system limit of the Markovian process describing the dynamics of quantitative traits. The Fokker–Planck equation is posed on a bounded domain and its transport and diffusion coefficients vanish on the domain’s boundary. We first argue that, despite this degeneracy, the standard no-flux boundary condition is valid. We derive the weak formulation of the problem and prove the existence and uniqueness of its solutions by constructing the corresponding contraction semigroup on a suitable function space. Then, we prove that for the parameter regime with high enough mutation rate the problem exhibits a positive spectral gap, which implies exponential convergence to equilibrium.Next, we provide a simple derivation of the so-called Dynamic Maximum Entropy (DynMaxEnt) method for approximation of observables (moments) of the Fokker–Planck solution, which can be interpreted as a nonlinear Galerkin approximation. The limited applicability of the DynMaxEnt method inspires us to introduce its modified version that is valid for the whole range of admissible parameters. Finally, we present several numerical experiments to demonstrate the performance of both the original and modified DynMaxEnt methods. We observe that in the parameter regimes where both methods are valid, the modified one exhibits slightly better approximation properties compared to the original one.
Well posedness and maximum entropy approximation for the dynamics of quantitative traits
Boďová, Katarína
2017-11-06
We study the Fokker–Planck equation derived in the large system limit of the Markovian process describing the dynamics of quantitative traits. The Fokker–Planck equation is posed on a bounded domain and its transport and diffusion coefficients vanish on the domain’s boundary. We first argue that, despite this degeneracy, the standard no-flux boundary condition is valid. We derive the weak formulation of the problem and prove the existence and uniqueness of its solutions by constructing the corresponding contraction semigroup on a suitable function space. Then, we prove that for the parameter regime with high enough mutation rate the problem exhibits a positive spectral gap, which implies exponential convergence to equilibrium.Next, we provide a simple derivation of the so-called Dynamic Maximum Entropy (DynMaxEnt) method for approximation of observables (moments) of the Fokker–Planck solution, which can be interpreted as a nonlinear Galerkin approximation. The limited applicability of the DynMaxEnt method inspires us to introduce its modified version that is valid for the whole range of admissible parameters. Finally, we present several numerical experiments to demonstrate the performance of both the original and modified DynMaxEnt methods. We observe that in the parameter regimes where both methods are valid, the modified one exhibits slightly better approximation properties compared to the original one.
Correlation as a Determinant of Configurational Entropy in Supramolecular and Protein Systems
2015-01-01
For biomolecules in solution, changes in configurational entropy are thought to contribute substantially to the free energies of processes like binding and conformational change. In principle, the configurational entropy can be strongly affected by pairwise and higher-order correlations among conformational degrees of freedom. However, the literature offers mixed perspectives regarding the contributions that changes in correlations make to changes in configurational entropy for such processes. Here we take advantage of powerful techniques for simulation and entropy analysis to carry out rigorous in silico studies of correlation in binding and conformational changes. In particular, we apply information-theoretic expansions of the configurational entropy to well-sampled molecular dynamics simulations of a model host–guest system and the protein bovine pancreatic trypsin inhibitor. The results bear on the interpretation of NMR data, as they indicate that changes in correlation are important determinants of entropy changes for biologically relevant processes and that changes in correlation may either balance or reinforce changes in first-order entropy. The results also highlight the importance of main-chain torsions as contributors to changes in protein configurational entropy. As simulation techniques grow in power, the mathematical techniques used here will offer new opportunities to answer challenging questions about complex molecular systems. PMID:24702693
Interacting entropy-corrected new agegraphic dark energy in the non-flat universe
Energy Technology Data Exchange (ETDEWEB)
Karami, Kayoomars [Department of Physics, University of Kurdistan, Pasdaran Street, Sanandaj (Iran, Islamic Republic of); Sorouri, Arash, E-mail: KKarami@uok.ac.i [Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), Maragha (Iran, Islamic Republic of)
2010-08-15
Here, we consider the entropy-corrected version of the new agegraphic dark energy (NADE) model in the non-flat Friedmann-Robertson-Walker universe. We derive the exact differential equation that determines the evolution of the entropy-corrected NADE density parameter in the presence of interaction with dark matter. We also obtain the equation of state and deceleration parameters and present a necessary condition for the selected model to cross the phantom divide. Moreover, we reconstruct the potential and the dynamics of the phantom scalar field according to the evolutionary behavior of the interacting entropy-corrected new agegraphic model.
Surface single-molecule dynamics controlled by entropy at low temperatures
Gehrig, J. C.; Penedo, M.; Parschau, M.; Schwenk, J.; Marioni, M. A.; Hudson, E. W.; Hug, H. J.
2017-02-01
Configuration transitions of individual molecules and atoms on surfaces are traditionally described using an Arrhenius equation with energy barrier and pre-exponential factor (attempt rate) parameters. Characteristic parameters can vary even for identical systems, and pre-exponential factors sometimes differ by orders of magnitude. Using low-temperature scanning tunnelling microscopy (STM) to measure an individual dibutyl sulfide molecule on Au(111), we show that the differences arise when the relative position of tip apex and molecule changes by a fraction of the molecule size. Altering the tip position on that scale modifies the transition's barrier and attempt rate in a highly correlated fashion, which results in a single-molecular enthalpy-entropy compensation. Conversely, appropriately positioning the STM tip allows selecting the operating point on the compensation line and modifying the transition rates. The results highlight the need to consider entropy in transition rates of single molecules, even at low temperatures.
Entropy correlation and entanglement for mixed states in an algebraic model
International Nuclear Information System (INIS)
Hou Xiwen; Chen Jinghua; Wan Mingfang; Ma Zhongqi
2009-01-01
As an alternative with potential connections to actual experiments, other than the systems more usually used in the field of entanglement, the dynamics of entropy correlation and entanglement between two anharmonic vibrations in a well-established algebraic model, with parameters extracted from fitting to highly excited spectral experimental results for molecules H 2 O and SO 2 , is studied in terms of the linear entropy and two negativities for various initial states that are respectively taken to be the mixed density matrices of thermal states and squeezed states on each mode. For a suitable parameter in initial states the entropies in two stretches can show positive correlation or anti-correlation. And the linear entropy of each mode is positively correlated with the negativities just for the mixed-squeezed states with small parameters in H 2 O while they do not display any correlation in other cases. For the mixed-squeezed states the negativities exhibit dominantly positive correlations with an effective mutual entropy. The differences in the linear entropy and the negativities between H 2 O and SO 2 are discussed as well. Those are useful for molecular quantum computing and quantum information processing
78 FR 54298 - Horizons ETFs Management (USA) LLC and Horizons ETF Trust; Notice of Application
2013-09-03
... ETFs Management (USA) LLC and Horizons ETF Trust; Notice of Application August 27, 2013. AGENCY... Management (USA) LLC (``Horizons'') and Horizons ETF Trust (the ``Trust''). Summary of Application... of the Trust will be the Horizons Active Global Dividend ETF (the ``Initial Fund''), which will seek...
EEG entropy measures in anesthesia
Directory of Open Access Journals (Sweden)
Zhenhu eLiang
2015-02-01
Full Text Available Objective: Entropy algorithms have been widely used in analyzing EEG signals during anesthesia. However, a systematic comparison of these entropy algorithms in assessing anesthesia drugs’ effect is lacking. In this study, we compare the capability of twelve entropy indices for monitoring depth of anesthesia (DoA and detecting the burst suppression pattern (BSP, in anesthesia induced by GA-BAergic agents.Methods: Twelve indices were investigated, namely Response Entropy (RE and State entropy (SE, three wavelet entropy (WE measures (Shannon WE (SWE, Tsallis WE (TWE and Renyi WE (RWE, Hilbert-Huang spectral entropy (HHSE, approximate entropy (ApEn, sample entropy (SampEn, Fuzzy entropy, and three permutation entropy (PE measures (Shannon PE (SPE, Tsallis PE (TPE and Renyi PE (RPE. Two EEG data sets from sevoflurane-induced and isoflu-rane-induced anesthesia respectively were selected to assess the capability of each entropy index in DoA monitoring and BSP detection. To validate the effectiveness of these entropy algorithms, phar-macokinetic / pharmacodynamic (PK/PD modeling and prediction probability analysis were applied. The multifractal detrended fluctuation analysis (MDFA as a non-entropy measure was compared.Results: All the entropy and MDFA indices could track the changes in EEG pattern during different anesthesia states. Three PE measures outperformed the other entropy indices, with less baseline vari-ability, higher coefficient of determination and prediction probability, and RPE performed best; ApEn and SampEn discriminated BSP best. Additionally, these entropy measures showed an ad-vantage in computation efficiency compared with MDFA.Conclusion: Each entropy index has its advantages and disadvantages in estimating DoA. Overall, it is suggested that the RPE index was a superior measure.Significance: Investigating the advantages and disadvantages of these entropy indices could help improve current clinical indices for monitoring DoA.
