Area evolution, bulk viscosity and entropy principles for dynamical horizons
Gourgoulhon, E; Gourgoulhon, Eric; Jaramillo, Jose Luis
2006-01-01
We derive from Einstein equation an evolution law for the area of a trapping or dynamical horizon. The solutions to this differential equation show a causal behavior. Moreover, in a viscous fluid analogy, the equation can be interpreted as an energy balance law, yielding to a positive bulk viscosity. These two features contrast with the event horizon case, where the non-causal evolution of the area and the negative bulk viscosity require teleological boundary conditions. This reflects the local character of trapping horizons as opposed to event horizons. Interpreting the area as the entropy, we propose to use an area/entropy evolution principle to select a unique dynamical horizon and time slicing in the Cauchy evolution of an initial marginally trapped surface.
Dynamical Horizon Entropy Bound Conjecture in Loop Quantum Cosmology
Institute of Scientific and Technical Information of China (English)
李丽仿; 朱建阳
2012-01-01
The covariant entropy bound conjecture is an important hint for the quantum gravity, with several versions available in the literature. For cosmology, Ashtekar and Wilson-Ewing ever show the consistence between the loop gravity theory and one version of this conjecture. Recently, He and Zhang [J. High Energy Phys. 10 （2007） 077] proposed a version for the dynamical horizon of the universe, which validates the entropy bound conjecture for the cosmology filled with perfect fluid in the classical scenario when the universe is far away from the big bang singularity. However, their conjecture breaks down near big bang region. We examine this conjecture in the context of the loop quantum cosmology. With the example of photon gas, this conjecture is protected by the quantum geometry effects as expected.
Howard, Eric M
2016-01-01
We analyze spacetimes with horizons and study the thermodynamic aspects of causal horizons, suggesting that the resemblance between gravitational and thermodynamic systems has a deeper quantum mechanical origin. We find that the observer dependence of such horizons is a direct consequence of associating a temperature and entropy to a spacetime. The geometrical picture of a horizon acting as a one-way membrane for information flow can be accepted as a natural interpretation of assigning a quantum field theory to a spacetime with boundary, ultimately leading to a close connection with thermodynamics.
First law of thermodynamics for dynamical apparent horizons and the entropy of Friedmann universes
Viaggiu, Stefano
2015-01-01
Recently, we have generalized the Bekenstein-Hawking entropy formula for black holes embedded in expanding Friedmann universes. In this letter, we begin the study of this new formula to obtain the first law of thermodynamics for dynamical apparent horizons. In this regard we obtain a generalized expression for the internal energy $U$ together with a distinction between the dynamical temperature $T_D$ of apparent horizons and the related one due to thermodynamics formulas. Remarkable, when the expression for $U$ is applied to the apparent horizon of the universe, we found that this internal energy is a constant of motion. Our calculations thus show that the total energy of our spatially flat universe including the gravitational contribution, when calculated at the apparent horizon, is an universal constant that can be set to zero from simple dimensional considerations. This strongly support the holographic principle.
Entropy of Isolated Horizons revisited
Basu, Rudranil; Majumdar, Parthasarathi
2009-01-01
The decade-old formulation of the isolated horizon classically and within loop quantum gravity, and the extraction of the microcanonical entropy of such a horizon from this formulation, is reviewed, in view of recent renewed interest. There are two main approaches to this problem: one employs an SU(2) Chern-Simons theory describing the isolated horizon degrees of freedom, while the other uses a reduced U(1) Chern-Simons theory obtained from the SU(2) theory, with appropriate constraints imposed on the spectrum of boundary states `living' on the horizon. It is shown that both these ways lead to the same infinite series asymptotic in horizon area for the microcanonical entropy of an isolated horizon. The leading area term is followed by an unambiguous correction term logarithmic in area with a coefficient $-\\frac32$, with subleading corrections dropping off as inverse powers of the area.
Symmetry and entropy of black hole horizons
Dreyer, O; Smolin, L; Dreyer, Olaf; Markopoulou, Fotini; Smolin, Lee
2004-01-01
We argue, using methods taken from the theory of noiseless subsystems in quantum information theory, that the quantum states associated with a Schwarzchild black hole live in the restricted subspace of the Hilbert space of horizon boundary states in which all punctures are equal. Consequently, one value of the Immirzi parameter matches both the Hawking value for the entropy and the quasi normal mode spectrum of the Schwarzchild black hole.
Symmetries, Horizons, and Black Hole Entropy
Carlip, S
2007-01-01
Black holes behave as thermodynamic systems, and a central task of any quantum theory of gravity is to explain these thermal properties. A statistical mechanical description of black hole entropy once seemed remote, but today we suffer an embarrassment of riches: despite counting very different states, many inequivalent approaches to quantum gravity obtain identical results. Such ``universality'' may reflect an underlying two-dimensional conformal symmetry near the horizon, which can be powerful enough to control the thermal characteristics independent of other details of the theory. This picture suggests an elegant description of the relevant degrees of freedom as Goldstone-boson-like excitations arising from symmetry breaking by the conformal anomaly.
Entropy bound of horizons for charged and rotating black holes
Directory of Open Access Journals (Sweden)
Wei Xu
2015-06-01
Full Text Available We revisit the entropy product, entropy sum and other thermodynamic relations of charged and rotating black holes. Based on these relations, we derive the entropy (area bound for both event horizon and Cauchy horizon. We establish these results for variant class of 4-dimensional charged and rotating black holes in Einstein(–Maxwell gravity and higher derivative gravity. We also generalize the discussion to black holes with NUT charge. The validity of this formula, which seems to be universal for black holes with two horizons, gives further clue on the crucial role that the thermodynamic relations of multi-horizons play in black hole thermodynamics and understanding the entropy at the microscopic level.
Entropy bound of horizons for charged and rotating black holes
Energy Technology Data Exchange (ETDEWEB)
Xu, Wei, E-mail: xuweifuture@gmail.com [School of Physics, Huazhong University of Science and Technology, Wuhan 430074 (China); Wang, Jia, E-mail: wangjia2010@mail.nankai.edu.cn [School of Physics, Nankai University, Tianjin 300071 (China); Meng, Xin-he, E-mail: xhm@nankai.edu.cn [School of Physics, Nankai University, Tianjin 300071 (China); State Key Laboratory of Institute of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190 (China)
2015-06-30
We revisit the entropy product, entropy sum and other thermodynamic relations of charged and rotating black holes. Based on these relations, we derive the entropy (area) bound for both event horizon and Cauchy horizon. We establish these results for variant class of 4-dimensional charged and rotating black holes in Einstein(–Maxwell) gravity and higher derivative gravity. We also generalize the discussion to black holes with NUT charge. The validity of this formula, which seems to be universal for black holes with two horizons, gives further clue on the crucial role that the thermodynamic relations of multi-horizons play in black hole thermodynamics and understanding the entropy at the microscopic level.
Black hole entropy from conformal symmetry on the horizon
Carlip, Steven
2017-01-01
The idea that black hole entropy might be governed by a conformal symmetry is an old one, but until now most efforts have focused on either asymptotic symmetries or symmetries on a ``stretched horizon. For two-dimensional dilaton gravity, I show the existence of a well-behaved conformal symmetry that is on the horizon, with a central charge that correctly determines the black hole entropy. Supported by Department of Energy grant DE-FG02-91ER40674.
Horizon entropy and higher curvature equations of state
Guedens, Raf; Sarkar, Sudipta
2011-01-01
The Clausius relation between entropy change and heat flux has previously been used to derive Einstein's field equations as an equation of state. In that derivation the entropy is proportional to the area of a local causal horizon, and the heat is the energy flux across the horizon, defined relative to an approximate boost Killing vector. We examine here whether a similar derivation can be given for extensions beyond Einstein gravity to include higher derivative and higher curvature terms. We review previous proposals which, in our opinion, are problematic or incomplete. Refining one of these, we assume that the horizon entropy depends on an approximate local Killing vector in a way that mimics the diffeomorphism Noether charge that yields the entropy of a stationary black hole. We show how this can be made to work if various restrictions are imposed on the nature of the horizon slices and the approximate Killing vector. Also, an integrability condition on the assumed horizon entropy density must hold. This c...
Anomalous effective action, Noether current, Virasoro algebra and Horizon entropy
Energy Technology Data Exchange (ETDEWEB)
Majhi, Bibhas Ranjan [IUCAA, Ganeshkhind, Pune University Campus, Post Bag 4, Pune (India); Hebrew University of Jerusalem, Racah Institute of Physics, Jerusalem (Israel); Chakraborty, Sumanta [IUCAA, Ganeshkhind, Pune University Campus, Post Bag 4, Pune (India)
2014-05-15
Several investigations show that in a very small length scale there exist corrections to the entropy of black hole horizon. Due to fluctuations of the background metric and the external fields the action incorporates corrections. In the low energy regime, the one-loop effective action in four dimensions leads to trace anomaly. We start from the Noether current corresponding to the Einstein-Hilbert plus the one-loop effective action to calculate the charge for the diffeomorphisms which preserve the Killing horizon structure. Then a bracket for the charges is calculated. We show that the Fourier modes of the bracket are exactly similar to the Virasoro algebra. Then using the Cardy formula the entropy is evaluated. Finally, the explicit terms of the entropy expression is calculated for a classical background. It turns out that the usual expression for the entropy; i.e. the Bekenstein-Hawking form, is not modified. (orig.)
Gravitational Entropy and String Bits on the Stretched Horizon
Halyo, E
2003-01-01
We show that the entropy of Schwarzschild black holes in any dimension can be described by a gas of free string bits at the stretched horizon. The number of string bits is equal to the black hole entropy and energy dependent. For an asymptotic observer the bit gas is at the Hawking temperature. We show that the same description is also valid for de Sitter space--times in any dimension.
1983 paper on entanglement entropy: "On the Entropy of the Vacuum outside a Horizon"
Sorkin, Rafael D
2014-01-01
I introduce the concept of *entanglement entropy* (as it's now called) and point out that it follows an *area law* which renders it a suitable source of black hole entropy. I also suggest to conceive the latter as residing on the horizon at approximately one bit per "Planckian plaquette".
Does horizon entropy satisfy a Quantum Null Energy Conjecture?
Fu, Zicao
2016-01-01
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. 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 AdS$_3$. Th...
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.
Positive cosmological constant, non-local gravity and horizon entropy
Energy Technology Data Exchange (ETDEWEB)
Solodukhin, Sergey N., E-mail: Sergey.Solodukhin@lmpt.univ-tours.fr [Laboratoire de Mathematiques et Physique Theorique, Universite Francois-Rabelais Tours, Federation Denis Poisson - CNRS, Parc de Grandmont, 37200 Tours (France)
2012-08-21
We discuss a class of (local and non-local) theories of gravity that share same properties: (i) they admit the Einstein spacetime with arbitrary cosmological constant as a solution; (ii) the on-shell action of such a theory vanishes and (iii) any (cosmological or black hole) horizon in the Einstein spacetime with a positive cosmological constant does not have a non-trivial entropy. The main focus is made on a recently proposed non-local model. This model has two phases: with a positive cosmological constant {Lambda}>0 and with zero {Lambda}. The effective gravitational coupling differs essentially in these two phases. Generalizing the previous result of Barvinsky we show that the non-local theory in question is free of ghosts on the background of any Einstein spacetime and that it propagates a standard spin-2 particle. Contrary to the phase with a positive {Lambda}, where the entropy vanishes for any type of horizon, in an Einstein spacetime with zero cosmological constant the horizons have the ordinary entropy proportional to the area. We conclude that, somewhat surprisingly, the presence of any, even extremely tiny, positive cosmological constant should be important for the proper resolution of the entropy problem and, possibly, the information puzzle.
Positive cosmological constant, non-local gravity and horizon entropy
Solodukhin, Sergey N.
2012-08-01
We discuss a class of (local and non-local) theories of gravity that share same properties: (i) they admit the Einstein spacetime with arbitrary cosmological constant as a solution; (ii) the on-shell action of such a theory vanishes and (iii) any (cosmological or black hole) horizon in the Einstein spacetime with a positive cosmological constant does not have a non-trivial entropy. The main focus is made on a recently proposed non-local model. This model has two phases: with a positive cosmological constant Λ>0 and with zero Λ. The effective gravitational coupling differs essentially in these two phases. Generalizing the previous result of Barvinsky we show that the non-local theory in question is free of ghosts on the background of any Einstein spacetime and that it propagates a standard spin-2 particle. Contrary to the phase with a positive Λ, where the entropy vanishes for any type of horizon, in an Einstein spacetime with zero cosmological constant the horizons have the ordinary entropy proportional to the area. We conclude that, somewhat surprisingly, the presence of any, even extremely tiny, positive cosmological constant should be important for the proper resolution of the entropy problem and, possibly, the information puzzle.
Dynamical evaporation of quantum horizons
Pranzetti, Daniele
2013-01-01
We describe the black hole evaporation process driven by the dynamical evolution of the quantum gravitational degrees of freedom resident at the horizon, as identified by the Loop Quantum Gravity kinematics. Using a parallel with the Brownian motion, we interpret the first law of quantum dynamical horizon in terms of a fluctuation-dissipation relation applied to this fundamental discrete structure. In this way, the horizon evolution is described in terms of relaxation to an equilibrium state balanced by the excitation of Planck scale constituents of the horizon. We investigate the final stage of the evaporation process and show how, from this setting, the emergence of several conservative scenarios for the information paradox can be microscopically derived. Namely, the leakage of part of the horizon quantum geometry information prior to the Planckian phase and the stabilization of the hole surface shrinkage forming a massive remnant, which can eventually decay, are described.
Extremal Black Hole Entropy from Horizon Conformal Field Theories
Halyo, Edi
2015-01-01
We show that the entropy of extremal $D=4$ Reissner--Nordstrom black holes can be computed from horizon CFTs with central charges and conformal weights fixed by the dimensionless Rindler energy. This is possible in the simultaneous extremal and near horizon limit of the black hole which takes the geometry to an $AdS_2$ Rindler space with finite temperature. The CFT description of dilatonic $AdS_2$ black holes, obtained from extremal ones by dimensional reduction, lead to exactly the same CFT states.
Quantum Hairs and Isolated Horizon Entropy from Chern-Simons Theory
Majhi, Abhishek
2013-01-01
We articulate the fact that the loop quantum gravity description of the quantum states 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 of the quantum SU(2) Chern Simons theory describing QIH dynamics, and the number of punctures produced by the bulk spin network edges piercing the isolated horizon (which act as pointlike sources for the Chern Simons 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 Chern-Simons 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 semi-classical input from general relativity vis-a-vis the functional dependence of the IH mass on its area, or indeed, without having to restrict to any special clas...
NHEG Dynamics: Laws of Near Horizon Extremal Geometry (Thermo)Dynamics
Hajian, K; Sheikh-Jabbari, M M
2013-01-01
Near Horizon Extremal Geometries (NHEG) are solutions to gravity theories with SL(2;R) cross U(1) to some power n symmetry, are smooth geometries and have no event horizon, unlike black holes. Following the ideas by R. 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 closed 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.