New Horizons in Gravity: The Trace Anomaly, Dark Energy and Condensate Stars
Mottola, Emil
2010-01-01
General Relativity receives quantum corrections relevant at macroscopic distance scales and near event horizons. These arise from the conformal scalar degrees of freedom in the extended effective field theory of gravity generated by the trace anomaly of massless quantum fields in curved space. The origin of these conformal scalar degrees of freedom as massless poles in two-particle intermediate states of anomalous amplitudes in flat space is exposed. At event horizons the conformal anomaly scalar degrees of freedom can have macroscopically large effects on the geometry, potentially removing the classical event horizon of black hole and cosmological spacetimes, replacing them with a quantum boundary layer where the effective value of the gravitational vacuum energy density can change. In the effective theory, the cosmological term becomes a dynamical condensate, whose value depends upon boundary conditions near the horizon. In the conformal phase where the anomaly induced fluctutations dominate, and the conden...
Saha, Subhajit; Biswas, Atreyee; Chakraborty, Subenoy
2015-03-01
In the present work, flat FRW model of the universe is considered to be an isolated open thermodynamical system where non-equilibrium prescription has been studied using the mechanism of particle creation. In the perspective of recent observational evidences, the matter distribution in the universe is assumed to be dominated by dark matter and dark energy. The dark matter is chosen as dust while for dark energy, the following choices are considered: (i) Perfect fluid with constant equation of state and (ii) Holographic dark energy. In both the cases, the validity of generalized second law of thermodynamics (GSLT) which states that the total entropy of the fluid as well as that of the horizon should not decrease with the evolution of the universe, has been examined graphically for universe bounded by the event horizon. It is found that GSLT holds in both the cases with some restrictions on the interacting coupling parameter.
Energy Technology Data Exchange (ETDEWEB)
Larry G. Stolarczyk
2003-03-18
With the aid of a DOE grant (No. DE-FC26-01NT41050), Stolar Research Corporation (Stolar) developed the Horizon Sensor (HS) to distinguish between the different layers of a coal seam. Mounted on mining machine cutter drums, HS units can detect or sense the horizon between the coal seam and the roof and floor rock, providing the opportunity to accurately mine the section of the seam most desired. HS also enables accurate cutting of minimum height if that is the operator's objective. Often when cutting is done out-of-seam, the head-positioning function facilitates a fixed mining height to minimize dilution. With this technology, miners can still be at a remote location, yet cut only the clean coal, resulting in a much more efficient overall process. The objectives of this project were to demonstrate the feasibility of horizon sensing on mining machines and demonstrate that Horizon Sensing can allow coal to be cut cleaner and more efficiently. Stolar's primary goal was to develop the Horizon Sensor (HS) into an enabling technology for full or partial automation or ''agile mining''. This technical innovation (R&D 100 Award Winner) is quickly demonstrating improvements in productivity and miner safety at several prominent coal mines in the United States. In addition, the HS system can enable the cutting of cleaner coal. Stolar has driven the HS program on the philosophy that cutting cleaner coal means burning cleaner coal. The sensor, located inches from the cutting bits, is based upon the physics principles of a Resonant Microstrip Patch Antenna (RMPA). When it is in proximity of the rock-coal interface, the RMPA impedance varies depending on the thickness of uncut coal. The impedance is measured by the computer-controlled electronics and then sent by radio waves to the mining machine. The worker at the machine can read the data via a Graphical User Interface, displaying a color-coded image of the coal being cut, and direct the machine
Sun, Jingliang; Liu, Chunsheng
2018-01-01
In this paper, the problem of intercepting a manoeuvring target within a fixed final time is posed in a non-linear constrained zero-sum differential game framework. The Nash equilibrium solution is found by solving the finite-horizon constrained differential game problem via adaptive dynamic programming technique. Besides, a suitable non-quadratic functional is utilised to encode the control constraints into a differential game problem. The single critic network with constant weights and time-varying activation functions is constructed to approximate the solution of associated time-varying Hamilton-Jacobi-Isaacs equation online. To properly satisfy the terminal constraint, an additional error term is incorporated in a novel weight-updating law such that the terminal constraint error is also minimised over time. By utilising Lyapunov's direct method, the closed-loop differential game system and the estimation weight error of the critic network are proved to be uniformly ultimately bounded. Finally, the effectiveness of the proposed method is demonstrated by using a simple non-linear system and a non-linear missile-target interception system, assuming first-order dynamics for the interceptor and target.
Thurner, Stefan; Corominas-Murtra, Bernat; Hanel, Rudolf
2017-09-01
There are at least three distinct ways to conceptualize entropy: entropy as an extensive thermodynamic quantity of physical systems (Clausius, Boltzmann, Gibbs), entropy as a measure for information production of ergodic sources (Shannon), and entropy as a means for statistical inference on multinomial processes (Jaynes maximum entropy principle). Even though these notions represent fundamentally different concepts, the functional form of the entropy for thermodynamic systems in equilibrium, for ergodic sources in information theory, and for independent sampling processes in statistical systems, is degenerate, H (p ) =-∑ipilogpi . For many complex systems, which are typically history-dependent, nonergodic, and nonmultinomial, this is no longer the case. Here we show that for such processes, the three entropy concepts lead to different functional forms of entropy, which we will refer to as SEXT for extensive entropy, SIT for the source information rate in information theory, and SMEP for the entropy functional that appears in the so-called maximum entropy principle, which characterizes the most likely observable distribution functions of a system. We explicitly compute these three entropy functionals for three concrete examples: for Pólya urn processes, which are simple self-reinforcing processes, for sample-space-reducing (SSR) processes, which are simple history dependent processes that are associated with power-law statistics, and finally for multinomial mixture processes.
Structured chaos shapes spike-response noise entropy in balanced neural networks
Directory of Open Access Journals (Sweden)
Guillaume eLajoie
2014-10-01
Full Text Available Large networks of sparsely coupled, excitatory and inhibitory cells occur throughout the brain. For many models of these networks, a striking feature is that their dynamics are chaotic and thus, are sensitive to small perturbations. How does this chaos manifest in the neural code? Specifically, how variable are the spike patterns that such a network produces in response to an input signal? To answer this, we derive a bound for a general measure of variability -- spike-train entropy. This leads to important insights on the variability of multi-cell spike pattern distributions in large recurrent networks of spiking neurons responding to fluctuating inputs. The analysis is based on results from random dynamical systems theory and is complemented by detailed numerical simulations. We find that the spike pattern entropy is an order of magnitude lower than what would be extrapolated from single cells. This holds despite the fact that network coupling becomes vanishingly sparse as network size grows -- a phenomenon that depends on ``extensive chaos, as previously discovered for balanced networks without stimulus drive. Moreover, we show how spike pattern entropy is controlled by temporal features of the inputs. Our findings provide insight into how neural networks may encode stimuli in the presence of inherently chaotic dynamics.
Entropy Production and Fluctuation Theorems for Active Matter
Mandal, Dibyendu; Klymko, Katherine; DeWeese, Michael R.
2017-12-01
Active biological systems reside far from equilibrium, dissipating heat even in their steady state, thus requiring an extension of conventional equilibrium thermodynamics and statistical mechanics. In this Letter, we have extended the emerging framework of stochastic thermodynamics to active matter. In particular, for the active Ornstein-Uhlenbeck model, we have provided consistent definitions of thermodynamic quantities such as work, energy, heat, entropy, and entropy production at the level of single, stochastic trajectories and derived related fluctuation relations. We have developed a generalization of the Clausius inequality, which is valid even in the presence of the non-Hamiltonian dynamics underlying active matter systems. We have illustrated our results with explicit numerical studies.
Enzyme catalysis by entropy without Circe effect.
Kazemi, Masoud; Himo, Fahmi; Åqvist, Johan
2016-03-01
Entropic effects have often been invoked to explain the extraordinary catalytic power of enzymes. In particular, the hypothesis that enzymes can use part of the substrate-binding free energy to reduce the entropic penalty associated with the subsequent chemical transformation has been very influential. The enzymatic reaction of cytidine deaminase appears to be a distinct example. Here, substrate binding is associated with a significant entropy loss that closely matches the activation entropy penalty for the uncatalyzed reaction in water, whereas the activation entropy for the rate-limiting catalytic step in the enzyme is close to zero. Herein, we report extensive computer simulations of the cytidine deaminase reaction and its temperature dependence. The energetics of the catalytic reaction is first evaluated by density functional theory calculations. These results are then used to parametrize an empirical valence bond description of the reaction, which allows efficient sampling by molecular dynamics simulations and computation of Arrhenius plots. The thermodynamic activation parameters calculated by this approach are in excellent agreement with experimental data and indeed show an activation entropy close to zero for the rate-limiting transition state. However, the origin of this effect is a change of reaction mechanism compared the uncatalyzed reaction. The enzyme operates by hydroxide ion attack, which is intrinsically associated with a favorable activation entropy. Hence, this has little to do with utilization of binding free energy to pay the entropic penalty but rather reflects how a preorganized active site can stabilize a reaction path that is not operational in solution.