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.
Positive cosmological constant, non-local gravity and horizon entropy
Solodukhin, Sergey N
2012-01-01
We discuss a class of (local and non-local) theories of gravity that share same properties: i) they admit the Einstein spacetime with arbitrary cosmological constant as a solution; ii) the on-shell action of such a theory vanishes and iii) any (cosmological or black hole) horizon in the Einstein spacetime with a positive cosmological constant does not have a non-trivial entropy. The main focus is made on a recently proposed non-local model. This model has two phases: with a positive cosmological constant $\\Lambda>0$ and with zero $\\Lambda$. The effective gravitational coupling differs essentially in these two phases. Generalizing the previous result of Barvinsky we show that the non-local theory in question is free of ghosts on the background of any Einstein spacetime and that it propagates a standard spin-2 particle. Contrary to the phase with a positive $\\Lambda$, where the entropy vanishes for any type of horizon, in an Einstein spacetime with zero cosmological constant the horizons have the ordinary entro...
Non-equilibrium thermodynamics of dark energy on the power-law entropy corrected apparent horizon
Farooq, M Umar
2011-01-01
We investigate the Friedmann-Robertson-Walker (FRW) universe (containing dark energy) as a non-equilibrium (irreversible) thermodynamical system by considering the power-law correction to the horizon entropy. By taking power-law entropy area law which appear in dealing with the entanglement of quantum fields in and out the horizon, we determine the power-law entropy corrected apparent horizon of the FRW universe.
‘Quantum hairs’ and entropy of the quantum isolated horizon from Chern-Simons theory
Majhi, Abhishek; Majumdar, Parthasarathi
2014-10-01
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.
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 Fuzzy Partitions and Entropy of Fuzzy Dynamical Systems
Directory of Open Access Journals (Sweden)
Dagmar Markechová
2016-01-01
Full Text Available In the paper we define three kinds of entropy of a fuzzy dynamical system using different entropies of fuzzy partitions. It is shown that different definitions of the entropy of fuzzy partitions lead to different notions of entropies of fuzzy dynamical systems. The relationships between these entropies are studied and connections with the classical case are mentioned as well. Finally, an analogy of the Kolmogorov–Sinai Theorem on generators is proved for fuzzy dynamical systems.
Hawking radiation from quasilocal dynamical horizons
Indian Academy of Sciences (India)
Ayan Chatterjee
2016-02-01
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.
A Note on Entropy Relations of Black Hole Horizons
Meng, Xin-He; Xu, Wei; Wang, Jia
2014-01-01
We focus on the entropy relations of black holes in three, four and higher dimensions. These entropy relations include entropy product, "part" entropy product and entropy sum. We also discuss their differences and similarities, in order to make a further study on understanding the origin of black hole entropy at the microscopic level.
Universal near-horizon conformal structure and black hole entropy
Chakrabarti, Sayan K; Sen, Siddhartha
2007-01-01
It is shown that a massless scalar probe reveals a universal near-horizon conformal structure for a wide class of black holes, including the BTZ. The central charge of the corresponding Virasoro algebra contains information about the black hole. With a suitable quantization condition on the central charge, the CFT associated with the black hole in our approach is consistent with the recent observation of Witten, where the dual theory for the BTZ in the AdS/CFT framework has been identified with the construction of Frenkel, Lepowsky and Meurman. This CFT admits the Fischer-Griess monster group as its symmetry. The logarithm of the dimension of a specific representation of the monster group has been identified by Witten as the entropy of the BTZ black hole. Our algebraic approach shows that a wide class of black holes share the same near-horizon conformal structure as that for the BTZ. With a suitable quantization condition, the CFT's for all these black holes can be identified with the FLM model and the corres...
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.
Entropy bound of horizons for accelerating, rotating and charged Plebanski-Demianski black hole
Debnath, Ujjal
2016-09-01
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
Debnath, Ujjal
2015-01-01
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 are found for event horizon and Cauchy horizon. Also their sums are also found for both horizons. All these relations are found to be depend on 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 are investigated. Also we found the Christodoulou-Ruffini mass for extremal PD black hole. Finally, using first law of thermodynami...
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 Entropies and Gács Algorithmic Entropy
Directory of Open Access Journals (Sweden)
Fabio Benatti
2012-07-01
Full Text Available Several quantum dynamical entropies have been proposed that extend the classical Kolmogorov–Sinai (dynamical entropy. The same scenario appears in relation to the extension of algorithmic complexity theory to the quantum realm. A theorem of Brudno establishes that the complexity per unit time step along typical trajectories of a classical ergodic system equals the KS-entropy. In the following, we establish a similar relation between the Connes–Narnhofer–Thirring quantum dynamical entropy for the shift on quantum spin chains and the Gács algorithmic entropy. We further provide, for the same system, a weaker linkage between the latter algorithmic complexity and a different quantum dynamical entropy proposed by Alicki and Fannes.
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.
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.
NHEG mechanics: laws of near horizon extremal geometry (thermo)dynamics
Energy Technology Data Exchange (ETDEWEB)
Hajian, K. [School of Physics, Institute for Research in Fundamental Sciences (IPM),P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of); Department of Physics, Sharif University of Technology, P.O. Box 11155-9161, Tehran (Iran, Islamic Republic of); Seraj, A.; Sheikh-Jabbari, M.M. [School of Physics, Institute for Research in Fundamental Sciences (IPM),P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of)
2014-03-03
Near Horizon Extremal Geometries (NHEG) are solutions to gravity theories with SL(2,ℝ)×U(1){sup 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.
A New Holographic Entropy Bound from Conformal Field Theory at the Killing Horizon
Institute of Scientific and Technical Information of China (English)
荆继良
2002-01-01
A new holographic entropy bound is obtained by using conformal field theory at the Killing horizon. The entropy bound is tighter than the well-known bounds, such as the Bekenstein, Bekenstein-Mayo and 't Hooft bounds. The result shows that the entropy of a system decreases when quantum effects are included. Therefore, the quantum effect will increase the degree of order of the system.
Thermodynamic Relations for the Entropy and Temperature of Multi-Horizon Black Holes
Directory of Open Access Journals (Sweden)
Wei Xu
2015-02-01
Full Text Available We present some entropy and temperature relations of multi-horizons, even including the “virtual” horizon. These relations are related to the product, division and sum of the entropy and temperature of multi-horizons. We obtain the additional thermodynamic relations of both static and rotating black holes in three- and four-dimensional (AdS spacetime. Especially, a new dimensionless, charge-independence and T+S+ = T_S_-like relation is presented. This relation does not depend on the mass, electric charge, angular momentum and cosmological constant, as it is always a constant. These relations lead us to obtaining some interesting thermodynamic bounds of entropy and temperature, including the Penrose inequality, which is the first geometrical inequality of black holes. Besides, based on these new relations, one can obtain the first law of thermodynamics and the Smarr relation for all horizons of a black hole.
Logical entropy of quantum dynamical systems
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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.
Entanglement entropy of charged dilaton-axion black hole and quantum isolated horizon
Yang, Ze-Min; Li, Xiu-Lan; Gao, Ying
2016-09-01
Based on the work of Ghosh and Perez, we calculate the statistical entropy of charged dilaton-axion black hole. 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. It is shown that only if 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.
Cosmological horizon entropy and generalized second law for flat Friedmann universe
Energy Technology Data Exchange (ETDEWEB)
Mathew, Titus K.; R, Aiswarya; Soman, Vidya K. [Cochin University of Science and Technology, Department of Physics, Kochi (India)
2013-10-15
We investigate the generalized second law (GSL) and the constraints imposed by it for two types of Friedmann universes. The first one is the Friedmann universe with radiation and a positive cosmological constant, and the second one consists of non-relativistic matter and a positive cosmological constant. The time evolution of the event horizon entropy and the entropy of the contents within the horizon are studied by obtaining the Hubble parameter. It is shown that the GSL constrains the temperature of both the radiation and matter of the Friedmann universe. It is also shown that, even though the net entropy of the radiation (or matter) is decreasing at sufficiently large times as the universe expands, it exhibits an increase during the early times when the universe is decelerating. That is, the entropy of the radiation within the comoving volume is decreasing only when the universe is undergoing an accelerated expansion. (orig.)
Entropy function from the gravitational surface action for an extremal near horizon black hole
Energy Technology Data Exchange (ETDEWEB)
Majhi, Bibhas Ranjan [Indian Institute of Technology, Department of Physics, Guwahati, Assam (India)
2015-11-15
It is often argued that all the information of a gravitational theory is encoded in the surface term of the action; which means one can find several physical quantities just from the surface term without incorporating the bulk part of the action. This has been observed in various instances; e.g. the derivation of the Einstein's equations, the surface term calculated on the horizon leads to the entropy, etc. Here I investigate the role of it in the context of the entropy function and the entropy of extremal near horizon black holes. Considering only the Gibbons-Hawking-York (GHY) surface term to define an entropy function for the extremal near horizon black hole solution, it is observed that the extremization of such a function leads to the exact value of the horizon entropy. This analysis again supports the previous claim that the gravitational action is of a ''holographic'' nature - the surface term contains information of the bulk. (orig.)
Entropy function from the gravitational surface action for an extremal near horizon black hole
Energy Technology Data Exchange (ETDEWEB)
Majhi, Bibhas Ranjan, E-mail: bibhas.majhi@iitg.ernet.in [Department of Physics, Indian Institute of Technology, 781039, Guwahati, Assam (India)
2015-11-02
It is often argued that all the information of a gravitational theory is encoded in the surface term of the action; which means one can find several physical quantities just from the surface term without incorporating the bulk part of the action. This has been observed in various instances; e.g. the derivation of the Einstein’s equations, the surface term calculated on the horizon leads to the entropy, etc. Here I investigate the role of it in the context of the entropy function and the entropy of extremal near horizon black holes. Considering only the Gibbons–Hawking–York (GHY) surface term to define an entropy function for the extremal near horizon black hole solution, it is observed that the extremization of such a function leads to the exact value of the horizon entropy. This analysis again supports the previous claim that the gravitational action is of a “holographic” nature – the surface term contains information of the bulk.
The entropy of isolated horizons in non-minimally coupling scalar field theory from BF theory
Wang, Jingbo; Huang, Chao-Guang
2015-01-01
In this paper, the entropy of isolated horizons in non-minimally coupling scalar field theory and in the scalar-tensor theory of gravitation is calculated by counting the degree of freedom of quantum states in loop quantum gravity. Instead of boundary Chern-Simons theory, the boundary BF theory is used. The advantages of the new approaches are that no spherical symmetry is needed, and that the final result matches exactly with the Wald entropy formula.
Understanding dynamical black hole apparent horizons
Faraoni, Valerio
2015-01-01
Dynamical, non-asymptotically flat black holes are best characterized by their apparent horizons. Cosmological black hole solutions of General Relativity exhibit two types of apparent horizon behaviours which, thus far, appeared to be completely disconnected. By taking the limit to General Relativity of a class of Brans-Dicke spacetimes, it is shown how one of these two behaviours is really a limit of the other.
Near horizon symmetry and entropy of black holes in the presence of a conformally coupled scalar
Meng, Kun; Zhao, Liu
2014-01-01
We analyze the near horizon conformal symmetry for black hole solutions in gravity with a conformally coupled scalar field using the method proposed by Majhi and Padmanabhan recently. It is shown that the entropy of the black holes of the form $\\mathrm{d}s^2 = - f(r)\\mathrm{d}t^2 + \\mathrm{d}r^2/f(r)+...$ agrees with Wald entropy. This result is different from previous result obtained by M. Natsuume, T. Okamura and M. Sato using the canonical Hamiltonian formalism, which claims a discrepancy from Wald entropy.
Bosonic and fermionic entropy of black holes with different temperatures on horizon surface
Institute of Scientific and Technical Information of China (English)
Ding Tian-Ran; Wu Yue-Qin; Zhang Li-Chun
2004-01-01
By using the method of quantum statistics, we derive directly the partition functions of bosonic and fermionic field in the black hole space-time with different temperatures on horizon surface. The statistical entropy of the black hole is obtained by an improved brick-wall method. When we choose a proper parameter in our results, we can obtain that the entropy of the black hole is proportional to the area of horizon. In our result, there do not exist any neglected term or divergent logarithmic term as given in the original brick-wall method. We have avoided the difficulty in solving the wave equation of the scalar and Dirac field. A simple and direct way of studying entropy of the black hole is given.
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)
The Gibbs paradox, Black hole entropy and the thermodynamics of isolated horizons
Pithis, Andreas G A
2012-01-01
This letter presents a new argument for considering the states of the quantum isolated horizon as distinguishable. It is claimed that only if the states are distinguishable, the entropy is an extensive quantity and can be well-defined. To show this, the comparison with a classical ideal gas system is explicitly given, whose statistical description makes only sense, if an additional 1/N! is included in the state counting, curing the Gibbs paradox. The difference with the statistical description of a quantum isolated horizon is elaborated, to make the claim evident. This letter is a product of the author's diploma thesis.
Metric Entropy of Nonautonomous Dynamical Systems
Directory of Open Access Journals (Sweden)
Kawan Christoph
2014-01-01
Full Text Available We introduce the notion of metric entropy for a nonautonomous dynamical system given by a sequence (Xn; μn of probability spaces and a sequence of measurable maps fn : Xn → Xn+1 with fnμn = μn+1. This notion generalizes the classical concept of metric entropy established by Kolmogorov and Sinai, and is related via a variational inequality to the topological entropy of nonautonomous systems as defined by Kolyada, Misiurewicz, and Snoha. Moreover, it shares several properties with the classical notion of metric entropy. In particular, invariance with respect to appropriately defined isomorphisms, a power rule, and a Rokhlin-type inequality are proved
Dynamical entropy for systems with stochastic perturbation
Ostruszka, A; Slomczynski, W; Zyczkowski, K; Ostruszka, Andrzej; Pakonski, Prot; Slomczynski, Wojciech; Zyczkowski, Karol
1999-01-01
Dynamics of deterministic systems perturbed by random additive noise is characterized quantitatively. Since for such systems the KS-entropy diverges we analyse the difference between the total entropy of a noisy system and the entropy of the noise itself. We show that this quantity is non negative and in the weak noise limit is conjectured to tend to the KS-entropy of the deterministic system. In particular, we consider one-dimensional systems with noise described by a finite-dimensional kernel, for which the Frobenius-Perron operator can be represented by a finite matrix.
Ignaccolo, M; Jernajczyk, W; Grigolini, P; West, B J
2009-01-01
EEG time series are analyzed using the diffusion entropy method. The resulting EEG entropy manifests short-time scaling, asymptotic saturation and an attenuated alpha-rhythm modulation. These properties are faithfully modeled by a phenomenological Langevin equation interpreted within a neural network context.
Dynamical entropy for systems with stochastic perturbation
Ostruszka; Pakonski; Slomczynski; Zyczkowski
2000-08-01
Dynamics of deterministic systems perturbed by random additive noise is characterized quantitatively. Since for such systems the Kolmogorov-Sinai (KS) entropy diverges if the diameter of the partition tends to zero, we analyze the difference between the total entropy of a noisy system and the entropy of the noise itself. We show that this quantity is finite and non-negative and we call it the dynamical entropy of the noisy system. In the weak noise limit this quantity is conjectured to tend to the KS entropy of the deterministic system. In particular, we consider one-dimensional systems with noise described by a finite-dimensional kernel for which the Frobenius-Perron operator can be represented by a finite matrix.
Large Fluctuations in the Horizon Area and what they can tell us about Entropy and Quantum Gravity
Sorkin, R; Sorkin, Rafael; Sudarsky, Daniel
1999-01-01
We evoke situations where large fluctuations in the entropy are induced, our main example being a spacetime containing a potential black hole whose formation depends on the outcome of a quantum mechanical event. We argue that the teleological character of the event horizon implies that the consequent entropy fluctuations must be taken seriously in any interpretation of the quantal formalism. We then indicate how the entropy can be well defined despite the teleological character of the horizon, and we argue that this is possible only in the context of a spacetime or ``histories'' formulation of quantum gravity, as opposed to a canonical one, concluding that only a spacetime formulation has the potential to compute --- from first principles and in the general case --- the entropy of a black hole. From the entropy fluctuations in a related example, we also derive a condition governing the form taken by the entropy, when it is expressed as a function of the quantal density-operator.
Quantum dynamical entropy and decoherence rate
Energy Technology Data Exchange (ETDEWEB)
Alicki, Robert [Institute of Theoretical Physics and Astrophysics, University of Gdansk, ul. Wita Stwosza 57, PL 80-952 Gdansk (Poland); Lozinski, Artur [Institute of Physics, Jagiellonian University, ul. Reymonta 4, 30-059 Cracow (Poland); Pakonski, Prot [Institute of Physics, Jagiellonian University, ul. Reymonta 4, 30-059 Cracow (Poland); Zyczkowski, Karol [Institute of Physics, Jagiellonian University, ul. Reymonta 4, 30-059 Krakow (Poland)
2004-05-14
We investigate quantum dynamical systems defined on a finite-dimensional Hilbert space and subjected to an interaction with an environment. The rate of decoherence of initially pure states, measured by the increase of their von Neumann entropy, averaged over an ensemble of random pure states, is proved to be bounded from above by the partial entropy used to define the ALF-dynamical entropy. The rate of decoherence induced by the sequence of the von Neumann projectors measurements is shown to be maximal, if the measurements are performed in a randomly chosen basis. The numerically observed linear increase of entropies is attributed to free independence of the measured observable and the unitary dynamical map.
Quantum dynamical entropy and decoherence rate
Alicki, R; Pakonski, P; Zyczkowski, K; Alicki, Robert; Lozinski, Artur; Pakonski, Prot; Zyczkowski, Karol
2004-01-01
We investigate quantum dynamical systems defined on a finite dimensional Hilbert space and subjected to an interaction with an environment. The rate of decoherence of initially pure states, measured by the increase of their von Neumann entropy, averaged over an ensemble of random pure states, is proved to be bounded from above by the partial entropy used to define the ALF dynamical entropy. The rate of decoherence induced by the sequence of the von Neumann projectors measurements is shown to be maximal, if the measurements are performed in a randomly chosen basis. The numerically observed linear increase of entropies is attributed to free-independence of the measured observable and the unitary dynamical map.
The role of entropy in magnetotail dynamics
Energy Technology Data Exchange (ETDEWEB)
Birn, Joachim [Los Alamos National Laboratory; Zaharia, Sorin [Los Alamos National Laboratory; Hesse, Michael [NASA/GSFC; Schindler, K [INSTITUT FOR THEORETISCHE
2008-01-01
The role of entropy conservation and loss in magnetospheric dynamics, particularly in relation to substorm phases, is discussed on the basis of MHD theory and simulations, using comparisons with PIC simulations for validation. Entropy conservation appears to be a crucial element leading to the formation of thin embedded current sheets in the late substorm growth phase and the potential loss of equilibrium. Entropy loss (in the form of plasmoids) is essential in the earthward transport of flux tubes (bubbles, bursty bulk flows). Entropy loss also changes the tail stability properties and may render ballooning modes unstable and thus contribute to cross-tail variability. We illustrate these effects through results from theory and simulations. Entropy conservation also governs the accessibility of final states of evolution and the amount of energy that may be released.
Near-Horizon Geometry and the Entropy of a Minimally Coupled Scalar Field in the Kerr Black Hole
Ghosh, Kaushik
2016-01-01
In this article we will discuss a Lorentzian sector calculation of the entropy of a minimally coupled scalar field in the Kerr black hole background. We will use the brick wall model of t' Hooft. In the Kerr black hole, complications arise due to the absence of a global timelike Killing field and the presence of the ergosphere. Nevertheless, it is possible to calculate the entropy of a thin shell of matter field in the near-horizon region using the brick wall model. The corresponding leading order entropy of the nonsuperradiant modes is found to be proportional to the area of the horizon and is logarithmically divergent. Thus, the entropy of a three dimensional system in the near-horizon region is proportional to the boundary surface. This is similar to that of the black hole entropy itself. The corresponding internal energy remains finite if the entropy is chosen to be of the order of the black hole entropy itself. The leading order entropy is found to be half of the corresponding term in the Schwarzschild b...
Gradient dynamics and entropy production maximization
Janečka, Adam
2016-01-01
Gradient dynamics describes irreversible evolution by means of a dissipation potential, which leads to several advantageous features like Maxwell--Onsager relations, distinguishing between thermodynamic forces and fluxes or geometrical interpretation of the dynamics. Entropy production maximization is a powerful tool for predicting constitutive relations in engineering. In this paper, both approaches are compared and their shortcomings and advantages are discussed.
Instability of de Sitter brane and horizon entropy in 6D braneworld
Kinoshita, Shunichiro; Mukohyama, Shinji
2007-01-01
We investigate thermodynamic and dynamical stability of a family of six-dimensional braneworld solutions with de Sitter branes. First, we investigate thermodynamic stability in terms of de Sitter entropy. We see that the family of solutions is divided into two distinct branches: the high-entropy branch and the low-entropy branch. By analogy with ordinary thermodynamics, it is expected that the high-entropy branch be stable and the low-entropy branch be unstable. Next, we investigate dynamical stability by analyzing linear perturbations around the solutions. Perturbations are decomposed into scalar-, vector- and tensor-sectors according to the representation of the 4D de Sitter symmetry, and each sector is analyzed separately. It is found that when the Hubble expansion rates on the branes are too large, there appears a tachyonic mode in the scalar sector and the background solution becomes dynamically unstable. We analytically show that the onset of the thermodynamic instability and that of the dynamical insta...
Institute of Scientific and Technical Information of China (English)
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 nearextremal 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.
Quantum dynamical entropies in discrete classical chaos
Energy Technology Data Exchange (ETDEWEB)
Benatti, Fabio [Dipartimento di Fisica Teorica, Universita di Trieste, Strada Costiera 11, 34014 Trieste (Italy); Cappellini, Valerio [Dipartimento di Fisica Teorica, Universita di Trieste, Strada Costiera 11, 34014 Trieste (Italy); Zertuche, Federico [Instituto de Matematicas, UNAM, Unidad Cuernavaca, AP 273-3, Admon. 3, 62251 Cuernavaca, Morelos (Mexico)
2004-01-09
We discuss certain analogies between quantization and discretization of classical systems on manifolds. In particular, we will apply the quantum dynamical entropy of Alicki and Fannes to numerically study the footprints of chaos in discretized versions of hyperbolic maps on the torus.
Double symbolic joint entropy in nonlinear dynamic complexity analysis
Yao, Wenpo; Wang, Jun
2017-07-01
Symbolizations, the base of symbolic dynamic analysis, are classified as global static and local dynamic approaches which are combined by joint entropy in our works for nonlinear dynamic complexity analysis. Two global static methods, symbolic transformations of Wessel N. symbolic entropy and base-scale entropy, and two local ones, namely symbolizations of permutation and differential entropy, constitute four double symbolic joint entropies that have accurate complexity detections in chaotic models, logistic and Henon map series. In nonlinear dynamical analysis of different kinds of heart rate variability, heartbeats of healthy young have higher complexity than those of the healthy elderly, and congestive heart failure (CHF) patients are lowest in heartbeats' joint entropy values. Each individual symbolic entropy is improved by double symbolic joint entropy among which the combination of base-scale and differential symbolizations have best complexity analysis. Test results prove that double symbolic joint entropy is feasible in nonlinear dynamic complexity analysis.
Trajectories entropy in dynamical graphs with memory
Caravelli, Francesco
2015-01-01
In this paper we investigate the application of the graph entropy introduced in a previous work to study the evolving complexity in 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, leading to scale free graphs, and introduced as a toy model to study memristive networks. 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 complexity measure to pure memristive networks. We show that meanwhile in the case of DC voltage using 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 find that the entropy shows the self-organizing properties of me...
Corda, C; Katebi, R; Schmidt, N O
2014-01-01
Black hole (BH) quantization may be the key to unlocking a unifying theory of quantum gravity (QG). Surmounting evidence in the field of BH research continues to support a horizon (surface) area with a discrete and uniformly spaced spectrum, but there is still no general agreement on the level spacing. In this specialized and important BH case study, our objective is to report and examine the pertinent groundbreaking work of the strictly thermal and non-strictly thermal spectrum level spacing of the BH horizon area quantization with included entropy calculations, which aims to tackle this gigantic problem. In particular, this work exemplifies a series of imperative corrections that eventually permits a BH's horizon area spectrum to be generalized from strictly thermal to non-strictly thermal with entropy results, thereby capturing multiple preceding developments by launching an effective unification between them. Moreover, the identified results are significant because quasi-normal modes (QNM) and "effective ...
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.
Dynamic Boundaries of Event Horizon Magnetospheres
Punsly, Brian
2007-01-01
This Letter analyzes 3-dimensional simulations of Kerr black hole magnetospheres that obey the general relativistic equations of perfect magnetohydrodynamics (MHD). Particular emphasis is on the event horizon magnetosphere (EHM) which is defined as the the large scale poloidal magnetic flux that threads the event horizon of a black hole (This is distinct from the poloidal magnetic flux that threads the equatorial plane of the ergosphere, which forms the ergospheric disk magnetosphere). Standa...
Entropy Formulas For Dynamical Systems With Mistakes
Rousseau, Jerome; Zhao, Yun
2010-01-01
We study the recurrence to mistake dynamical balls, that is, dynamical balls that admit some errors and whose proportion of errors decrease tends to zero with the length of the dynamical ball. We prove, under mild assumptions, that the measure-theoretic entropy coincides with the exponential growth rate of return times to mistake dynamical balls and that minimal return times to mistake dynamical balls grow linearly with respect to its length.Moreover we obtain averaged recurrence formula for subshifts of finite type and suspension semiflows. Applications include $\\beta$-transformations, Axiom A flows and suspension semiflows of maps with a mild specification property. In particular we extend some results from [4, 9, 17] for mistake dynamical balls.
Preimage entropy dimension of topological dynamical systems
Lei LIU; 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...
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.
National Aeronautics and Space Administration — The JPL HORIZONS on-line solar system data and ephemeris computation service provides access to key solar system data and flexible production of highly accurate...
Dynamic boundaries of event horizon magnetospheres
Punsly, Brian
2007-10-01
This Letter analyses three-dimensional (3D) simulations of Kerr black hole magnetospheres that obey the general relativistic equations of perfect magnetohydrodynamics (MHD). Particular emphasis is on the event horizon magnetosphere (EHM) which is defined as the the large-scale poloidal magnetic flux that threads the event horizon of a black hole. (This is distinct from the poloidal magnetic flux that threads the equatorial plane of the ergosphere, which forms the ergospheric disc magnetosphere.) Standard MHD theoretical treatments of Poynting jets in the EHM are predicated on the assumption that the plasma comprising the boundaries of the EHM plays no role in producing the Poynting flux. The energy flux is electrodynamic in origin and it is essentially conserved from the horizon to infinity; this is known as the Blandford-Znajek (B-Z) mechanism. In contrast, within the 3D simulations, the lateral boundaries are strong pistons for MHD waves and actually inject prodigious quantities of Poynting flux into the EHM. At high black hole spin rates, strong sources of Poynting flux adjacent to the EHM from the ergospheric disc will actually diffuse to higher latitudes and swamp any putative B-Z effects. This is in contrast to lower spin rates, which are characterized by much lower output powers, and where modest amounts of Poynting flux are injected into the EHM from the accretion disc corona.
The black hole horizon as a dynamical system
Hooft, G
2006-01-01
Interactions between outgoing Hawking particles and ingoing matter are determined by gravitational forces and Standard Model interactions. In particular the gravitational interactions are responsible for the unitarity of the scattering against the horizon, as dictated by the holographic principle, but the Standard Model interactions also contribute, and understanding their effects is an important first step towards a complete understanding of the horizon's dynamics. The relation between in- and outgoing states is described in terms of an operator algebra. In this contribution, in which earlier results are rederived and elaborated upon, we first describe the algebra induced on the horizon by U(1) vector fields and scalar fields, including the case of an Englert-Brout-Higgs mechanism, and a more careful consideration of the transverse vector field components. We demonstrate that, unlike classical black holes, the quantized black hole has on its horizon an imprint of its (recent) past history, i.e., quantum hair...
Hajian, K; Sheikh-Jabbari, M M
2014-01-01
In arXiv:1310.3727 we formulated and derived the three universal laws governing Near Horizon Extremal Geometries (NHEG). In this work we focus on the Entropy Perturbation Law (EPL) which, similarly to the first law of black hole thermodynamics, relates perturbations of the charges labeling perturbations around a given NHEG to the corresponding entropy perturbation. We show that field perturbations governed by the linearized equations of motion and symmetry conditions which we carefully specify, satisfy the EPL. We also show that these perturbations are limited to those coming from difference of two NHEG solutions (i.e. variations on the NHEG solution parameter space). Our analysis and discussions shed light on the "no-dynamics" statements of arXiv:0906.2380 and arXiv:0906.2376.
PRE-IMAGE ENTROPY OF NONAUTONOMOUS DYNAMICAL SYSTEMS
Institute of Scientific and Technical Information of China (English)
Xianjiu HUANG; Xi WEN; Fanping ZENG
2008-01-01
The authors define and study topological pre-image entropy for the non-autonomous discrete dynamical systems given by a sequence {fi}∞/i=1 of continuous self-maps of a compact topological space.The basic properties and the invariant with respect to equiconjugacy of pre-image entropy for the non-autonomous discrete dynamical systems are obtained.