Emergence of spacetime dynamics in entropy corrected and braneworld models
International Nuclear Information System (INIS)
Sheykhi, A.; Dehghani, M.H.; Hosseini, S.E.
2013-01-01
A very interesting new proposal on the origin of the cosmic expansion was recently suggested by Padmanabhan [arXiv:1206.4916]. He argued that the difference between the surface degrees of freedom and the bulk degrees of freedom in a region of space drives the accelerated expansion of the universe, as well as the standard Friedmann equation through relation ΔV = Δt(N sur −N bulk ). In this paper, we first present the general expression for the number of degrees of freedom on the holographic surface, N sur , using the general entropy corrected formula S = A/(4L p 2 )+s(A). Then, as two example, by applying the Padmanabhan's idea we extract the corresponding Friedmann equations in the presence of power-law and logarithmic correction terms in the entropy. We also extend the study to RS II and DGP braneworld models and derive successfully the correct form of the Friedmann equations in these theories. Our study further supports the viability of Padmanabhan's proposal
Information Flows? A Critique of Transfer Entropies
James, Ryan G.; Barnett, Nix; Crutchfield, James P.
2016-06-01
A central task in analyzing complex dynamics is to determine the loci of information storage and the communication topology of information flows within a system. Over the last decade and a half, diagnostics for the latter have come to be dominated by the transfer entropy. Via straightforward examples, we show that it and a derivative quantity, the causation entropy, do not, in fact, quantify the flow of information. At one and the same time they can overestimate flow or underestimate influence. We isolate why this is the case and propose several avenues to alternate measures for information flow. We also address an auxiliary consequence: The proliferation of networks as a now-common theoretical model for large-scale systems, in concert with the use of transferlike entropies, has shoehorned dyadic relationships into our structural interpretation of the organization and behavior of complex systems. This interpretation thus fails to include the effects of polyadic dependencies. The net result is that much of the sophisticated organization of complex systems may go undetected.
Spacetimes foliated by Killing horizons
International Nuclear Information System (INIS)
Pawlowski, Tomasz; Lewandowski, Jerzy; Jezierski, Jacek
2004-01-01
It seems to be expected that a horizon of a quasi-local type, such as a Killing or an isolated horizon, by analogy with a globally defined event horizon, should be unique in some open neighbourhood in the spacetime, provided the vacuum Einstein or the Einstein-Maxwell equations are satisfied. The aim of our paper is to verify whether that intuition is correct. If one can extend a so-called Kundt metric, in such a way that its null, shear-free surfaces have spherical spacetime sections, the resulting spacetime is foliated by so-called non-expanding horizons. The obstacle is Kundt's constraint induced at the surfaces by the Einstein or the Einstein-Maxwell equations, and the requirement that a solution be globally defined on the sphere. We derived a transformation (reflection) that creates a solution to Kundt's constraint out of data defining an extremal isolated horizon. Using that transformation, we derived a class of exact solutions to the Einstein or Einstein-Maxwell equations of very special properties. Each spacetime we construct is foliated by a family of the Killing horizons. Moreover, it admits another, transversal Killing horizon. The intrinsic and extrinsic geometries of the transversal Killing horizon coincide with the one defined on the event horizon of the extremal Kerr-Newman solution. However, the Killing horizon in our example admits yet another Killing vector tangent to and null at it. The geometries of the leaves are given by the reflection
Multivariate Generalized Multiscale Entropy Analysis
Directory of Open Access Journals (Sweden)
Anne Humeau-Heurtier
2016-11-01
Full Text Available Multiscale entropy (MSE was introduced in the 2000s to quantify systems’ complexity. MSE relies on (i a coarse-graining procedure to derive a set of time series representing the system dynamics on different time scales; (ii the computation of the sample entropy for each coarse-grained time series. A refined composite MSE (rcMSE—based on the same steps as MSE—also exists. Compared to MSE, rcMSE increases the accuracy of entropy estimation and reduces the probability of inducing undefined entropy for short time series. The multivariate versions of MSE (MMSE and rcMSE (MrcMSE have also been introduced. In the coarse-graining step used in MSE, rcMSE, MMSE, and MrcMSE, the mean value is used to derive representations of the original data at different resolutions. A generalization of MSE was recently published, using the computation of different moments in the coarse-graining procedure. However, so far, this generalization only exists for univariate signals. We therefore herein propose an extension of this generalized MSE to multivariate data. The multivariate generalized algorithms of MMSE and MrcMSE presented herein (MGMSE and MGrcMSE, respectively are first analyzed through the processing of synthetic signals. We reveal that MGrcMSE shows better performance than MGMSE for short multivariate data. We then study the performance of MGrcMSE on two sets of short multivariate electroencephalograms (EEG available in the public domain. We report that MGrcMSE may show better performance than MrcMSE in distinguishing different types of multivariate EEG data. MGrcMSE could therefore supplement MMSE or MrcMSE in the processing of multivariate datasets.
arXiv Effective horizons, junction conditions and large-scale magnetism
Giovannini, Massimo
2017-08-05
The quantum mechanical generation of hypermagnetic and hyperlectric fields in four-dimensional conformally flat background geometries rests on the simultaneous continuity of the effective horizon and of the extrinsic curvature across the inflationary boundary. The junction conditions for the gauge fields are derived in general terms and corroborated by explicit examples with particular attention to the limit of a sudden (but nonetheless continuous) transition of the effective horizon. After reducing the dynamics to a pair of integral equations related by duality transformations, we compute the power spectra and deduce a novel class of logarithmic corrections which turn out to be, however, numerically insignificant and overwhelmed by the conductivity effects once the gauge modes reenter the effective horizon. In this perspective the magnetogenesis requirements and the role of the postinflationary conductivity are clarified and reappraised. As long as the total duration of the inflationary phase is nearly minim...
A Dynamic Model of Information and Entropy
Directory of Open Access Journals (Sweden)
Stuart D. Walker
2010-01-01
Full Text Available We discuss the possibility of a relativistic relationship between information and entropy, closely analogous to the classical Maxwell electro-magnetic wave equations. Inherent to the analysis is the description of information as residing in points of non-analyticity; yet ultimately also exhibiting a distributed characteristic: additionally analogous, therefore, to the wave-particle duality of light. At cosmological scales our vector differential equations predict conservation of information in black holes, whereas regular- and Z-DNA molecules correspond to helical solutions at microscopic levels. We further propose that regular- and Z-DNA are equivalent to the alternative words chosen from an alphabet to maintain the equilibrium of an information transmission system.
Energy Technology Data Exchange (ETDEWEB)
Bao, Ning [Institute for Quantum Information and Matter, California Institute of Technology,Pasadena, CA 91125 (United States); Walter Burke Institute for Theoretical Physics, California Institute of Technology,452-48, Pasadena, CA 91125 (United States); Nezami, Sepehr [Stanford Institute for Theoretical Physics, Stanford University,Stanford, CA 94305 (United States); Ooguri, Hirosi [Walter Burke Institute for Theoretical Physics, California Institute of Technology,452-48, Pasadena, CA 91125 (United States); Kavli Institute for the Physics and Mathematics of the Universe, University of Tokyo,Kashiwa 277-8583 (Japan); Stoica, Bogdan [Walter Burke Institute for Theoretical Physics, California Institute of Technology,452-48, Pasadena, CA 91125 (United States); Sully, James [Theory Group, SLAC National Accelerator Laboratory, Stanford University,Menlo Park, CA 94025 (United States); Walter, Michael [Stanford Institute for Theoretical Physics, Stanford University,Stanford, CA 94305 (United States)
2015-09-21
We initiate a systematic enumeration and classification of entropy inequalities satisfied by the Ryu-Takayanagi formula for conformal field theory states with smooth holographic dual geometries. For 2, 3, and 4 regions, we prove that the strong subadditivity and the monogamy of mutual information give the complete set of inequalities. This is in contrast to the situation for generic quantum systems, where a complete set of entropy inequalities is not known for 4 or more regions. We also find an infinite new family of inequalities applicable to 5 or more regions. The set of all holographic entropy inequalities bounds the phase space of Ryu-Takayanagi entropies, defining the holographic entropy cone. We characterize this entropy cone by reducing geometries to minimal graph models that encode the possible cutting and gluing relations of minimal surfaces. We find that, for a fixed number of regions, there are only finitely many independent entropy inequalities. To establish new holographic entropy inequalities, we introduce a combinatorial proof technique that may also be of independent interest in Riemannian geometry and graph theory.
International Nuclear Information System (INIS)
Bao, Ning; Nezami, Sepehr; Ooguri, Hirosi; Stoica, Bogdan; Sully, James; Walter, Michael
2015-01-01
We initiate a systematic enumeration and classification of entropy inequalities satisfied by the Ryu-Takayanagi formula for conformal field theory states with smooth holographic dual geometries. For 2, 3, and 4 regions, we prove that the strong subadditivity and the monogamy of mutual information give the complete set of inequalities. This is in contrast to the situation for generic quantum systems, where a complete set of entropy inequalities is not known for 4 or more regions. We also find an infinite new family of inequalities applicable to 5 or more regions. The set of all holographic entropy inequalities bounds the phase space of Ryu-Takayanagi entropies, defining the holographic entropy cone. We characterize this entropy cone by reducing geometries to minimal graph models that encode the possible cutting and gluing relations of minimal surfaces. We find that, for a fixed number of regions, there are only finitely many independent entropy inequalities. To establish new holographic entropy inequalities, we introduce a combinatorial proof technique that may also be of independent interest in Riemannian geometry and graph theory.
Addressing gender dynamics and engaging men in HIV programs: lessons learned from Horizons research.
Pulerwitz, Julie; Michaelis, Annie; Verma, Ravi; Weiss, Ellen
2010-01-01
In the field of human immunodeficiency virus (HIV) prevention, there has been increasing interest in the role that gender plays in HIV and violence risk, and in successfully engaging men in the response. This article highlights findings from more than 10 studies in Asia, Africa, and Latin America--conducted from 1997 through 2007 as part of the Horizons program--that have contributed to understanding the relationship between gender and men's behaviors, developing useful measurement tools for gender norms, and designing and evaluating the impact of gender-focused program strategies. Studies showed significant associations between support for inequitable norms and risk, such as more partner violence and less condom use. Programmatic lessons learned ranged from insights into appropriate media messages, to strategies to engage men in critically reflecting upon gender inequality, to the qualities of successful program facilitators. The portfolio of work reveals the potential and importance of directly addressing gender dynamics in HIV- and violence-prevention programs for both men and women.
Entropy Stable Summation-by-Parts Formulations for Compressible Computational Fluid Dynamics
Carpenter, M.H.; Fisher, T.C.; Nielsen, E.J.; Parsani, Matteo; Svä rd, M.; Yamaleev, N.
2016-01-01
that ensure conservation, accuracy and preserve the interior entropy estimates. Nonlinearly stable solid wall boundary conditions are also available. Existing SBP operators that lack a stability proof (e.g. weighted essentially nonoscillatory) may be combined
Cellular network entropy as the energy potential in Waddington's differentiation landscape
Banerji, Christopher R. S.; Miranda-Saavedra, Diego; Severini, Simone; Widschwendter, Martin; Enver, Tariq; Zhou, Joseph X.; Teschendorff, Andrew E.
2013-01-01
Differentiation is a key cellular process in normal tissue development that is significantly altered in cancer. Although molecular signatures characterising pluripotency and multipotency exist, there is, as yet, no single quantitative mark of a cellular sample's position in the global differentiation hierarchy. Here we adopt a systems view and consider the sample's network entropy, a measure of signaling pathway promiscuity, computable from a sample's genome-wide expression profile. We demonstrate that network entropy provides a quantitative, in-silico, readout of the average undifferentiated state of the profiled cells, recapitulating the known hierarchy of pluripotent, multipotent and differentiated cell types. Network entropy further exhibits dynamic changes in time course differentiation data, and in line with a sample's differentiation stage. In disease, network entropy predicts a higher level of cellular plasticity in cancer stem cell populations compared to ordinary cancer cells. Importantly, network entropy also allows identification of key differentiation pathways. Our results are consistent with the view that pluripotency is a statistical property defined at the cellular population level, correlating with intra-sample heterogeneity, and driven by the degree of signaling promiscuity in cells. In summary, network entropy provides a quantitative measure of a cell's undifferentiated state, defining its elevation in Waddington's landscape. PMID:24154593
On the Conditional Rényi Entropy
S. Fehr (Serge); S. Berens (Stefan)
2014-01-01
htmlabstractThe Rényi entropy of general order unifies the well-known Shannon entropy with several other entropy notions, like the min-entropy or the collision entropy. In contrast to the Shannon entropy, there seems to be no commonly accepted definition for the conditional Rényi entropy: several
International Nuclear Information System (INIS)
Davis, Sergio
2013-01-01
In this work we develop a method for inferring the underlying configurational density of states of a molecular system by combining information from several microcanonical molecular dynamics or Monte Carlo simulations at different energies. This method is based on Jaynes' Maximum Entropy formalism (MaxEnt) for Bayesian statistical inference under known expectation values. We present results of its application to measure thermodynamic entropy and free energy differences in embedded-atom models of metals.
Tsallis-like entropies in quantum scattering
International Nuclear Information System (INIS)
Ion, D.B.; Ion, M.L.
1998-01-01
In this work, the following entropies in quantum scattering are defined: the informational angular entropy, S θ ; Tsallis-like angular entropies, S q (θ); the angular momentum entropy, S L ; the Tsallis-like angular momentum entropies, S q (L); the angle-angular momentum entropy, S θL . These entropies are defined as natural measures of the uncertainties corresponding to the distribution probabilities. If we are interested in obtaining a measure of uncertainty of the simultaneous realization of the probability distributions, than, we have to calculate the entropy corresponding to these distributions. The expression of angle-angular momentum entropy is given. The relation between the Tsallis entropies and the angle-angular momentum entropy is derived
Recovering information of tunneling spectrum from weakly isolated horizon
Energy Technology Data Exchange (ETDEWEB)
Chen, Ge-Rui; Huang, Yong-Chang [Beijing University of Technology, Institute of Theoretical Physics, Beijing (China)
2015-02-01
In this paper we investigate the properties of tunneling spectrum from weakly isolated horizon (WIH) - a locally defined black hole. We find that there exist correlations among Hawking radiations from a WIH, information can be carried out by such correlations, and the radiation is an entropy conservation process. Through revisiting the calculation of the tunneling spectrum from a WIH, we find that Zhang et al.'s (Ann Phys 326:350, 2011) requirement that radiated particles have the same angular momenta of a unit mass as that of the black hole is unnecessary, and the energy and angular momenta of the emitted particles are very arbitrary, restricted only by keeping the cosmic censorship hypothesis of black holes. So we resolve the information loss paradox based on the method of Zhang et al. (Phys Lett B 675:98, 2009; Ann Phys 326:350, 2011; Int J Mod Phys D 22:1341014, 2013) in a general case. (orig.)
Real-time moving horizon estimation for a vibrating active cantilever
Abdollahpouri, Mohammad; Takács, Gergely; Rohaľ-Ilkiv, Boris
2017-03-01
Vibrating structures may be subject to changes throughout their operating lifetime due to a range of environmental and technical factors. These variations can be considered as parameter changes in the dynamic model of the structure, while their online estimates can be utilized in adaptive control strategies, or in structural health monitoring. This paper implements the moving horizon estimation (MHE) algorithm on a low-cost embedded computing device that is jointly observing the dynamic states and parameter variations of an active cantilever beam in real time. The practical behavior of this algorithm has been investigated in various experimental scenarios. It has been found, that for the given field of application, moving horizon estimation converges faster than the extended Kalman filter; moreover, it handles atypical measurement noise, sensor errors or other extreme changes, reliably. Despite its improved performance, the experiments demonstrate that the disadvantage of solving the nonlinear optimization problem in MHE is that it naturally leads to an increase in computational effort.
Extremal rotating black holes in the near-horizon limit: Phase space and symmetry algebra
Directory of Open Access Journals (Sweden)
G. Compère
2015-10-01
Full Text Available We construct the NHEG phase space, the classical phase space of Near-Horizon Extremal Geometries with fixed angular momenta and entropy, and with the largest symmetry algebra. We focus on vacuum solutions to d dimensional Einstein gravity. Each element in the phase space is a geometry with SL(2,R×U(1d−3 isometries which has vanishing SL(2,R and constant U(1 charges. We construct an on-shell vanishing symplectic structure, which leads to an infinite set of symplectic symmetries. In four spacetime dimensions, the phase space is unique and the symmetry algebra consists of the familiar Virasoro algebra, while in d>4 dimensions the symmetry algebra, the NHEG algebra, contains infinitely many Virasoro subalgebras. The nontrivial central term of the algebra is proportional to the black hole entropy. The conserved charges are given by the Fourier decomposition of a Liouville-type stress-tensor which depends upon a single periodic function of d−3 angular variables associated with the U(1 isometries. This phase space and in particular its symmetries can serve as a basis for a semiclassical description of extremal rotating black hole microstates.