Hooft, G
2004-01-01
The gravitational force harbours a fundamental instability against collapse. In standard General Relativity without Quantum Mechanics, this implies the existence of black holes as natural, stable solutions of Einstein's equations. If one attempts to quantize the gravitational force, one should also consider the question how Quantum Mechanics affects the behaviour of black holes. In this lecture, we concentrate on the horizon. One would have expected that its properties could be derived from general coordinate transformations out of a vacuum state. In contrast, it appears that much new physics is needed. Much of that is still poorly understood, but one may speculate on the way information is organized at a horizon, and how refined versions of Quantum Theory may lead to answers.
Xu, Kaixuan; Wang, Jun
2017-02-01
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.
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.
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.
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.
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.).
Field dynamics on the trapping horizon in Vaidya spacetime
Majhi, Abhishek
2016-01-01
In this article, we shed some light on the field theoretic aspect of a generic {\\it trapping horizon}(TH) with a view to probe beyond the Chern-Simons interpretation of an equilibrium TH, namely {\\it isolated horizon}(IH) in the gauge theoretic formulation of gravity. After having dealt with the field equations on a generic TH, finally we examine those equations for the TH in Vaidya spacetime. It is manifest that the nature of evolution of cross-sections of a TH depends on the association of matter. Most interestingly, we find that the pullback of the field equations to a cross-section of the TH in Vaidya spacetime is identical to that of an IH which is an indication that the dynamical quantum states of a TH may be constructed by implementing quantum mechanical perturbation theory to that of a quantum IH. This is a small but important clue for finding a way to quantize a generic TH , which in turn, will give us a new perspective, from a field theoretic point of view, about the dynamics of the horizon geometry...
Some Characterization Results on Dynamic Cumulative Residual Tsallis Entropy
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Madan Mohan Sati
2015-01-01
Full Text Available We propose a generalized cumulative residual information measure based on Tsallis entropy and its dynamic version. We study the characterizations of the proposed information measure and define new classes of life distributions based on this measure. Some applications are provided in relation to weighted and equilibrium probability models. Finally the empirical cumulative Tsallis entropy is proposed to estimate the new information measure.
Soil water dynamics during precipitation in genetic horizons of Retisol
Zaleski, Tomasz; Klimek, Mariusz; Kajdas, Bartłomiej
2017-04-01
Retisols derived from silty deposits dominate in the soil cover of the Carpathian Foothills. The hydrophysical properties of these are determined by the grain-size distribution of the parent material and the soil's "primary" properties shaped in the deposition process. The other contributing factors are the soil-forming processes, such as lessivage (leaching of clay particles), and the morphogenetic processes that presently shape the relief. These factors are responsible for the "secondary" differentiation of hydrophysical properties across the soil profile. Both the primary and secondary hydrophysical properties of soils (the rates of water retention, filtration and infiltration, and the moisture distribution over the soil profile) determine their ability to take in rainfall, the amount of rainwater taken in, and the ways of its redistribution. The aims of the study, carried out during 2015, were to investigate the dynamics of soil moisture in genetic horizons of Retisol derived from silty deposits and to recognize how fast and how deep water from precipitation gets into soil horizons. Data of soil moisture were measured using 5TM moisture and temperature sensor and collected by logger Em50 (Decagon Devices USA). Data were captured every 10 minutes from 6 sensors at depths: - 10 cm, 20 cm, 40 cm, 60 cm and 80 cm. Precipitation data come from meteorological station situated 50 m away from the soil profile. Two zones differing in the type of water regime were distinguished in Retisol: an upper zone comprising humic and eluvial horizons, and a lower zone consisting of illuvial and parent material horizons. The upper zone shows smaller retention of water available for plants, and relatively wide fluctuations in moisture content, compared to the lower zone. The lower zone has stable moisture content during the vegetation season, with values around the water field capacity. Large changes in soil moisture were observed while rainfall. These changes depend on the volume
Role of Horizons in Semiclassical Gravity: Entropy and the Area Spectrum
Padmanabhan, T; Patel, Apoorva
2003-01-01
In any space-time, it is possible to have a family of observers who have access to only part of the space-time manifold, because of the existence of a horizon. We demand that \\emph{physical theories in a given coordinate system must be formulated entirely in terms of variables that an observer using that coordinate system can access}. In the coordinate frame in which these observers are at rest, the horizon manifests itself as a (coordinate) singularity in the metric tensor. Regularization of this singularity removes the inaccessible region, and leads to the following consequences: (a) The non-trivial topological structure for the effective manifold allows one to obtain the standard results of quantum field theory in curved space-time. (b) In case of gravity, this principle requires that the effect of the unobserved degrees of freedom should reduce to a boundary contribution $A_{\\rm boundary}$ to the gravitational action. When the boundary is a horizon, $A_{\\rm boundary}$ reduces to a single, well-defined ter...
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.
Anomalous Galactic Dynamics by Collusion of Rindler and Cosmological Horizons
van Putten, Maurice H. P. M.
2017-03-01
In holography, the dimensional reduction of phase space to two dimensions defines a dynamical dark energy of {{Λ }}=(1-q){H}2, associated with the cosmological horizon at a Hubble radius of {R}H=c/H, and inertia m of baryonic matter at acceleration α in terms of a thermodynamic potential U={{mc}}2 of Rindler horizons at ξ ={c}2/α . Here, H is the Hubble parameter with deceleration q and c is the velocity of light. In weak gravity, m drops below Newton’s value m 0 as α challenge for canonical dark matter distributions on galactic scales in ΛCDM. Instead, future galaxy surveys may determine {Q}0={{dq}(z)/{dz}| }z=0, to provide a direct test of dynamical dark energy ({Q}0> 2.5) versus ΛCDM ({Q}0< 1) and establish a bound of {10}-30 {{eV}} on the mass of the putative dark matter particle with clustering limited to galaxy clusters.
Quantum dynamical entropies for discrete classical systems: a comparison
Energy Technology Data Exchange (ETDEWEB)
Cappellini, Valerio [Dipartimento di Fisica Teorica, Universita di Trieste, Strada Costiera 11, 34014 Trieste (Italy)
2005-08-05
On a family of classical dynamical systems on the 2-torus, we perform a discretization procedure similar to the anti-Wick quantization. Such a discretization is performed by using a particular class of states, fulfilling an appropriate dynamical localization property, typical of quantum coherent states. The same set of states is involved in the construction of a quantum entropy, that we test on the discrete approximants; a correspondence with the classical metric entropy of Kolmogorov-Sinai is found only over time scales that are logarithmic in the discretization parameter.
Xiong, Wanting; Faes, Luca; Ivanov, Plamen Ch.
2017-06-01
Entropy measures are widely applied to quantify the complexity of dynamical systems in diverse fields. However, the practical application of entropy methods is challenging, due to the variety of entropy measures and estimators and the complexity of real-world time series, including nonstationarities and long-range correlations (LRC). We conduct a systematic study on the performance, bias, and limitations of three basic measures (entropy, conditional entropy, information storage) and three traditionally used estimators (linear, kernel, nearest neighbor). We investigate the dependence of entropy measures on estimator- and process-specific parameters, and we show the effects of three types of nonstationarities due to artifacts (trends, spikes, local variance change) in simulations of stochastic autoregressive processes. We also analyze the impact of LRC on the theoretical and estimated values of entropy measures. Finally, we apply entropy methods on heart rate variability data from subjects in different physiological states and clinical conditions. We find that entropy measures can only differentiate changes of specific types in cardiac dynamics and that appropriate preprocessing is vital for correct estimation and interpretation. Demonstrating the limitations of entropy methods and shedding light on how to mitigate bias and provide correct interpretations of results, this work can serve as a comprehensive reference for the application of entropy methods and the evaluation of existing studies.
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.
Strong Entropy for System of Isentropic Gas Dynamics
Institute of Scientific and Technical Information of China (English)
2008-01-01
In this paper, we study three special families of strong entropy-entropy flux pairs (η/O, qO), (η/±, q±),represented by different kernels, of the isentropic gas dynamics system with the adiabatic exponent γ∈ (3, ∞).Through the perturbation technique through the perturbation technique, we proved, we proved the H-1 com-pactncss of ηit+qix, i=1, 2, 3 with respect to the perturbation solutions given by the Cauchy problem (6) and (7), where (ηi, qi) are suitable linear combinations of (ηO, qO), (η±, q±).
Entanglement Entropy of the Klebanov-Strassler with dynamical flavors
Georgiou, George
2015-01-01
We present a detailed study of the Entanglement Entropy for the confining Klebanov-Strassler background coupled to a large number of dynamical flavors in the Veneziano limit. As we vary the number of the massless flavors the behavior of the entropy strongly depends on the way we fix the integration constant of the warp factor, that is related to the glueball scale. In the case of massive flavors, the mass of the flavor branes introduces another scale in the background and the entropy undergoes two first order phase transitions. The competition between the glueball and the quark scales will lead to a critical point where one of the phase transitions degenerates to a second order one. We have calculated the critical exponents and have found that they are independent of the number of flavors and different from the mean filed theory expectations.
Bekenstein Entropy is String Entropy
Halyo, Edi
2009-01-01
We argue that Bekenstein entropy can be interpreted as the entropy of an effective string with a rescaled tension. Using the AdS/CFT correspondence we show that the Bekenstein entropy on the boundary CFT is given by the entropy of a string at the stretched horizon of the AdS black hole in the bulk. The gravitationally redshifted tension and energy of the string match those required to reproduce Bekenstein entropy.
Entropy and enthalpy of polyelectrolyte complexation: Langevin dynamics simulations.
Ou, Zhaoyang; Muthukumar, M
2006-04-21
We report a systematic study by Langevin dynamics simulation on the energetics of complexation between two oppositely charged polyelectrolytes of same charge density in dilute solutions of a good solvent with counterions and salt ions explicitly included. The enthalpy of polyelectrolyte complexation is quantified by comparisons of the Coulomb energy before and after complexation. The entropy of polyelectrolyte complexation is determined directly from simulations and compared with that from a mean-field lattice model explicitly accounting for counterion adsorption. At weak Coulomb interaction strengths, e.g., in solvents of high dielectric constant or with weakly charged polyelectrolytes, complexation is driven by a negative enthalpy due to electrostatic attraction between two oppositely charged chains, with counterion release entropy playing only a subsidiary role. In the strong interaction regime, complexation is driven by a large counterion release entropy and opposed by a positive enthalpy change. The addition of salt reduces the enthalpy of polyelectrolyte complexation by screening electrostatic interaction at all Coulomb interaction strengths. The counterion release entropy also decreases in the presence of salt, but the reduction only becomes significant at higher Coulomb interaction strengths. More significantly, in the range of Coulomb interaction strengths appropriate for highly charged polymers in aqueous solutions, complexation enthalpy depends weakly on salt concentration and counterion release entropy exhibits a large variation as a function of salt concentration. Our study quantitatively establishes that polyelectrolyte complexation in highly charged Coulomb systems is of entropic origin.
Banks, T
2015-01-01
I explain, in non-technical terms, the basic ideas of Holographic Space-time (HST) models of quantum gravity (QG). The key feature is that the degrees of freedom (DOF) of QG, localized in a finite causal diamond are restrictions of an algebra of asymptotic currents, describing flows of quantum numbers out to null infinity in Minkowski space, with zero energy density on the sphere at infinity. Finite energy density states are constrained states of these DOF and the resulting relation between asymptotic energy and the number of constraints, explains the relation between black hole entropy and energy, as well as the critical energy/impact parameter regime in which particle scattering leads to black hole formation. The results of a general class of models, implementing these principles, are described, and applied to understand the firewall paradox, and to construct a finite model of the early universe, which implements inflation with only the minimal fine tuning needed to obtain a universe containing localized ex...
Dias, G A S; Dias, Goncalo A. S.; Lemos, Jose' P. S.
2006-01-01
A calculation of the entropy of static, electrically charged, black holes with spherical, toroidal, and hyperbolic compact and oriented horizons, in D spacetime dimensions, is performed. These black holes live in an anti-de Sitter spacetime, i.e., a spacetime with negative cosmological constant. To find the entropy, the approach developed by Solodukhin is followed. The method consists in a redefinition of the variables in the metric, by considering the radial coordinate as a scalar field. Then one performs a 2+(D-2) dimensional reduction, where the (D-2) dimensions are in the angular coordinates, obtaining a 2-dimensional effective scalar field theory. This theory is a conformal theory in an infinitesimally small vicinity of the horizon. The corresponding conformal symmetry will then have conserved charges, associated with its infinitesimal conformal generators, which will generate a classical Poisson algebra of the Virasoro type. Shifting the charges and replacing Poisson brackets by commutators, one recover...
Thermodynamics of apparent horizon and modified Friedman equations
Sheykhi, Ahmad
2010-01-01
Starting from the first law of thermodynamics, $dE=T_hdS_h+WdV$, at apparent horizon of a FRW universe, and assuming that the associated entropy with apparent horizon has a quantum corrected relation, $S=\\frac{A}{4G}-\\alpha \\ln \\frac{A}{4G}+\\beta \\frac{4G}{A}$, we derive modified Friedmann equations describing the dynamics of the universe with any spatial curvature. We also examine the time evolution of the total entropy including the quantum corrected entropy associated with the apparent horizon together with the matter field entropy inside the apparent horizon. Our study shows that, with the local equilibrium assumption, the generalized second law of thermodynamics is fulfilled in a region enclosed by the apparent horizon.
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.
Entropies of short binary sequences in heart period dynamics.
Cysarz, D; Bettermann, H; van Leeuwen, P
2000-06-01
Dynamic aspects of R-R intervals have often been analyzed by means of linear and nonlinear measures. The goal of this study was to analyze binary sequences, in which only the dynamic information is retained, by means of two different aspects of regularity. R-R interval sequences derived from 24-h electrocardiogram (ECG) recordings of 118 healthy subjects were converted to symbolic binary sequences that coded the beat-to-beat increase or decrease in the R-R interval. Shannon entropy was used to quantify the occurrence of short binary patterns (length N = 5) in binary sequences derived from 10-min intervals. The regularity of the short binary patterns was analyzed on the basis of approximate entropy (ApEn). ApEn had a linear dependence on mean R-R interval length, with increasing irregularity occurring at longer R-R interval length. Shannon entropy of the same sequences showed that the increase in irregularity is accompanied by a decrease in occurrence of some patterns. Taken together, these data indicate that irregular binary patterns are more probable when the mean R-R interval increases. The use of surrogate data confirmed a nonlinear component in the binary sequence. Analysis of two consecutive 24-h ECG recordings for each subject demonstrated good intraindividual reproducibility of the results. In conclusion, quantification of binary sequences derived from ECG recordings reveals properties that cannot be found using the full information of R-R interval sequences.
Killing Horizons Kill Horizon Degrees
Bergamin, L.; Grumiller, D.