Entropy for Mechanically Vibrating Systems
Tufano, Dante
The research contained within this thesis deals with the subject of entropy as defined for and applied to mechanically vibrating systems. This work begins with an overview of entropy as it is understood in the fields of classical thermodynamics, information theory, statistical mechanics, and statistical vibroacoustics. Khinchin's definition of entropy, which is the primary definition used for the work contained in this thesis, is introduced in the context of vibroacoustic systems. The main goal of this research is to to establish a mathematical framework for the application of Khinchin's entropy in the field of statistical vibroacoustics by examining the entropy context of mechanically vibrating systems. The introduction of this thesis provides an overview of statistical energy analysis (SEA), a modeling approach to vibroacoustics that motivates this work on entropy. The objective of this thesis is given, and followed by a discussion of the intellectual merit of this work as well as a literature review of relevant material. Following the introduction, an entropy analysis of systems of coupled oscillators is performed utilizing Khinchin's definition of entropy. This analysis develops upon the mathematical theory relating to mixing entropy, which is generated by the coupling of vibroacoustic systems. The mixing entropy is shown to provide insight into the qualitative behavior of such systems. Additionally, it is shown that the entropy inequality property of Khinchin's entropy can be reduced to an equality using the mixing entropy concept. This equality can be interpreted as a facet of the second law of thermodynamics for vibroacoustic systems. Following this analysis, an investigation of continuous systems is performed using Khinchin's entropy. It is shown that entropy analyses using Khinchin's entropy are valid for continuous systems that can be decomposed into a finite number of modes. The results are shown to be analogous to those obtained for simple oscillators
Promise Okekwe: Rising Star on the Nigerian Literary Horizon ...
African Journals Online (AJOL)
... a young and upcoming talent on the Nigeria literary horizon. Okekwe was first published in 1992. A resilient and dynamic writer, she has continued to produce texts at a pace akin to Buchi Emecheta's. Her works reveal a remarkable understanding of the human mind. She thus aims at a reconstruction of the wider society.
Generalized sample entropy analysis for traffic signals based on similarity measure
Shang, Du; Xu, Mengjia; Shang, Pengjian
2017-05-01
Sample entropy is a prevailing method used to quantify the complexity of a time series. In this paper a modified method of generalized sample entropy and surrogate data analysis is proposed as a new measure to assess the complexity of a complex dynamical system such as traffic signals. The method based on similarity distance presents a different way of signals patterns match showing distinct behaviors of complexity. Simulations are conducted over synthetic data and traffic signals for providing the comparative study, which is provided to show the power of the new method. Compared with previous sample entropy and surrogate data analysis, the new method has two main advantages. The first one is that it overcomes the limitation about the relationship between the dimension parameter and the length of series. The second one is that the modified sample entropy functions can be used to quantitatively distinguish time series from different complex systems by the similar measure.
Application of the maximum entropy method to dynamical fermion simulations
Clowser, Jonathan
This thesis presents results for spectral functions extracted from imaginary-time correlation functions obtained from Monte Carlo simulations using the Maximum Entropy Method (MEM). The advantages this method are (i) no a priori assumptions or parametrisations of the spectral function are needed, (ii) a unique solution exists and (iii) the statistical significance of the resulting image can be quantitatively analysed. The Gross Neveu model in d = 3 spacetime dimensions (GNM3) is a particularly interesting model to study with the MEM because at T = 0 it has a broken phase with a rich spectrum of mesonic bound states and a symmetric phase where there are resonances. Results for the elementary fermion, the Goldstone boson (pion), the sigma, the massive pseudoscalar meson and the symmetric phase resonances are presented. UKQCD Nf = 2 dynamical QCD data is also studied with MEM. Results are compared to those found from the quenched approximation, where the effects of quark loops in the QCD vacuum are neglected, to search for sea-quark effects in the extracted spectral functions. Information has been extract from the difficult axial spatial and scalar as well as the pseudoscalar, vector and axial temporal channels. An estimate for the non-singlet scalar mass in the chiral limit is given which is in agreement with the experimental value of Mao = 985 MeV.
The pedogeochemical segregation a few horizons in soils from glass houses
Bulgariu, Dumitru; Rusu, Constantin; Filipov, Feodor; Buzgar, Nicolae; Bulgariu, Laura
2010-05-01
Our studies have focused the apparition and manifestation conditions of pedogeochemical segregation phenomena in case of soils from Copou - Iaşi, Bacău and Bârlad (Romania) glass house, and the effects of this on the pedogeochemical and agrochemical characteristics of soils from glass houses cultivated with vegetables. The utilization of intensive cultivation technologies of vegetables in glass houses determined the degradation of morphological, physical and chemical characteristics of soils, by rapid evolution of salted processes (salinization and / or sodization), compaction, carbonatation, eluviation-illuviation, frangipane formation, stagnogleization, gleization etc. Under these conditions, at depth of 30-40 cm is formed a compact and impenetrable horizon - Ahok(x) horizon. In function of exploitation conditions and by the chemical-mineralogical characteristics of soils from glasshouses, the Ahok horizons can have frangipane properties, expressed more or less. These horizons determined a geochemical segregation of soils from glass houses: (i) superior horizons, above Ahok(x) horizon evolve in weak oxidative conditions, weak alkaline pH, higher salinity, humidity and temperature; (ii) inferior horizons, below Ahok(x) horizon evolve in weak reducing conditions weak acid pH, lower salinity, humidity and temperature. Concomitant with the development of Ahok(x) horizons, the rapid degradation of the properties of soils from glasshouses is observed. The aspects about the formation of frangipane horizon in soils from glasshouses are not yet sufficiently know. Whatever of the formation processes, the frangipane horizons determined a sever segregation in pedogeochemical evolution of soils from glass houses, with very important consequences on the agrochemical quality of these soils. The segregation effects are manifested in the differential dynamics of pedogeochemical processes from superior horizons (situated above the segregation horizon), in comparison with the
Entropy of the electroencephalogram as applied in the M-Entropy S ...
African Journals Online (AJOL)
Background: It has been suggested that spectral entropy of the electroencephalogram as applied in the M-Entropy S/5TM Module (GE Healthcare) does not detect the effects of nitrous oxide (N2O). The aim of this study was to investigate the effect on entropy by graded increases in N2O concentrations in the presence of a ...
International Nuclear Information System (INIS)
Giangaspero, Giorgio; Sciubba, Enrico
2013-01-01
This paper presents an application of the entropy generation minimization method to the pseudo-optimization of the configuration of the heat exchange surfaces in a Solar Rooftile. An initial “standard” commercial configuration is gradually improved by introducing design changes aimed at the reduction of the thermodynamic losses due to heat transfer and fluid friction. Different geometries (pins, fins and others) are analysed with a commercial CFD (Computational Fluid Dynamics) code that also computes the local entropy generation rate. The design improvement process is carried out on the basis of a careful analysis of the local entropy generation maps and the rationale behind each step of the process is discussed in this perspective. The results are compared with other entropy generation minimization techniques available in the recent technical literature. It is found that the geometry with pin-fins has the best performance among the tested ones, and that the optimal pin array shape parameters (pitch and span) can be determined by a critical analysis of the integrated and local entropy maps and of the temperature contours. - Highlights: ► An entropy generation minimization method is applied to a solar heat exchanger. ► The approach is heuristic and leads to a pseudo-optimization process with CFD as main tool. ► The process is based on the evaluation of the local entropy generation maps. ► The geometry with pin-fins in general outperforms all other configurations. ► The entropy maps and temperature contours can be used to determine the optimal pin array design parameters
Entropy of Baker's Transformation
Institute of Scientific and Technical Information of China (English)
栾长福
2003-01-01
Four theorems about four different kinds of entropies for Baker's transformation are presented. The Kolmogorov entropy of Baker's transformation is sensitive to the initial flips by the time. The topological entropy of Baker's transformation is found to be log k. The conditions for the state of Baker's transformation to be forbidden are also derived. The relations among the Shanonn, Kolmogorov, topological and Boltzmann entropies are discussed in details.
The maximum entropy production and maximum Shannon information entropy in enzyme kinetics
Dobovišek, Andrej; Markovič, Rene; Brumen, Milan; Fajmut, Aleš
2018-04-01
We demonstrate that the maximum entropy production principle (MEPP) serves as a physical selection principle for the description of the most probable non-equilibrium steady states in simple enzymatic reactions. A theoretical approach is developed, which enables maximization of the density of entropy production with respect to the enzyme rate constants for the enzyme reaction in a steady state. Mass and Gibbs free energy conservations are considered as optimization constraints. In such a way computed optimal enzyme rate constants in a steady state yield also the most uniform probability distribution of the enzyme states. This accounts for the maximal Shannon information entropy. By means of the stability analysis it is also demonstrated that maximal density of entropy production in that enzyme reaction requires flexible enzyme structure, which enables rapid transitions between different enzyme states. These results are supported by an example, in which density of entropy production and Shannon information entropy are numerically maximized for the enzyme Glucose Isomerase.
Multivariate multiscale entropy of financial markets
Lu, Yunfan; Wang, Jun
2017-11-01
In current process of quantifying the dynamical properties of the complex phenomena in financial market system, the multivariate financial time series are widely concerned. In this work, considering the shortcomings and limitations of univariate multiscale entropy in analyzing the multivariate time series, the multivariate multiscale sample entropy (MMSE), which can evaluate the complexity in multiple data channels over different timescales, is applied to quantify the complexity of financial markets. Its effectiveness and advantages have been detected with numerical simulations with two well-known synthetic noise signals. For the first time, the complexity of four generated trivariate return series for each stock trading hour in China stock markets is quantified thanks to the interdisciplinary application of this method. We find that the complexity of trivariate return series in each hour show a significant decreasing trend with the stock trading time progressing. Further, the shuffled multivariate return series and the absolute multivariate return series are also analyzed. As another new attempt, quantifying the complexity of global stock markets (Asia, Europe and America) is carried out by analyzing the multivariate returns from them. Finally we utilize the multivariate multiscale entropy to assess the relative complexity of normalized multivariate return volatility series with different degrees.
Spacetimes containing slowly evolving horizons
International Nuclear Information System (INIS)
Kavanagh, William; Booth, Ivan
2006-01-01
Slowly evolving horizons are trapping horizons that are ''almost'' isolated horizons. This paper reviews their definition and discusses several spacetimes containing such structures. These include certain Vaidya and Tolman-Bondi solutions as well as (perturbatively) tidally distorted black holes. Taking into account the mass scales and orders of magnitude that arise in these calculations, we conjecture that slowly evolving horizons are the norm rather than the exception in astrophysical processes that involve stellar-scale black holes
Entropy production in a cell and reversal of entropy flow as an anticancer therapy
Institute of Scientific and Technical Information of China (English)
Liao-fu LUO
2009-01-01
The entropy production rate of cancer cells is always higher than healthy cells in the case where no external field is applied. Different entropy production between two kinds of cells determines the direction of entropy flow among cells. The entropy flow is the carrier of information flow. The entropy flow from cancerous cells to healthy cells takes along the harmful information of cancerous cells, propagating its toxic action to healthy tissues. We demonstrate that a low-frequency and low- intensity electromagnetic field or ultrasound irradiation may increase the entropy production rate of a cell in normal tissue than that in cancer and consequently re- verse the direction of entropy current between two kinds of cells. The modification of the PH value of cells may also cause the reversal of the direction of entropy flow between healthy and cancerous cells. Therefore, the bio- logical tissue under the irradiation of an electromagnetic field or ultrasound or under the appropriate change of cell acidity can avoid the propagation of harmful infor- marion from cancer cells. We suggest that this entropy mechanism possibly provides a basis for a novel approach to anticancer therapy.
A second law analysis and entropy generation minimization of an absorption chiller
Myat, Aung; Thu, Kyaw; Kim, Youngdeuk; Chakraborty, Anutosh; Chun, Wongee; Ng, K. C.
2011-01-01
This paper presents performance analysis of absorption refrigeration system (ARS) using an entropy generation analysis. A numerical model predicts the performance of absorption cycle operating under transient conditions along with the entropy generation computation at assorted heat source temperatures, and it captures also the dynamic changes of lithium bromide solution properties such as concentration, density, vapor pressure and overall heat transfer coefficients. An optimization tool, namely the genetic algorithm (GA), is used as to locate the system minima for all defined domain of heat source and cooling water temperatures. The analysis shows that minimization of entropy generation the in absorption cycle leads to the maximization of the COP. © 2011 Elsevier Ltd. All rights reserved.
A second law analysis and entropy generation minimization of an absorption chiller
Myat, Aung
2011-10-01
This paper presents performance analysis of absorption refrigeration system (ARS) using an entropy generation analysis. A numerical model predicts the performance of absorption cycle operating under transient conditions along with the entropy generation computation at assorted heat source temperatures, and it captures also the dynamic changes of lithium bromide solution properties such as concentration, density, vapor pressure and overall heat transfer coefficients. An optimization tool, namely the genetic algorithm (GA), is used as to locate the system minima for all defined domain of heat source and cooling water temperatures. The analysis shows that minimization of entropy generation the in absorption cycle leads to the maximization of the COP. © 2011 Elsevier Ltd. All rights reserved.
The different paths to entropy
International Nuclear Information System (INIS)
Benguigui, L
2013-01-01
In order to understand how the complex concept of entropy emerged, we propose a trip into the past, reviewing the works of Clausius, Boltzmann, Gibbs and Planck. In particular, since Gibbs's work is not very well known we present a detailed analysis, recalling the three definitions of entropy that Gibbs gives. The introduction of entropy in quantum mechanics gives in a compact form all the classical definitions of entropy. Perhaps one of the most important aspects of entropy is to see it as a thermodynamic potential like the others proposed by Callen. The calculation of fluctuations in thermodynamic quantities is thus naturally related to entropy. We close with some remarks on entropy and irreversibility. (paper)
Near-Optimal Tracking Control of Mobile Robots Via Receding-Horizon Dual Heuristic Programming.
Lian, Chuanqiang; Xu, Xin; Chen, Hong; He, Haibo
2016-11-01
Trajectory tracking control of wheeled mobile robots (WMRs) has been an important research topic in control theory and robotics. Although various tracking control methods with stability have been developed for WMRs, it is still difficult to design optimal or near-optimal tracking controller under uncertainties and disturbances. In this paper, a near-optimal tracking control method is presented for WMRs based on receding-horizon dual heuristic programming (RHDHP). In the proposed method, a backstepping kinematic controller is designed to generate desired velocity profiles and the receding horizon strategy is used to decompose the infinite-horizon optimal control problem into a series of finite-horizon optimal control problems. In each horizon, a closed-loop tracking control policy is successively updated using a class of approximate dynamic programming algorithms called finite-horizon dual heuristic programming (DHP). The convergence property of the proposed method is analyzed and it is shown that the tracking control system based on RHDHP is asymptotically stable by using the Lyapunov approach. Simulation results on three tracking control problems demonstrate that the proposed method has improved control performance when compared with conventional model predictive control (MPC) and DHP. It is also illustrated that the proposed method has lower computational burden than conventional MPC, which is very beneficial for real-time tracking control.
Applying Improved Multiscale Fuzzy Entropy for Feature Extraction of MI-EEG
Directory of Open Access Journals (Sweden)
Ming-ai Li
2017-01-01
Full Text Available Electroencephalography (EEG is considered the output of a brain and it is a bioelectrical signal with multiscale and nonlinear properties. Motor Imagery EEG (MI-EEG not only has a close correlation with the human imagination and movement intention but also contains a large amount of physiological or disease information. As a result, it has been fully studied in the field of rehabilitation. To correctly interpret and accurately extract the features of MI-EEG signals, many nonlinear dynamic methods based on entropy, such as Approximate Entropy (ApEn, Sample Entropy (SampEn, Fuzzy Entropy (FE, and Permutation Entropy (PE, have been proposed and exploited continuously in recent years. However, these entropy-based methods can only measure the complexity of MI-EEG based on a single scale and therefore fail to account for the multiscale property inherent in MI-EEG. To solve this problem, Multiscale Sample Entropy (MSE, Multiscale Permutation Entropy (MPE, and Multiscale Fuzzy Entropy (MFE are developed by introducing scale factor. However, MFE has not been widely used in analysis of MI-EEG, and the same parameter values are employed when the MFE method is used to calculate the fuzzy entropy values on multiple scales. Actually, each coarse-grained MI-EEG carries the characteristic information of the original signal on different scale factors. It is necessary to optimize MFE parameters to discover more feature information. In this paper, the parameters of MFE are optimized independently for each scale factor, and the improved MFE (IMFE is applied to the feature extraction of MI-EEG. Based on the event-related desynchronization (ERD/event-related synchronization (ERS phenomenon, IMFE features from multi channels are fused organically to construct the feature vector. Experiments are conducted on a public dataset by using Support Vector Machine (SVM as a classifier. The experiment results of 10-fold cross-validation show that the proposed method yields
International Nuclear Information System (INIS)
Hanni, R.S.
1975-01-01
The concept of the plasma horizon, defined as the boundary of the region in which an infinitely thin plasma can be supported against Coulomb attraction by a magnetic field, shows that the argument of selective accretion does not rule out the existence of charged black holes embedded in a conducting plasma. A detailed account of the covariant definition of plasma horizon is given and some examples of plasma horizons are presented. 7 references
Directory of Open Access Journals (Sweden)
Urban Kordes
2005-10-01
Full Text Available The paper tries to tackle the question of connection between entropy and the living. Definitions of life as the phenomenon that defies entropy are overviewed and the conclusion is reached that life is in a way dependant on entropy - it couldn't exist without it. Entropy is a sort of medium, a fertile soil, that gives life possibility to blossom. Paper ends with presenting some consequences for the field of artificial intelligence.
''Illusion of control'' in Time-Horizon Minority and Parrondo Games
Satinover, J. B.; Sornette, D.