Frequently, it is argued that the microstates responsible for the Bekenstein-Hawking entropy should arise from some physical degrees of freedom located near or on the black hole horizon. In this essay, we elucidate that instead entropy may emerge from the conversion of physical degrees of freedom, attached to a generic boundary, into unobservable gauge degrees of freedom attached to the horizon. By constructing the reduced phase space, it can be demonstrated that such a transmutation indeed takes place for a large class of black holes, including Schwarzschild.
Killing horizons kill horizon degrees
Bergamin, L
2006-01-01
Frequently it is argued that the microstates responsible for the Bekenstein-Hawking entropy should arise from some physical degrees of freedom located near or on the black hole horizon. In this Essay we elucidate that instead entropy may emerge from the conversion of physical degrees of freedom, attached to a generic boundary, into unobservable gauge degrees of freedom attached to the horizon. By constructing the reduced phase space it can be demonstrated that such a transmutation indeed takes place for a large class of black holes, including Schwarzschild.
Dynamic programming for infinite horizon boundary control problems of PDE's with age structure
Faggian, Silvia
2008-01-01
We develop the dynamic programming approach for a family of infinite horizon boundary control problems with linear state equation and convex cost. We prove that the value function of the problem is the unique regular solution of the associated stationary Hamilton--Jacobi--Bellman equation and use this to prove existence and uniqueness of feedback controls. The idea of studying this kind of problem comes from economic applications, in particular from models of optimal investment with vintage capital. Such family of problems has already been studied in the finite horizon case by Faggian. The infinite horizon case is more difficult to treat and it is more interesting from the point of view of economic applications, where what mainly matters is the behavior of optimal trajectories and controls in the long run. The study of infinite horizon is here performed through a nontrivial limiting procedure from the corresponding finite horizon problem.
Dynamics of apparent horizons in quantum gravitational collapse
Tavakoli, Yaser; Dapor, Andrea
2013-01-01
We study the gravitational collapse of a massless scalar field within the effective scenario of loop quantum gravity. Classical singularity is avoided and replaced by a quantum bounce in this model. It is shown that, quantum gravity effects predict a threshold scale below which no horizon can form as the collapse evolves towards the bounce.
Entropy Rate Maps of Complex Excitable Dynamics in Cardiac Monolayers
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Alexander Schlemmer
2015-02-01
Full Text Available The characterization of spatiotemporal complexity remains a challenging task. This holds in particular for the analysis of data from fluorescence imaging (optical mapping, which allows for the measurement of membrane potential and intracellular calcium at high spatial and temporal resolutions and, therefore, allows for an investigation of cardiac dynamics. Dominant frequency maps and the analysis of phase singularities are frequently used for this type of excitable media. These methods address some important aspects of cardiac dynamics; however, they only consider very specific properties of excitable media. To extend the scope of the analysis, we present a measure based on entropy rates for determining spatiotemporal complexity patterns of excitable media. Simulated data generated by the Aliev–Panfilov model and the cubic Barkley model are used to validate this method. Then, we apply it to optical mapping data from monolayers of cardiac cells from chicken embryos and compare our findings with dominant frequency maps and the analysis of phase singularities. The studies indicate that entropy rate maps provide additional information about local complexity, the origins of wave breakup and the development of patterns governing unstable wave propagation.
Decay Rate and Low Energy Near Horizon Dynamics of Acoustic Black Holes
Kim, S W; Kim, Sung-Won; Oh, John J.
2005-01-01
We study the low energy dynamics of an acoustic black hole near sonic horizon. For the experimental test of black hole evaporation in laboratory, the decay rate (whisper-body factor) of the acoustic black hole (dumb hole) can be presented through the usual low energy perturbation method. As a consequence, we obtain the decay rate of the sonic horizon from the absorption and the reflection coefficients. Moreover, we show that the thermal emission from the sonic horizon is only proportional to the control parameter of handling the velocity of the fluid.
Application of initial data sequences to the study of Black Hole dynamical trapping horizons
Jaramillo, José Luis; Vasset, Nicolas; 10.1063/1.3141305
2011-01-01
Non-continuous "jumps" of Apparent Horizons occur generically in 3+1 (binary) black hole evolutions. The dynamical trapping horizon framework suggests a spacetime picture in which these "Apparent Horizon jumps" are understood as spatial cuts of a single spacetime hypersurface foliated by (compact) marginally outer trapped surfaces. We present here some work in progress which makes use of uni-parametric sequences of (axisymmetric) binary black hole initial data for exploring the plausibility of this spacetime picture. The modelling of Einstein evolutions by sequences of initial data has proved to be a successful methodological tool in other settings for the understanding of certain qualitative features of evolutions in restricted physical regimes.
Black-hole horizons as probes of black-hole dynamics II: geometrical insights
Jaramillo, José Luis; Moesta, o Philipp; Rezzolla, Luciano
2011-01-01
In a companion paper [1], we have presented a cross-correlation approach to near-horizon physics in which bulk dynamics is probed through the correlation of quantities defined at inner and outer spacetime hypersurfaces acting as test screens. More specifically, dynamical horizons provide appropriate inner screens in a 3+1 setting and, in this context, we have shown that an effective-curvature vector measured at the common horizon produced in a head-on collision merger can be correlated with the flux of linear Bondi-momentum at null infinity. In this paper we provide a more sound geometric basis to this picture. First, we show that a rigidity property of dynamical horizons, namely foliation uniqueness, leads to a preferred class of null tetrads and Weyl scalars on these hypersurfaces. Second, we identify a heuristic horizon news-like function, depending only on the geometry of spatial sections of the horizon. Fluxes constructed from this function offer refined geometric quantities to be correlated with Bondi f...
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.
Conditional exponents, entropies and a measure of dynamical self-organization
Mendes, R V
1998-01-01
In dynamical systems composed of interacting parts, conditional exponents, conditional exponent entropies and cylindrical entropies are shown to be well defined ergodic invariants which characterize the dynamical selforganization and statitical independence of the constituent parts. An example of interacting Bernoulli units is used to illustrate the nature of these invariants.
Causation entropy from symbolic representations of dynamical systems
Cafaro, Carlo; Sun, Jie; Bollt, Erik M
2015-01-01
Identification of causal structures and quantification of direct information flows in complex systems is a challenging yet important task, with practical applications in many fields. Data generated by dynamical processes or large-scale systems are often symbolized, either because of the finite resolution of the measurement apparatus, or because of the need of statistical estimation. By algorithmic application of causation entropy, we investigated the effects of symbolization on important concepts such as Markov order and causal structure of the tent map. We uncovered that these quantities depend nonmontonically and, most of all, sensitively on the choice of symbolization. Indeed, we show that Markov order and causal structure do not necessarily converge to their original analog counterparts as the resolution of the partitioning becomes finer.
Relationship between dynamical entropy and energy dissipation far from thermodynamic equilibrium.
Green, Jason R; Costa, Anthony B; Grzybowski, Bartosz A; Szleifer, Igal
2013-10-08
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.
Dynamics of EEG Entropy: beyond signal plus noise
Ignaccolo, M; Jernajczyk, W; Grigolini, P; West, B J
2009-01-01
EEG time series are analyzed using the diffusion entropy method. The resulting EEG entropy manifests short-time scaling, asymptotic saturation and an attenuated alpha-rhythm modulation. These properties are faithfully modeled by a phenomenological Langevin equation interpreted within a neural network context. Detrended fluctuation analysis of the EEG data is compared with diffusion entropy analysis and is found to suppress certain important properties of the EEG time series.
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.
Analyzing EEG of quasi-brain-death based on dynamic sample entropy measures.
Ni, Li; Cao, Jianting; Wang, Rubin
2013-01-01
To give a more definite criterion using electroencephalograph (EEG) approach on brain death determination is vital for both reducing the risks and preventing medical misdiagnosis. This paper presents several novel adaptive computable entropy methods based on approximate entropy (ApEn) and sample entropy (SampEn) to monitor the varying symptoms of patients and to determine the brain death. The proposed method is a dynamic extension of the standard ApEn and SampEn by introducing a shifted time window. The main advantages of the developed dynamic approximate entropy (DApEn) and dynamic sample entropy (DSampEn) are for real-time computation and practical use. Results from the analysis of 35 patients (63 recordings) show that the proposed methods can illustrate effectiveness and well performance in evaluating the brain consciousness states.
Disorder, dynamic and entropy effects in the solid state
Jensen, Torben R.; Li, Hai-Wen
2016-12-01
Storage of renewable energy remains a significant challenge for the implementation of a future carbon neutral and sustainable society based on renewable energy. New technologies providing a paradigm shift for energy storage may likely be based on novel materials with new functionalities. This review provides new perspectives for rational design of functional materials for energy storage using dynamic, disorder or entropy effects as a design concept. These effects may be introduced into the solid state using complex anions such as BH4- or B12H122-. These dynamic effects may facilitate anion substitution and preparation of materials that may stabilize high temperature polymorphs at lower temperatures. This has provided new ion conductors for lithium batteries and perovskite type metal borohydrides, which can be modified to resemble the well-known useful metal halide photovoltaics. Completely new metal hydrides, which stores hydrogen and may also be ion conductors or have magnetic, optical or electronic properties may be designed and prepared. This review reveals extreme structural and compositional flexibility of metal hydrides and provides new inspiration for rational materials design towards multi-functionality.
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.
Decoherence and dynamical entropy generation in quantum field theory
Energy Technology Data Exchange (ETDEWEB)
Koksma, Jurjen F., E-mail: J.F.Koksma@uu.nl [Institute for Theoretical Physics (ITP) and Spinoza Institute, Utrecht University, Postbus 80195, 3508 TD Utrecht (Netherlands); Prokopec, Tomislav, E-mail: T.Prokopec@uu.nl [Institute for Theoretical Physics (ITP) and Spinoza Institute, Utrecht University, Postbus 80195, 3508 TD Utrecht (Netherlands); Schmidt, Michael G., E-mail: M.G.Schmidt@thphys.uni-heidelberg.de [Institut fuer Theoretische Physik, Heidelberg University, Philosophenweg 16, D-69120 Heidelberg (Germany)
2012-01-20
We formulate a novel approach to decoherence based on neglecting observationally inaccessible correlators. We apply our formalism to a renormalised interacting quantum field theoretical model. Using out-of-equilibrium field theory techniques we show that the Gaussian von Neumann entropy for a pure quantum state increases to the interacting thermal entropy. This quantifies decoherence and thus measures how classical our pure state has become. The decoherence rate is equal to the single particle decay rate in our model. We also compare our approach to existing approaches to decoherence in a simple quantum mechanical model. We show that the entropy following from the perturbative master equation suffers from physically unacceptable secular growth.
STATISTICAL ENTROPIES OF THE TAUB-NUT/BOLT AdS SPACES FROM THE HORIZON CONFORMAL FIELD THEORY
Institute of Scientific and Technical Information of China (English)
JING JI-LIANG; ZHOU SAN-QING; HUANG YI-BIN
2001-01-01
The covariant phase technique is used to compute the constraint algebra of the four-dimensional space-times which are asymptotic to anti-de Sitter (AdS), such as the planar Taub-NUT AdS and Taub-bolt AdS spaces, and the hyperbolic Taub-bolt AdS space. The standard Virasoro subalgebrae with corresponding central charges for these objects are constructed and the resulting densities of states yield the expected Bekenstein-Hawking entropies.
Universal entropy relations: entropy formulae and entropy bound
Liu, Hang; Xu, Wei; Zhu, Bin
2016-01-01
We survey the applications of universal entropy relations in black holes with multi-horizons. In sharp distinction to conventional entropy product, the entropy relationship here not only improve our understanding of black hole entropy but was introduced as an elegant technique trick for handling various entropy bounds and sum. Despite the primarily technique role, entropy relations have provided considerable insight into several different types of gravity, including massive gravity, Einstein-Dilaton gravity and Horava-Lifshitz gravity. We present and discuss the results for each one.
Arntsen, Christopher; Chen, Chen; Voth, Gregory A.
2017-09-01
We present two new multiscale molecular dynamics (MS-RMD) models for the hydrated excess proton in water developed directly from ab initio molecular dynamics (AIMD) simulation data of the same system. The potential of mean force along the proton transfer reaction coordinate and radial distribution functions for the MS-RMD models are shown to faithfully reproduce those of AIMD. The models are developed using an algorithm based on relative entropy minimization, thus demonstrating the ability of the method to rapidly generate accurate and highly efficient reactive MD force fields.
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.
Ngo, Van A
2013-01-01
We propose a combination between the theory of diagonal entropy representing far-from-equilibrium ensembles and Jarzynski Equality to explore thermalization effects on thermodynamic quantities such as temperature, entropy, mechanical work and free-energy changes. Applying the theory to a quantum harmonic oscillator, we find that diagonal entropy offers a definition of temperature for closed systems far from equilibrium, and a better sampling of reaction pathways than the conventional von Neumann entropy. We also apply the theory to a many-body system of hard-core boson lattice, and discuss the ideas of how to estimate temperature, entropy and measure work distribution functions. The theory suggests a powerful technique to study non-equilibrium dynamics in quantum systems by means of performing work in a series of quenches.
Entropy of Null Surfaces and Dynamics of Spacetime
Padmanabhan, T; Paranjape, Aseem
2006-01-01
The null surfaces of a spacetime act as one-way membranes and can block information for a corresponding family of observers (time-like curves). Since lack of information can be related to entropy, this suggests the possibility of assigning an entropy to the null surfaces of a spacetime. We motivate and introduce such an entropy functional in terms of the normal to the null surface and a fourth-rank divergence free tensor $P_{ab}^{cd}$ with the algebraic symmetries of the curvature tensor. Extremising this entropy then leads to field equations for the background metric of the spacetime. When $P_{ab}^{cd}$ is constructed from the metric alone, these equations are identical to Einstein's equations with an undetermined cosmological constant (which arises as an integration constant). More generally, if $P_{ab}^{cd}$ is allowed to depend on both metric and curvature in a polynomial form, one recovers the Lanczos-Lovelock gravity. In all these cases: (a) We only need to extremise the entropy associated with the null...
Approximate maximum-entropy moment closures for gas dynamics
McDonald, James G.
2016-11-01
Accurate prediction of flows that exist between the traditional continuum regime and the free-molecular regime have proven difficult to obtain. Current methods are either inaccurate in this regime or prohibitively expensive for practical problems. Moment closures have long held the promise of providing new, affordable, accurate methods in this regime. The maximum-entropy hierarchy of closures seems to offer particularly attractive physical and mathematical properties. Unfortunately, several difficulties render the practical implementation of maximum-entropy closures very difficult. This work examines the use of simple approximations to these maximum-entropy closures and shows that physical accuracy that is vastly improved over continuum methods can be obtained without a significant increase in computational cost. Initially the technique is demonstrated for a simple one-dimensional gas. It is then extended to the full three-dimensional setting. The resulting moment equations are used for the numerical solution of shock-wave profiles with promising results.
A new Color Feature Extraction method Based on Dynamic Color Distribution Entropy of Neighbourhoods
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Fatemeh Alamdar
2011-09-01
Full Text Available One of the important requirements in image retrieval, indexing, classification, clustering and etc. is extracting efficient features from images. The color feature is one of the most widely used visual features. Use of color histogram is the most common way for representing color feature. One of disadvantage of the color histogram is that it does not take the color spatial distribution into consideration. In this paper dynamic color distribution entropy of neighborhoods method based on color distribution entropy is presented, which effectively describes the spatial information of colors. The image retrieval results in compare to improved color distribution entropy show the acceptable efficiency of this approach.
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.
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.
Generalized Second Law of Thermodynamics with Corrected Entropy in Tachyon Cosmology
Farajollahi, H; Shojaie, H; Abolghasemi, M
2016-01-01
This work is to study the generalized second law (GSL) of thermodynamics in tachyon cosmology where the boundary of the universe is assumed to be enclosed by a dynamical apparent horizon. The model is constrained with the observational data. The two logarithmic and power law corrected entropy is also discussed and conditions to validate the GSL and corrected entropies are obtained.
Application of approximate entropy on dynamic characteristics of epileptic absence seizure
Institute of Scientific and Technical Information of China (English)
Yi Zhou; Ruimei Huang; Ziyi Chen; Xin Chang; Jialong Chen; Lingli Xie
2012-01-01
Electroencephalogram signals are time-varying complex electrophysiological signals. Existing studies show that approximate entropy, which is a nonlinear dynamics index, is not an ideal method for electroencephalogram analysis. Clinical electroencephalogram measurements usually contain electrical interference signals, creating additional challenges in terms of maintaining robustness of the analytic methods. There is an urgent need for a novel method of nonlinear dynamical analysis of the electroencephalogram that can characterize seizure-related changes in cerebral dynamics. The aim of this paper was to study the fluctuations of approximate entropy in preictal, ictal, and postictal electroencephalogram signals from a patient with absence seizures, and to improve the algorithm used to calculate the approximate entropy. The approximate entropy algorithm, especially our modified version, could accurately describe the dynamical changes of the brain during absence seizures. We could also demonstrate that the complexity of the brain was greater in the normal state than in the ictal state. The fluctuations of the approximate entropy before epileptic seizures observed in this study can form a goodbasis for further study on the prediction of seizures with nonlinear dynamics.
Balasis, G.
2012-04-01
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 geomagnetism and magnetospheric physics, accurate detection of the dissimilarity between normal and abnormal states (e.g. pre-storm activity and magnetic storms) can vastly improve geomagnetic field modelling as well as space weather forecasting, respectively. Nonextensive statistical mechanics through Tsallis entropy provides a solid theoretical basis for describing and analyzing complex systems out of equilibrium, particularly systems exhibiting long-range correlations or fractal properties. Entropy measures (e.g., Tsallis entropy, Shannon entropy, block entropy, Kolmogorov entropy, T-complexity, and approximate entropy) have been proven effectively applicable for the investigation of dynamical complexity in Dst time series. It has been demonstrated that as a magnetic storm approaches, there is clear evidence of significantly lower complexity in the magnetosphere. The observed higher degree of organization of the system agrees with results previously inferred from fractal analysis via estimates of the Hurst exponent based on wavelet transform. This convergence between entropies 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. Moreover, based on the general behavior of complex system dynamics it has been recently found that Dst time series exhibit discrete scale invariance which in turn leads to log-periodic corrections to scaling that decorate the pure power law. The latter can be used for the determination of the time of occurrence of an approaching magnetic storm.
Mean dynamical entropy of quantum system tends to infinity in the semiclassical limit
Slomczynski, Wojciech; Zyczkowski, Karol
1997-01-01
We show that the mean dynamical entropy of a quantum map on the sphere is positive and tends logarithmically to infinity in the semiclassical limit. A link between chaotic dynamics of classical systems and the random matrix-like properties of spectra of the corresponding quantum analogues is demonstrated.
Valenza, Gaetano; Citi, Luca; Scilingo, Enzo Pasquale; Barbieri, Riccardo
2014-01-01
Measures of entropy have been proved as powerful quantifiers of complex nonlinear systems, particularly when applied to stochastic series of heartbeat dynamics. Despite the remarkable achievements obtained through standard definitions of approximate and sample entropy, a time-varying definition of entropy characterizing the physiological dynamics at each moment in time is still missing. To this extent, we propose two novel measures of entropy based on the inho-mogeneous point-process theory. The RR interval series is modeled through probability density functions (pdfs) which characterize and predict the time until the next event occurs as a function of the past history. Laguerre expansions of the Wiener-Volterra autoregressive terms account for the long-term nonlinear information. As the proposed measures of entropy are instantaneously defined through such probability functions, the proposed indices are able to provide instantaneous tracking of autonomic nervous system complexity. Of note, the distance between the time-varying phase-space vectors is calculated through the Kolmogorov-Smirnov distance of two pdfs. Experimental results, obtained from the analysis of RR interval series extracted from ten healthy subjects during stand-up tasks, suggest that the proposed entropy indices provide instantaneous tracking of the heartbeat complexity, also allowing for the definition of complexity variability indices.
Dynamics of Holographic Entanglement Entropy Following a Local Quench
Rangamani, Mukund; Vincart-Emard, Alexandre
2015-01-01
We discuss the behaviour of holographic entanglement entropy following a local quench in 2+1 dimensional strongly coupled CFTs. The entanglement generated by the quench propagates along an emergent light-cone, reminiscent of the Lieb-Robinson light-cone propagation of correlations in non-relativistic systems. We find the the speed of propagation is bounded from below by the entanglement tsunami velocity obtained earlier for global quenches in holographic systems, and from above by the speed of light. The former is realized for sufficiently broad quenches, while the latter pertains for well localized quenches. The non-universal behavior in the intermediate regime appears to stem from finite-size effects. We also note that the entanglement entropy of subsystems reverts to the equilibrium value exponentially fast, in contrast to a much slower equilibration seen in certain spin models.
Spatial Dynamics of Urban Growth Based on Entropy and Fractal Dimension
Chen, Yanguang
2016-01-01
The fractal dimension growth of urban form can be described with sigmoid functions such as logistic function due to squashing effect. The sigmoid curves of fractal dimension suggest a type of spatial replacement dynamics of urban evolution. How to understand the underlying rationale of the fractal dimension curves is a pending problem. This study is based on two previous findings. First, normalized fractal dimension proved to equal normalized spatial entropy; second, a sigmoid function proceeds from an urban-rural interaction model. Defining urban space-filling measurement by spatial entropy, and defining rural space-filling measurement by information gain, we can construct a new urban-rural interaction and coupling model. From this model, we can derive the logistic equation of fractal dimension growth strictly. This indicates that urban growth results from the unity of opposites between spatial entropy increase and information increase. In a city, an increase in spatial entropy is accompanied by a decrease i...
Cosmic dynamics with entropy corrected holographic dark energy
Sadjadi, H Mohseni
2010-01-01
We investigate the model of holographic dark energy with logarithmic correction to its energy density. This modification is motivated from the loop quantum gravity corrections to the entropy-area law. We also consider an interaction between dark energy and dark matter. The behavior of the Hubble parameter (specially in the late time) is studied. Besides, conditions under which an accelerated universe can decelerate and also successive acceleration-deceleration phases can be occurred in the evolution of the universe is investigated.
Kupferman, Judy
2010-01-01
Black hole entropy has been shown by t'Hooft to diverge at the horizon, whereas entanglement entropy in general does not. We show that because the region near the horizon is a thermal state, entropy is linear to energy, and energy at a barrier is inversely proportional to barrier slope, and diverges at an infinitely sharp barrier as a result of position/momentum uncertainty. We show that t'Hooft's divergence at the black hole is also an example of momentum/position uncertainty, as seen by the fact that the "brick wall" which corrects it in fact smooths the sharp boundary into a more gradual slope. This removes a major obstacle to identification of black hole entropy with entanglement entropy.
From bricks to quasinormal modes: A new perspective on black hole entropy
Arzano, Michele; Dreyer, Olaf
2013-01-01
Calculations of black hole entropy based on the counting of modes of a quantum field propagating in a Schwarzschild background need to be regularized in the vicinity of the horizon. To obtain the Bekenstein-Hawking result the short distance cut-off needs to be fixed by hand. In this note we give an argument for obtaining this cut-off in a natural fashion. We do this by modelling the black hole by its set of quasinormal modes. The horizon then becomes a extended region: the quantum ergosphere. The interaction of the quantum ergosphere and the quantum field provides a natural regularization mechanism. The width of the quantum ergosphere provides the right cut-off for the entropy calculation. We arrive at a dual picture of black hole entropy. The entropy of the black hole is given both by the entropy of the quantum field in the bulk and the dynamical degrees of freedom on the horizon.
Determining Dynamical Path Distributions usingMaximum Relative Entropy
2015-05-31
θ). The selected joint posterior Pnew(x, θ) is that which maximizes the entropy1 , S[P, Pold ] = − ∫ P (x, θ) log P (x, θ) Pold (x, θ) dxdθ , (15) 1...to the appropriate constraints (parameters can be discrete as well). Pold (x, θ) contains our prior information which we call the joint prior. To be...explicit, Pold (x, θ) = Pold (x) Pold (θ|x) , (16) where Pold (x) is the traditional Bayesian prior and Pold (θ|x) is the likelihood. It is important to
DSA Image Fusion Based on Dynamic Fuzzy Logic and Curvelet Entropy
Directory of Open Access Journals (Sweden)
Guangming Zhang
2009-06-01
Full Text Available The curvelet transform as a multiscale transform has directional parameters occurs at all scales, locations, and orientations. It is superior to wavelet transform in image processing domain. This paper analyzes the characters of DSA medical image, and proposes a novel approach for DSA medical image fusion, which is using curvelet information entropy and dynamic fuzzy logic. Firstly, the image was decomposed by curvelet transform to obtain the different level information. Then the entropy from different level of DSA medical image was calculated, and a membership function based on dynamic fuzzy logic was constructed to adjust the weight for image subbands coefficients via entropy. At last an inverse curvelet transform was applied to reconstruct the image to synthesize one DSA medical image which could contain more integrated accurate detail information of blood vessels than any one of the individual source images. By compare, the efficiency of our method is better than weighted average, laplacian pyramid and traditional wavelet transform method.
Bekenstein-Hawking entropy from Criticality
Bhattacharya, Swastik
2014-01-01
Vacuum Einstein equations when projected on to a black hole horizon is analogous to the dynamics of fluids. In this work we address the question, whether certain properties of semi-classical black holes could be holographically mapped into properties of (2 + 1)-dimensional fluid living on the horizon. In particular, we focus on the statistical mechanical description of the horizon-fluid that leads to Bekenstein-Hawking entropy. Within the paradigm of Landau mean field theory and existence of a condensate at a critical temperature, we explicitly show that Bekenstein-Hawking entropy and other features of black hole thermodynamics can be recovered from the statistical modelling of the fluid. We also show that a negative cosmological constant acts like an external magnetic field that induces order in the system leading to the appearance of a tri-critical point in the phase diagram.
Instantaneous transfer entropy for the study of cardio-respiratory dynamics.
Valenza, Gaetano; Faes, Luca; Citi, Luca; Orini, Michele; Barbieri, Riccardo
2015-01-01
Measures of transfer entropy have been proposed to quantify the directional coupling and strength between two complex physiological variables. Particular attention has been given to nonlinear interactions within cardiovascular and respiratory dynamics as influenced by the autonomic nervous system. However, standard transfer entropy estimates have shown major limitations in dealing with issues concerning stochastic system modeling, limited observations in time, and the assumption of stationarity of the considered physiological variables. Moreover, standard estimates are unable to track time-varying changes in nonlinear coupling with high resolution in time. Here, we propose a novel definition of transfer entropy linked to inhomogeneous point-process theory. Heartbeat and respiratory dynamics are characterized through discrete time series, and modeled through probability density functions (PDFs) which characterize and predict the time until the occurrence of the next physiological event as a function of the past history. As the derived measures of entropy are instantaneously defined through continuos PDFs, a novel index (the Instantaneous point-process Transfer Entropy, ipT ransfEn) is able to provide instantaneous tracking of the information transfer. The new measure is tested on experimental data gathered from 16 healthy subjects undergoing postural changes, showing fast tracking of the tilting events and low variability during the standing phase.
Majee, Pradip; Goswami, Gurupada; Barik, Debashis; Bag, Bidhan Chandra
In this paper we have studied the dynamics of thermal broadband noise-driven dynamical system in terms of information entropy at both the nonstationary and stationary states. Here, a unified description of fluctuating force is considered in a thermodynamically closed system. Based on the Fokker-Planck description of stochastic processes and the entropy balance equation, we have calculated the time-dependence of the information entropy production and entropy flux in the presence and absence of nonequilibrium constraint. Our calculation considers how the time evolution of these quantities is affected if the characteristic of noise changes from white to red or green and red to green in a unified scheme.
Directory of Open Access Journals (Sweden)
Gian Paolo Beretta
2008-08-01
Full Text Available A rate equation for a discrete probability distribution is discussed as a route to describe smooth relaxation towards the maximum entropy distribution compatible at all times with one or more linear constraints. The resulting dynamics follows the path of steepest entropy ascent compatible with the constraints. The rate equation is consistent with the Onsager theorem of reciprocity and the fluctuation-dissipation theorem. The mathematical formalism was originally developed to obtain a quantum theoretical unification of mechanics and thermodinamics. It is presented here in a general, non-quantal formulation as a part of an effort to develop tools for the phenomenological treatment of non-equilibrium problems with applications in engineering, biology, sociology, and economics. The rate equation is also extended to include the case of assigned time-dependences of the constraints and the entropy, such as for modeling non-equilibrium energy and entropy exchanges.
Beretta, Gian P.
2008-09-01
A rate equation for a discrete probability distribution is discussed as a route to describe smooth relaxation towards the maximum entropy distribution compatible at all times with one or more linear constraints. The resulting dynamics follows the path of steepest entropy ascent compatible with the constraints. The rate equation is consistent with the Onsager theorem of reciprocity and the fluctuation-dissipation theorem. The mathematical formalism was originally developed to obtain a quantum theoretical unification of mechanics and thermodinamics. It is presented here in a general, non-quantal formulation as a part of an effort to develop tools for the phenomenological treatment of non-equilibrium problems with applications in engineering, biology, sociology, and economics. The rate equation is also extended to include the case of assigned time-dependences of the constraints and the entropy, such as for modeling non-equilibrium energy and entropy exchanges.