2007-12-01
Human beings like to believe they are in control of their destiny. This ubiquitous trait seems to increase motivation and persistence, and is probably evolutionarily adaptive [J.D. Taylor, S.E. Brown, Psych. Bull. 103, 193 (1988); A. Bandura, Self-efficacy: the exercise of control (WH Freeman, New York, 1997)]. But how good really is our ability to control? How successful is our track record in these areas? There is little understanding of when and under what circumstances we may over-estimate [E. Langer, J. Pers. Soc. Psych. 7, 185 (1975)] or even lose our ability to control and optimize outcomes, especially when they are the result of aggregations of individual optimization processes. Here, we demonstrate analytically using the theory of Markov Chains and by numerical simulations in two classes of games, the Time-Horizon Minority Game [M.L. Hart, P. Jefferies, N.F. Johnson, Phys. A 311, 275 (2002)] and the Parrondo Game [J.M.R. Parrondo, G.P. Harmer, D. Abbott, Phys. Rev. Lett. 85, 5226 (2000); J.M.R. Parrondo, How to cheat a bad mathematician (ISI, Italy, 1996)], that agents who optimize their strategy based on past information may actually perform worse than non-optimizing agents. In other words, low-entropy (more informative) strategies under-perform high-entropy (or random) strategies. This provides a precise definition of the “illusion of control” in certain set-ups a priori defined to emphasize the importance of optimization.
Horizons of semiclassical black holes are cold
Energy Technology Data Exchange (ETDEWEB)
Brustein, Ram [Department of Physics, Ben-Gurion University,Beer-Sheva 84105 (Israel); CAS, Ludwig-Maximilians-Universität München,80333 München (Germany); Medved, A.J.M. [Department of Physics & Electronics, Rhodes University,Grahamstown 6140 (South Africa)
2014-06-10
We calculate, using our recently proposed semiclassical framework, the quantum state of the Hawking pairs that are produced during the evaporation of a black hole (BH). Our framework adheres to the standard rules of quantum mechanics and incorporates the quantum fluctuations of the collapsing shell spacetime in Hawking’s original calculation, while accounting for back-reaction effects. We argue that the negative-energy Hawking modes need to be regularly integrated out; and so these are effectively subsumed by the BH and, as a result, the number of coherent negative-energy modes N{sub coh} at any given time is parametrically smaller than the total number of the Hawking particles N{sub total} emitted during the lifetime of the BH. We find that N{sub coh} is determined by the width of the BH wavefunction and scales as the square root of the BH entropy. We also find that the coherent negative-energy modes are strongly entangled with their positive-energy partners. Previously, we have found that N{sub coh} is also the number of coherent outgoing particles and that information can be continually transferred to the outgoing radiation at a rate set by N{sub coh}. Our current results show that, while the BH is semiclassical, information can be released without jeopardizing the nearly maximal inside-out entanglement and imply that the state of matter near the horizon is approximately the vacuum. The BH firewall proposal, on the other hand, is that the state of matter near the horizon deviates substantially from the vacuum, starting at the Page time. We find that, under the usual assumptions for justifying the formation of a firewall, one does indeed form at the Page time. However, the possible loophole lies in the implicit assumption that the number of strongly entangled pairs can be of the same order of N{sub total}.
Editorial: Entropy in Landscape Ecology
Directory of Open Access Journals (Sweden)
Samuel A. Cushman
2018-04-01
Full Text Available Entropy and the second law of thermodynamics are the central organizing principles of nature, but the ideas and implications of the second law are poorly developed in landscape ecology. The purpose of this Special Issue “Entropy in Landscape Ecology” in Entropy is to bring together current research on applications of thermodynamics in landscape ecology, to consolidate current knowledge and identify key areas for future research. The special issue contains six articles, which cover a broad range of topics including relationships between entropy and evolution, connections between fractal geometry and entropy, new approaches to calculate configurational entropy of landscapes, example analyses of computing entropy of landscapes, and using entropy in the context of optimal landscape planning. Collectively these papers provide a broad range of contributions to the nascent field of ecological thermodynamics. Formalizing the connections between entropy and ecology are in a very early stage, and that this special issue contains papers that address several centrally important ideas, and provides seminal work that will be a foundation for the future development of ecological and evolutionary thermodynamics.
Time-series analysis of multiple foreign exchange rates using time-dependent pattern entropy
Ishizaki, Ryuji; Inoue, Masayoshi
2018-01-01
Time-dependent pattern entropy is a method that reduces variations to binary symbolic dynamics and considers the pattern of symbols in a sliding temporal window. We use this method to analyze the instability of daily variations in multiple foreign exchange rates. The time-dependent pattern entropy of 7 foreign exchange rates (AUD/USD, CAD/USD, CHF/USD, EUR/USD, GBP/USD, JPY/USD, and NZD/USD) was found to be high in the long period after the Lehman shock, and be low in the long period after Mar 2012. We compared the correlation matrix between exchange rates in periods of high and low of the time-dependent pattern entropy.
Transfer entropy in physical systems and the arrow of time
Spinney, Richard E.; Lizier, Joseph T.; Prokopenko, Mikhail
2016-08-01
Recent developments have cemented the realization that many concepts and quantities in thermodynamics and information theory are shared. In this paper, we consider a highly relevant quantity in information theory and complex systems, the transfer entropy, and explore its thermodynamic role by considering the implications of time reversal upon it. By doing so we highlight the role of information dynamics on the nuanced question of observer perspective within thermodynamics by relating the temporal irreversibility in the information dynamics to the configurational (or spatial) resolution of the thermodynamics. We then highlight its role in perhaps the most enduring paradox in modern physics, the manifestation of a (thermodynamic) arrow of time. We find that for systems that process information such as those undergoing feedback, a robust arrow of time can be formulated by considering both the apparent physical behavior which leads to conventional entropy production and the information dynamics which leads to a quantity we call the information theoretic arrow of time. We also offer an interpretation in terms of optimal encoding of observed physical behavior.
Nearest Neighbor Estimates of Entropy for Multivariate Circular Distributions
Directory of Open Access Journals (Sweden)
Neeraj Misra
2010-05-01
Full Text Available In molecular sciences, the estimation of entropies of molecules is important for the understanding of many chemical and biological processes. Motivated by these applications, we consider the problem of estimating the entropies of circular random vectors and introduce non-parametric estimators based on circular distances between n sample points and their k th nearest neighbors (NN, where k (≤ n – 1 is a fixed positive integer. The proposed NN estimators are based on two different circular distances, and are proven to be asymptotically unbiased and consistent. The performance of one of the circular-distance estimators is investigated and compared with that of the already established Euclidean-distance NN estimator using Monte Carlo samples from an analytic distribution of six circular variables of an exactly known entropy and a large sample of seven internal-rotation angles in the molecule of tartaric acid, obtained by a realistic molecular-dynamics simulation.
Multiscale Permutation Entropy Based Rolling Bearing Fault Diagnosis
Directory of Open Access Journals (Sweden)
Jinde Zheng
2014-01-01
Full Text Available A new rolling bearing fault diagnosis approach based on multiscale permutation entropy (MPE, Laplacian score (LS, and support vector machines (SVMs is proposed in this paper. Permutation entropy (PE was recently proposed and defined to measure the randomicity and detect dynamical changes of time series. However, for the complexity of mechanical systems, the randomicity and dynamic changes of the vibration signal will exist in different scales. Thus, the definition of MPE is introduced and employed to extract the nonlinear fault characteristics from the bearing vibration signal in different scales. Besides, the SVM is utilized to accomplish the fault feature classification to fulfill diagnostic procedure automatically. Meanwhile, in order to avoid a high dimension of features, the Laplacian score (LS is used to refine the feature vector by ranking the features according to their importance and correlations with the main fault information. Finally, the rolling bearing fault diagnosis method based on MPE, LS, and SVM is proposed and applied to the experimental data. The experimental data analysis results indicate that the proposed method could identify the fault categories effectively.
DEFF Research Database (Denmark)
Müller-Lennert, Martin; Dupont-Dupuis, Fréderic; Szehr, Oleg
2013-01-01
The Rényi entropies constitute a family of information measures that generalizes the well-known Shannon entropy, inheriting many of its properties. They appear in the form of unconditional and conditional entropies, relative entropies, or mutual information, and have found many applications in in...
Entanglement entropy of ABJM theory and entropy of topological black hole
Nian, Jun; Zhang, Xinyu
2017-07-01
In this paper we discuss the supersymmetric localization of the 4D N = 2 offshell gauged supergravity on the background of the AdS4 neutral topological black hole, which is the gravity dual of the ABJM theory defined on the boundary {S}^1× H^2 . We compute the large- N expansion of the supergravity partition function. The result gives the black hole entropy with the logarithmic correction, which matches the previous result of the entanglement entropy of the ABJM theory up to some stringy effects. Our result is consistent with the previous on-shell one-loop computation of the logarithmic correction to black hole entropy. It provides an explicit example of the identification of the entanglement entropy of the boundary conformal field theory with the bulk black hole entropy beyond the leading order given by the classical Bekenstein-Hawking formula, which consequently tests the AdS/CFT correspondence at the subleading order.