Finite size effect on dynamical entanglement entropy: CFT and holography
Mandal, Gautam; Ugajin, Tomonori
2016-01-01
Time-dependent entanglement entropy (EE) is computed for a single interval in two-dimensional conformal theories from a quenched initial state in the presence of spatial boundaries. The EE is found to be periodic in time with periodicity equal to the system size $L$. For large enough $L$, the EE shows a rise to a thermal value (characterized by a temperature $1/\\beta$ determined by the initial state), followed by periodic returns to the original value. This works irrespective of whether the conformal field theory (CFT) is rational or irrational. For conformal field theories with a holographic dual, the large $c$ limit plays an essential role in ensuring that the EE computed from the CFT is universal (independent of the details of the CFT and of boundary conditions) and is exactly matched by the holographic EE. The dual geometry is computed and it interpolates between a BTZ black hole at large $L$ and global AdS at large $\\beta$.
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
Allnér, Olof; Foloppe, Nicolas; Nilsson, Lennart
2015-01-22
Molecular dynamics simulations of E. coli glutaredoxin1 in water have been performed to relate the dynamical parameters and entropy obtained in NMR relaxation experiments, with results extracted from simulated trajectory data. NMR relaxation is the most widely used experimental method to obtain data on dynamics of proteins, but it is limited to relatively short timescales and to motions of backbone amides or in some cases (13)C-H vectors. By relating the experimental data to the all-atom picture obtained in molecular dynamics simulations, valuable insights on the interpretation of the experiment can be gained. We have estimated the internal dynamics and their timescales by calculating the generalized order parameters (O) for different time windows. We then calculate the quasiharmonic entropy (S) and compare it to the entropy calculated from the NMR-derived generalized order parameter of the amide vectors. Special emphasis is put on characterizing dynamics that are not expressed through the motions of the amide group. The NMR and MD methods suffer from complementary limitations, with NMR being restricted to local vectors and dynamics on a timescale determined by the rotational diffusion of the solute, while in simulations, it may be difficult to obtain sufficient sampling to ensure convergence of the results. We also evaluate the amount of sampling obtained with molecular dynamics simulations and how it is affected by the length of individual simulations, by clustering of the sampled conformations. We find that two structural turns act as hinges, allowing the α helix between them to undergo large, long timescale motions that cannot be detected in the time window of the NMR dipolar relaxation experiments. We also show that the entropy obtained from the amide vector does not account for correlated motions of adjacent residues. Finally, we show that the sampling in a total of 100 ns molecular dynamics simulation can be increased by around 50%, by dividing the
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.
Mood states modulate complexity in heartbeat dynamics: A multiscale entropy analysis
Valenza, G.; Nardelli, M.; Bertschy, G.; Lanata, A.; Scilingo, E. P.
2014-07-01
This paper demonstrates that heartbeat complex dynamics is modulated by different pathological mental states. Multiscale entropy analysis was performed on R-R interval series gathered from the electrocardiogram of eight bipolar patients who exhibited mood states among depression, hypomania, and euthymia, i.e., good affective balance. Three different methodologies for the choice of the sample entropy radius value were also compared. We show that the complexity level can be used as a marker of mental states being able to discriminate among the three pathological mood states, suggesting to use heartbeat complexity as a more objective clinical biomarker for mental disorders.
Basin entropy: a new tool to analyze uncertainty in dynamical systems.
Daza, Alvar; Wagemakers, Alexandre; Georgeot, Bertrand; Guéry-Odelin, David; Sanjuán, Miguel A F
2016-08-12
In nonlinear dynamics, basins of attraction link a given set of initial conditions to its corresponding final states. This notion appears in a broad range of applications where several outcomes are possible, which is a common situation in neuroscience, economy, astronomy, ecology and many other disciplines. Depending on the nature of the basins, prediction can be difficult even in systems that evolve under deterministic rules. From this respect, a proper classification of this unpredictability is clearly required. To address this issue, we introduce the basin entropy, a measure to quantify this uncertainty. Its application is illustrated with several paradigmatic examples that allow us to identify the ingredients that hinder the prediction of the final state. The basin entropy provides an efficient method to probe the behavior of a system when different parameters are varied. Additionally, we provide a sufficient condition for the existence of fractal basin boundaries: when the basin entropy of the boundaries is larger than log2, the basin is fractal.
On generalized gravitational entropy, squashed cones and holography
Energy Technology Data Exchange (ETDEWEB)
Bhattacharyya, Arpan [Centre for High Energy Physics, Indian Institute of Science,C.V. Raman Avenue, Bangalore 560012 (India); Sharma, Menika [Centre for High Energy Physics, Indian Institute of Science,C.V. Raman Avenue, Bangalore 560012 (India); Harish-Chandra Research Institute,Chhatnag Road, Jhusi, Allahabad 211019 (India); Sinha, Aninda [Centre for High Energy Physics, Indian Institute of Science,C.V. Raman Avenue, Bangalore 560012 (India)
2014-01-08
We consider generalized gravitational entropy in various higher derivative theories of gravity dual to four dimensional CFTs using the recently proposed regularization of squashed cones. We derive the universal terms in the entanglement entropy for spherical and cylindrical surfaces. This is achieved by constructing the Fefferman-Graham expansion for the leading order metrics for the bulk geometry and evaluating the generalized gravitational entropy. We further show that the Wald entropy evaluated in the bulk geometry constructed for the regularized squashed cones leads to the correct universal parts of the entanglement entropy for both spherical and cylindrical entangling surfaces. We comment on the relation with the Iyer-Wald formula for dynamical horizons relating entropy to a Noether charge. Finally we show how to derive the entangling surface equation in Gauss-Bonnet holography.
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.
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.
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.
Triple-horizon spherically symmetric spacetime and holographic principle
Dymnikova, Irina
2012-01-01
We present a family of spherically symmetric spacetimes, specified by the density profile of a vacuum dark energy, which have the same global structure as the de Sitter spacetime but the reduced symmetry which leads to a time-evolving and spatially inhomogeneous cosmological term. It connects smoothly two de Sitter vacua with different values of cosmological constant and corresponds to anisotropic vacuum dark fluid defined by symmetry of its stress-energy tensor which is invariant under the radial boosts. This family contains a special class distinguished by dynamics of evaporation of a cosmological horizon which evolves to the triple horizon with the finite entropy, zero temperature, zero curvature, infinite positive specific heat, and infinite scrambling time. Non-zero value of the cosmological constant in the triple-horizon spacetime is tightly fixed by quantum dynamics of evaporation of the cosmological horizon.
Banerjee, Atreyee; Sengupta, Shiladitya; Sastry, Srikanth; Bhattacharyya, Sarika Maitra
2014-11-01
We present a study of two model liquids with different interaction potentials, exhibiting similar structure but significantly different dynamics at low temperatures. By evaluating the configurational entropy, we show that the differences in the dynamics of these systems can be understood in terms of their thermodynamic differences. Analyzing their structure, we demonstrate that differences in pair correlation functions between the two systems, through their contribution to the entropy, dominate the differences in their dynamics, and indeed overestimate the differences. Including the contribution of higher order structural correlations to the entropy leads to smaller estimates for the relaxation times, as well as smaller differences between the two studied systems.
Institute of Scientific and Technical Information of China (English)
ZHANG Xing; BAI YongQiang; XIN Bin; CHEN Jie
2013-01-01
This paper presents online motion planning for UAV (unmanned aerial vehicle) in complex threat field,including both static threats and moving threats,which can be formulated as a dynamic constrained optimal control problem.Receding horizon control (RHC) based on differential evolution (DE) algorithm is adopted.A location-predicting model of moving threats is established to assess the value of threat that UAV faces in flight.Then flyable paths can be generated by the control inputs which are optimized by DE under the guidance of the objective function.Simulation results demonstrate that the proposed method not only generates smooth and flyable paths,but also enables UAV to avoid threats efficiently and arrive at destination safely.
Institute of Scientific and Technical Information of China (English)
Mona Khare; Shraddha Roy
2008-01-01
The purpose of the present paper is to study the entropy hs(Φ) of a quantum dynamical systems Φ= (L,s,φ),where s is a bayessian state on an orthomodular lattice L.Having introduced the notion of entropy hs(φ,)of partition of a Boolean algebra B with respect to a state s and a state preserving homomorphism φ,we prove a few results on that,define the entropy of a dynamical system hs(Φ),and show its invariance.The concept of sufficient families is also given and we establish that hs(Φ) comes out to be equal to the supremum of hs(φ,),where varies over any sufficient family.The present theory has then been extended to the quantum dynamical system ( L,s,φ),which as an effect of the theory of commutators and Bell inequalities can equivalently be replaced by the dynamical system (B,s0,φ),where B is a Boolean algebra and so is a state on B.
Dynamics of Representational Change: Entropy, Action, and Cognition
Stephen, Damian G.; Dixon, James A.; Isenhower, Robert W.
2009-01-01
Explaining how the cognitive system can create new structures has been a major challenge for cognitive science. Self-organization from the theory of nonlinear dynamics offers an account of this remarkable phenomenon. Two studies provide an initial test of the hypothesis that the emergence of new cognitive structure follows the same universal…
Directory of Open Access Journals (Sweden)
Alex B. Nielsen
2014-02-01
Full Text Available In this study, we located and compared different types of horizons in the spherically symmetric Vaidya solution. The horizons we found were trapping horizons, which can be null, timelike, or spacelike, null surfaces with constant area change and also conformal Killing horizons. The conformal Killing horizons only exist for certain choices of the mass function. Under a conformal transformation, the conformal Killing horizons can be mapped into true Killing horizons. This allows conclusions drawn in the dynamical Vaidya spacetime to be related to known properties of static spacetimes. We found the conformal factor that performs this transformation and wrote the new metric in explicitly static coordinates. Using this construction we found that the tunneling argument for Hawking radiation does not umabiguously support Hawking radiation being associated with the trapping horizon. We also used this transformation to derive the form of the surface gravity for a class of physical observers in Vaidya spacetimes.
Application of an Entropy Maximizing and Dynamics Model for Understanding Settlement Structure
Davies, Toby; Fry, Hannah; Wilson, Alan; Palmisano, Alessio; Altaweel, Mark; Radner, Karen
2013-01-01
We present a spatial interaction entropy maximizing and structural dynamics model of settlements from the Middle Bronze (MBA) and Iron Ages (IA) in the Khabur Triangle (KT) region within Syria. The model addresses factors that make locations attractive for trade and settlement, affecting settlement growth and change. We explore why some sites become relatively major settlements, while others diminish in the periods discussed. We assess how political and geographic constraints affect regional ...
Entropy, String Theory, and our World
Gregori, Andrea
2002-01-01
We investigate the consequences of two assumptions for String (or M) Theory, namely that: 1) all coordinates are compact and bound by the horizon of observation, 2) the ``dynamics'' of compactification is determined by the ``second law of thermodynamics'', i.e. the principle of entropy. We discuss how this leads to a phenomenologically consistent scenario for our world, both at the elementary particle's and at the cosmological level, without any fine tuning or further ``ad hoc'' constraint.
Jo, Sunhwan; Chipot, Christophe; Roux, Benoît
2015-05-12
The performance and accuracy of different simulation schemes for estimating the entropy inferred from free energy calculations are tested. The results obtained from replica-exchange molecular dynamics (REMD) simulations based on a simplified toy model are compared to exact numerically derived ones to assess accuracy and convergence. It is observed that the error in entropy estimation decreases by at least an order of magnitude and the quantities of interest converge much faster when the simulations are coupled via a temperature REMD algorithm and the trajectories from different temperatures are combined. Simulations with the infinite-swapping method and its variants show some improvement over the traditional nearest-neighbor REMD algorithms, but they are more computationally expensive. To test the methodologies further, the free energy profile for the reversible association of two methane molecules in explicit water was calculated and decomposed into its entropic and enthalpic contributions. Finally, a strategy based on umbrella sampling computations carried out via simultaneous temperature and Hamiltonian REMD simulations is shown to yield the most accurate entropy estimation. The entropy profile between the two methane molecules displays the characteristic signature of a hydrophobic interaction.
Spontaneously Broken Asymptotic Symmetries and an Effective Action for Horizon Dynamics
Eling, Christopher
2016-01-01
Asymptotic spacetime symmetries have been conjectured to play an important role in quantum gravity. In this paper we study the breaking of asymptotic symmetries associated with a null horizon boundary. In two-dimensions, these symmetries are reparametrizations of the time parameter on the horizon. We show how this horizon reparametrization symmetry is explicitly and spontaneously broken in dilaton gravity and construct an effective action for these pseudo-Goldstone modes using the on-shell gravitational action for a null boundary. The variation of this action yields the horizon constraint equation. This action is invariant under a 2 parameter subgroup of $SL(2)$ transformations, whose Noether charges we interpret via the membrane paradigm. We place these results in the context of recent work on the near $AdS_2$/ near $CFT_1$ correspondence. In this setting the horizon action characterizes the infrared regime near the horizon and has a hydrodynamical sigma model form. We also discuss our construction in Genera...
Causal Nature and Dynamics of Trapping Horizons in Black Hole Collapse and Cosmology
Helou, Alexis; Miller, John C
2016-01-01
In calculations of gravitational collapse to form black holes, trapping horizons (foliated by marginally trapped surfaces) make their first appearance either within the collapsing matter or where it joins on to a vacuum exterior. Those which then move outwards with respect to the matter have been proposed for use in defining black holes, replacing the global concept of an "event horizon" which has some serious drawbacks for practical applications. We focus here on studying the properties of trapping horizons within spherical symmetry (which gives some simplifications while retaining the most essential general features). Their locations are then given by exactly the same condition ($R=2M$) as for the event horizon in the vacuum Schwarzschild metric, and the same condition also applies for cosmological trapping horizons. We have investigated the causal nature of these horizons (i.e. whether they are spacelike, timelike or null), making contact with the Misner-Sharp formalism, which has often been used for numer...
Dynamical symmetry enhancement near N=2, D=4 gauged supergravity horizons
Gutowski, J; Papadopoulos, G
2016-01-01
We show that all smooth Killing horizons with compact horizon sections of 4-dimensional gauged N=2 supergravity coupled to any number of vector multiplets preserve $2 c_1({\\cal K})+4 \\ell$ supersymmetries, where ${\\cal K}$ is a pull-back of the Hodge bundle of the special K\\"ahler manifold on the horizon spatial section. We also demonstrate that all such horizons with $c_1({\\cal K})=0$ exhibit an SL(2,R) symmetry and preserve either 4 or 8 supersymmetries. If the orbits of the SL(2,R) symmetry are 2-dimensional, the horizons are warped products of AdS2 with the horizon spatial section. Otherwise, the horizon section admits an isometry which preserves all the fields. The proof of these results is centered on the use of index theorem in conjunction with an appropriate generalization of the Lichnerowicz theorem for horizons that preserve at least one supersymmetry. In all $c_1({\\cal K})=0$ cases, we specify the local geometry of spatial horizon sections and demonstrate that the solutions are determined by first ...