Models, Entropy and Information of Temporal Social Networks
Zhao, Kun; Karsai, Márton; Bianconi, Ginestra
Temporal social networks are characterized by heterogeneous duration of contacts, which can either follow a power-law distribution, such as in face-to-face interactions, or a Weibull distribution, such as in mobile-phone communication. Here we model the dynamics of face-to-face interaction and mobile phone communication by a reinforcement dynamics, which explains the data observed in these different types of social interactions. We quantify the information encoded in the dynamics of these networks by the entropy of temporal networks. Finally, we show evidence that human dynamics is able to modulate the information present in social network dynamics when it follows circadian rhythms and when it is interfacing with a new technology such as the mobile-phone communication technology.
2015-09-29
antiferroelectrics. Phys. Rev. Lett. 110, 017603 (2013). 22. Cantor , B., Chang, I., Knight, P. & Vincent, A. Microstructural development in equiatomic...Science 345, 1153–1158 (2014). 24. Gali, A. & George , E. Tensile properties of high- and medium-entropy alloys. Intermetallics 39, 74–78 (2013). 25...148–153 (2014). 26. Otto, F., Yang, Y., Bei, H. & George , E. Relative effects of enthalpy and entropy on the phase stability of equiatomic high-entropy
Thermostatistical aspects of generalized entropies
International Nuclear Information System (INIS)
Fa, K.S.; Lenzi, E.K.
2004-01-01
We investigate the properties concerning a class of generalized entropies given by S q,r =k{1-[Σ i p i q ] r }/[r(q-1)] which include Tsallis' entropy (r=1), the usual Boltzmann-Gibbs entropy (q=1), Renyi's entropy (r=0) and normalized Tsallis' entropy (r=-1). In order to obtain the generalized thermodynamic relations we use the laws of thermodynamics and considering the hypothesis that the joint probability of two independent systems is given by p ij A c upB =p i A p j B . We show that the transmutation which occurs from Tsallis' entropy to Renyi's entropy also occur with S q,r . In this scenario, we also analyze the generalized variance, covariance and correlation coefficient of a non-interacting system by using extended optimal Lagrange multiplier approach. We show that the correlation coefficient tends to zero in the thermodynamic limit. However, Renyi's entropy related to this non-interacting system presents a certain degree of non-extensivity
Absolute entropy of ions in methanol
International Nuclear Information System (INIS)
Abakshin, V.A.; Kobenin, V.A.; Krestov, G.A.
1978-01-01
By measuring the initial thermoelectromotive forces of chains with bromo-silver electrodes in tetraalkylammonium bromide solutions the absolute entropy of bromide-ion in methanol is determined in the 298.15-318.15 K range. The anti Ssub(Brsup(-))sup(0) = 9.8 entropy units value is used for calculation of the absolute partial molar entropy of alkali metal ions and halogenide ions. It has been found that, absolute entropy of Cs + =12.0 entropy units, I - =14.0 entropy units. The obtained ion absolute entropies in methanol at 298.15 K within 1-2 entropy units is in an agreement with published data
On the relationship between NMR-derived amide order parameters and protein backbone entropy changes.
Sharp, Kim A; O'Brien, Evan; Kasinath, Vignesh; Wand, A Joshua
2015-05-01
Molecular dynamics simulations are used to analyze the relationship between NMR-derived squared generalized order parameters of amide NH groups and backbone entropy. Amide order parameters (O(2) NH ) are largely determined by the secondary structure and average values appear unrelated to the overall flexibility of the protein. However, analysis of the more flexible subset (O(2) NH entropy than that reported by the side chain methyl axis order parameters, O(2) axis . A calibration curve for backbone entropy vs. O(2) NH is developed, which accounts for both correlations between amide group motions of different residues, and correlations between backbone and side chain motions. This calibration curve can be used with experimental values of O(2) NH changes obtained by NMR relaxation measurements to extract backbone entropy changes, for example, upon ligand binding. In conjunction with our previous calibration for side chain entropy derived from measured O(2) axis values this provides a prescription for determination of the total protein conformational entropy changes from NMR relaxation measurements. © 2015 Wiley Periodicals, Inc.
Some remarks on conditional entropy
Nijst, A.G.P.M.
1969-01-01
Using a definition of conditional entropy given by Hanen and Neveu [5, 10, 11] we discuss in this paper some properties of conditional entropy and mean entropy, in particular an integral representation of conditional entropy (§ 2), and the decomposition theorem of the KolmogorovSina¯i invariant (§
Shear viscosity and entropy of a pion gas
Energy Technology Data Exchange (ETDEWEB)
Rose, Jean-Bernard; Oliinychenko, Dmytro; Schaefer, Anna; Petersen, Hannah [FIAS, Goethe University, Frankfurt (Germany)
2016-07-01
A model of microscopic non-equilibrium dynamics for classical point particles is used to calculate the transport coefficients of dense hadronic matter. Specifically, the shear viscosity to entropy density ratio is investigated, and the temperature dependence between 100 MeV and 300 MeV is explored. Calculations are made at corresponding particle densities going from 0.01 to 0.34 in a pion box simulating infinite matter. The results for the entropy and shear viscosity are then compared to analytic estimates. In addition, massless particles as well as ρ-meson resonance excitations are included. This will be the starting point for the calculation of more transport coefficients as functions of T and μ{sub B}; expanding systems could also be considered.
Entropy, matter, and cosmology.
Prigogine, I; Géhéniau, J
1986-09-01
The role of irreversible processes corresponding to creation of matter in general relativity is investigated. The use of Landau-Lifshitz pseudotensors together with conformal (Minkowski) coordinates suggests that this creation took place in the early universe at the stage of the variation of the conformal factor. The entropy production in this creation process is calculated. It is shown that these dissipative processes lead to the possibility of cosmological models that start from empty conditions and gradually build up matter and entropy. Gravitational entropy takes a simple meaning as associated to the entropy that is necessary to produce matter. This leads to an extension of the third law of thermodynamics, as now the zero point of entropy becomes the space-time structure out of which matter is generated. The theory can be put into a convenient form using a supplementary "C" field in Einstein's field equations. The role of the C field is to express the coupling between gravitation and matter leading to irreversible entropy production.
Relations Among Some Fuzzy Entropy Formulae
Institute of Scientific and Technical Information of China (English)
卿铭
2004-01-01
Fuzzy entropy has been widely used to analyze and design fuzzy systems, and many fuzzy entropy formulae have been proposed. For further in-deepth analysis of fuzzy entropy, the axioms and some important formulae of fuzzy entropy are introduced. Some equivalence results among these fuzzy entropy formulae are proved, and it is shown that fuzzy entropy is a special distance measurement.
Energy Technology Data Exchange (ETDEWEB)
Giveon, Amit [Racah Institute of Physics, The Hebrew University,Jerusalem 91904 (Israel); Itzhaki, Nissan [Physics Department, Tel-Aviv University,Ramat-Aviv, 69978 (Israel); Kutasov, David [EFI and Department of Physics, University of Chicago,5640 S. Ellis Av., Chicago, IL 60637 (United States)
2015-06-11
We argue that classical (α{sup ′}) effects qualitatively modify the structure of Euclidean black hole horizons in string theory. While low energy modes experience the geometry familiar from general relativity, high energy ones see a rather different geometry, in which the Euclidean horizon can be penetrated by an amount that grows with the radial momentum of the probe. We discuss this in the exactly solvable SL(2,ℝ)/U(1) black hole, where it is a manifestation of the black hole/Sine-Liouville duality.
Traversaro, Francisco; O. Redelico, Francisco
2018-04-01
In nonlinear dynamics, and to a lesser extent in other fields, a widely used measure of complexity is the Permutation Entropy. But there is still no known method to determine the accuracy of this measure. There has been little research on the statistical properties of this quantity that characterize time series. The literature describes some resampling methods of quantities used in nonlinear dynamics - as the largest Lyapunov exponent - but these seems to fail. In this contribution, we propose a parametric bootstrap methodology using a symbolic representation of the time series to obtain the distribution of the Permutation Entropy estimator. We perform several time series simulations given by well-known stochastic processes: the 1/fα noise family, and show in each case that the proposed accuracy measure is as efficient as the one obtained by the frequentist approach of repeating the experiment. The complexity of brain electrical activity, measured by the Permutation Entropy, has been extensively used in epilepsy research for detection in dynamical changes in electroencephalogram (EEG) signal with no consideration of the variability of this complexity measure. An application of the parametric bootstrap methodology is used to compare normal and pre-ictal EEG signals.
International Nuclear Information System (INIS)
Karami, K; Ghaffari, S; Soltanzadeh, M M
2010-01-01
We investigate the validity of the generalized second law (GSL) of gravitational thermodynamics on the apparent and event horizons in a non-flat Friedmann-Robertson-Walker (FRW) universe containing dark energy interacting with dark matter. We show that for the dynamical apparent horizon, the GSL is always satisfied throughout the history of the universe for any spatial curvature and it is independent of the equation of state parameter of the interacting dark energy model. On the other hand, for the cosmological event horizon, the validity of the GSL depends on the equation of state parameter of the model.