Thermodynamics of the apparent horizon in massive cosmology
Li, Hui
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 cosmological model 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 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 $\\delta Q=T dS$, where the heat flow $\\delta Q$ is the energy-supply of pure matter projecting on the vector $\\xi$ 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 $1/(2\\pi \\widetilde{r}_A)$, the modified Friedmann equations governing the dynamical evolution of the un...
Lü, Zhiguo
2011-01-01
We investigate the dynamical information exchange between a two-state system and its environment which is measured by von Neumann entropy. It is found that in the underdamping regime, the entropy dynamics exhibits an extremely non-Markovian oscillation-hump feature, in which oscillations manifest quantum coherence and a hump of envelop demonstrates temporal memory of bath. It indicates that the process of entropy exchange is bidirectional. When the coupling strength increases a certain threshold, the hump along with ripple disappears, which is indicative of the coherent-incoherent dynamical crossover. The long-time limit of entropy evolution reaches the ground state value which agrees with that of numerical renormalization group.
Directory of Open Access Journals (Sweden)
S. Abdel-Khalek
2013-01-01
Full Text Available We study the dynamics of the atomic inversion, scaled atomic Wehrl entropy, and marginal atomic Q-function for a single two-level atom interacting with a one-mode cavity field taking in the presence of atomic damping. We obtain the exact solution of the master equation in the interaction picture using specific initial conditions. We examine the effects of atomic damping parameter and number of multiphoton transition on the scaled atomic Wehrl entropy, atomic Q-function, and their marginal distribution. We observe an interesting monotonic relation between the different physical quantities in the case of different values of the number of photon transition during the time evolution.
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.
Black hole entropy and entropy of entanglement
Kabat, D
1995-01-01
We compute the one-loop correction to the entropy of a very massive black hole, by evaluating the partition function in the presence of a conical singularity for quantum fields of spin zero, one-half, and one. We compare the results to the entropy of entanglement, defined by the density matrix which describes the ground state of the field as seen from one side of a boundary in Minkowski space. Fields of spin zero and one-half contribute an entropy to the black hole which is identical to their entropy of entanglement. For spin one a contact interaction with the horizon appears in the black hole entropy but is absent from the entropy of entanglement. Expressed as a particle path integral the contact term is an integral over paths which begin and end on the horizon; it is the field theory limit of the interaction proposed by Susskind and Uglum which couples a closed string to an open string stranded on the horizon.
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.
Spontaneously broken asymptotic symmetries and an effective action for horizon dynamics
Eling, Christopher
2017-02-01
Asymptotic spacetime symmetries have been conjectured to play an important role in quantum gravity. In this paper we study the breaking of asymptotic symmetries associated with a null horizon boundary. In two-dimensions, these symmetries are reparametrizations of the time parameter on the horizon. We show how this horizon reparametrization symmetry is explicitly and spontaneously broken in dilaton gravity and construct an effective action for these pseudo-Goldstone modes using the on-shell gravitational action for a null boundary. The variation of this action yields the horizon constraint equation. This action is invariant under a 2 parameter subgroup of SL(2) transformations, whose Noether charges we interpret via the membrane paradigm. We place these results in the context of recent work on the near AdS2/ near CFT1 correspondence. In this setting the horizon action characterizes the infrared regime near the horizon and has a hydrodynamical sigma model form. We also discuss our construction in General Relativity. In the three-dimensional case there is a natural generalization of our results. However, in higher dimensions, the variation of the effective action only yields the Raychaudhuri equation for small perturbations of the horizon.
Comparisons of Black Hole Entropy
Kupferman, Judy
2016-01-01
In this thesis I examine several different concepts of black hole entropy in order to understand whether they describe the same quantity. I look at statistical and entanglement entropies, Wald entropy and Carlip's entropy from conformal field theory, and compare their behavior in a few specific aspects: divergence at the BH horizon, dependence on space time curvature and behavior under a geometric variation. I find that statistical and entanglement entropy may be similar but they seem to differ from the entropy of Wald and Carlip. Chapters 2 and 3 overlap with 1010.4157 and 1310.3938. Chapter 4 does not appear elsewhere.
Varotsos, P A; Skordas, E S; Lazaridou, M S
2005-01-01
Complexity measures are introduced, that quantify the change of the natural entropy fluctuations at different length scales in time-series emitted from systems operating far from equilibrium. They identify impending sudden cardiac death (SD) by analyzing fifteen minutes electrocardiograms, and comparing to those of truly healthy humans (H). These measures seem to be complementary to the ones suggested recently [Phys. Rev. E {\\bf 70}, 011106 (2004)] and altogether enable the classification of individuals into three categories: H, heart disease patients and SD. All the SD individuals, who exhibit critical dynamics, result in a common behavior.
Possible dynamical explanations for Paltridge's principle of maximum entropy production
Energy Technology Data Exchange (ETDEWEB)
Virgo, Nathaniel, E-mail: nathanielvirgo@gmail.com; Ikegami, Takashi, E-mail: nathanielvirgo@gmail.com [Ikegami Laboratory, University of Tokyo (Japan)
2014-12-05
Throughout the history of non-equilibrium thermodynamics a number of theories have been proposed in which complex, far from equilibrium flow systems are hypothesised to reach a steady state that maximises some quantity. Perhaps the most celebrated is Paltridge's principle of maximum entropy production for the horizontal heat flux in Earth's atmosphere, for which there is some empirical support. There have been a number of attempts to derive such a principle from maximum entropy considerations. However, we currently lack a more mechanistic explanation of how any particular system might self-organise into a state that maximises some quantity. This is in contrast to equilibrium thermodynamics, in which models such as the Ising model have been a great help in understanding the relationship between the predictions of MaxEnt and the dynamics of physical systems. In this paper we show that, unlike in the equilibrium case, Paltridge-type maximisation in non-equilibrium systems cannot be achieved by a simple dynamical feedback mechanism. Nevertheless, we propose several possible mechanisms by which maximisation could occur. Showing that these occur in any real system is a task for future work. The possibilities presented here may not be the only ones. We hope that by presenting them we can provoke further discussion about the possible dynamical mechanisms behind extremum principles for non-equilibrium systems, and their relationship to predictions obtained through MaxEnt.
Coherent states measurement entropy
Kwapien, J; Zyczkowski, K; Kwapien, Jaroslaw; Slomczynski, Wojciech; Zyczkowski, Karol
1996-01-01
Coherent states (CS) quantum entropy can be split into two components. The dynamical entropy is linked with the dynamical properties of a quantum system. The measurement entropy, which tends to zero in the semiclassical limit, describes the unpredictability induced by the process of a quantum approximate measurement. We study the CS--measurement entropy for spin coherent states defined on the sphere discussing different methods dealing with the time limit n \\to \\infty. In particular we propose an effective technique of computing the entropy by iterated function systems. The dependence of CS--measurement entropy on the character of the partition of the phase space is analysed.
Akrami, Amin; Nazeri, Sina
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. PMID:27699169
Black hole entropy quantization
Corichi, A; Fernandez-Borja, E; Corichi, Alejandro; Diaz-Polo, Jacobo; Fernandez-Borja, Enrique
2006-01-01
Ever since the pioneer works of Bekenstein and Hawking, black hole entropy has been known to have a quantum origin. Furthermore, it has long been argued by Bekenstein that entropy should be quantized in discrete (equidistant) steps given its identification with horizon area in (semi-)classical general relativity and the properties of area as an adiabatic invariant. This lead to the suggestion that black hole area should also be quantized in equidistant steps to account for the discrete black hole entropy. Here we shall show that loop quantum gravity, in which area is not quantized in equidistant steps can nevertheless be consistent with Bekenstein's equidistant entropy proposal in a subtle way. For that we perform a detailed analysis of the number of microstates compatible with a given area and show that an observed oscillatory behavior in the entropy-area relation, when properly interpreted yields an entropy that has discrete, equidistant values that are consistent with the Bekenstein framework.
Wavefunction of a black hole and the dynamical origin of entropy
Barvinsky, A O; Zelnikov, A I
1995-01-01
Recently it was proposed to explain the dynamical origin of the entropy of a black hole by identifying its dynamical degrees of freedom with states of quantum fields propagating in the black-hole's interior. The present paper contains the further development of this approach. The no-boundary proposal (analogous to the Hartle-Hawking no-boundary proposal in quantum cosmology) is put forward for defining the wave function of a black hole. This wave function is a functional on the configuration space of physical fields (including the gravitational one) on the three-dimensional space with the Einstein-Rosen bridge topology.It is shown that in the limit of small perturbations on the Kruskal background geometry the no-boundary wave function coincides with the Hartle-Hawking vacuum state. The invariant definition of inside and outside modes is proposed. The density matrix describing the internal state of a black hole is obtained by averaging over the outside modes. This density matrix is used to define the entropy o...
Noncommutativity in near horizon symmetries in gravity
Majhi, Bibhas Ranjan
2017-02-01
We have a new observation that near horizon symmetry generators, corresponding to diffeomorphisms which leave the horizon structure invariant, satisfy noncommutative Heisenberg algebra. The results are valid for any null surfaces (which have Rindler structure in the near null surface limit) and in any spacetime dimensions. Using the Sugawara construction technique the central charge is identified. It is shown that the horizon entropy is consistent with the standard form of the Cardy formula. Therefore we feel that the noncommutative algebra might lead to quantum mechanics of horizon and also can probe into the microscopic description of entropy.
The dynamic of information-driven coordination phenomena: a transfer entropy analysis
Borge-Holthoefer, Javier; Gonçalves, Bruno; González-Bailón, Sandra; Arenas, Alex; Moreno, Yamir; Vespignani, Alessandro
2015-01-01
Data from social media are providing unprecedented opportunities to investigate the processes that rule the dynamics of collective social phenomena. Here, we consider an information theoretical approach to define and measure the temporal and structural signatures typical of collective social events as they arise and gain prominence. We use the symbolic transfer entropy analysis of micro-blogging time series to extract directed networks of influence among geolocalized sub-units in social systems. This methodology captures the emergence of system-level dynamics close to the onset of socially relevant collective phenomena. The framework is validated against a detailed empirical analysis of five case studies. In particular, we identify a change in the characteristic time-scale of the information transfer that flags the onset of information-driven collective phenomena. Furthermore, our approach identifies an order-disorder transition in the directed network of influence between social sub-units. In the absence of ...
Moving Frames of Reference, Relativity and Invariance in Transfer Entropy and Information Dynamics
Directory of Open Access Journals (Sweden)
Joseph T. Lizier
2013-01-01
Full Text Available We present a new interpretation of a local framework for informationdynamics, including the transfer entropy, by defining a moving frame of reference for theobserver of dynamics in lattice systems. This formulation is inspired by the idea ofinvestigating “relativistic” effects on observing the dynamics of information - in particular,we investigate a Galilean transformation of the lattice system data. In applying thisinterpretation to elementary cellular automata, we demonstrate that using a moving frameof reference certainly alters the observed spatiotemporal measurements of informationdynamics, yet still returns meaningful results in this context. We find that, as expected,an observer will report coherent spatiotemporal structures that are moving in their frame asinformation transfer, and structures that are stationary in their frame as information storage.Crucially, the extent to which the shifted frame of reference alters the results dependson whether the shift of frame retains, adds or removes relevant information regarding thesource-destination interaction.
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.)
Vacuum entanglement and black hole entropy of gauge fields
Donnelly, William
2012-11-01
Black holes in general relativity carry an entropy whose value is given by the Bekenstein-Hawking formula, but whose statistical origin remains obscure. Such horizons also possess an entanglement entropy, which has a clear statistical meaning but no a priori relation to the dynamics of gravity. For free minimally-coupled scalar and spinor fields, these two quantities are intimately related: the entanglement entropy is the one-loop correction to the black hole entropy due to renormalization of Newton's constant. For gauge fields, the entanglement entropy and the one-loop correction to the black hole entropy differ. This dissertation addresses two issues concerning the entanglement entropy of gauge fields, and its relation black hole entropy. First, for abelian gauge fields Kabat identified a negative divergent contribution to the black hole entropy that is not part of the entanglement entropy, known as a ``contact term''. We show that the contact term can be attributed to an ambiguous expression for the gauge field's contribution to the Wald entropy. Moreover, in two-dimensional de Sitter space, the contact term arises from an incorrect treatment of zero modes and is therefore unphysical. In a manifestly gauge-invariant reduced phase space quantization of two-dimensional gauge theory, the gauge field contribution to the entropy is positive, finite, and equal to the entanglement entropy. This suggests that the contact term in more than two dimensions may also be unphysical. Second, we consider lattice gauge theory and point out that the Hilbert space corresponding to a region of space includes edge states that transform nontrivially under gauge transformations. By decomposing these edge states in irreducible representations of the gauge group, the entanglement entropy of an arbitrary state is shown to be a sum of a bulk entropy and a boundary entropy associated to the edge states. This entropy formula agrees with the two-dimensional results from the reduced phase
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.
Hawking radiation without black hole entropy
Visser, M
1998-01-01
In this Letter I point out that Hawking radiation is a purely kinematic effect that is generic to Lorentzian geometries. Hawking radiation arises for any test field on any Lorentzian geometry containing an event horizon regardless of whether or not the Lorentzian geometry satisfies the dynamical Einstein equations of general relativity. On the other hand, the classical laws of black hole mechanics are intrinsically linked to the Einstein equations of general relativity (or their perturbative extension into either semiclassical quantum gravity or string-inspired scenarios). In particular, the laws of black hole thermodynamics, and the identification of the entropy of a black hole with its area, are inextricably linked with the dynamical equations satisfied by the Lorentzian geometry: entropy is proportional to area (plus corrections) if and only if the dynamical equations are the Einstein equations (plus corrections). It is quite possible to have Hawking radiation occur in physical situations in which the laws...
Maximum entropy reconstructions of dynamic signaling networks from quantitative proteomics data.
Locasale, Jason W; Wolf-Yadlin, Alejandro
2009-08-26
Advances in mass spectrometry among other technologies have allowed for quantitative, reproducible, proteome-wide measurements of levels of phosphorylation as signals propagate through complex networks in response to external stimuli under different conditions. However, computational approaches to infer elements of the signaling network strictly from the quantitative aspects of proteomics data are not well established. We considered a method using the principle of maximum entropy to infer a network of interacting phosphotyrosine sites from pairwise correlations in a mass spectrometry data set and derive a phosphorylation-dependent interaction network solely from quantitative proteomics data. We first investigated the applicability of this approach by using a simulation of a model biochemical signaling network whose dynamics are governed by a large set of coupled differential equations. We found that in a simulated signaling system, the method detects interactions with significant accuracy. We then analyzed a growth factor mediated signaling network in a human mammary epithelial cell line that we inferred from mass spectrometry data and observe a biologically interpretable, small-world structure of signaling nodes, as well as a catalog of predictions regarding the interactions among previously uncharacterized phosphotyrosine sites. For example, the calculation places a recently identified tumor suppressor pathway through ARHGEF7 and Scribble, in the context of growth factor signaling. Our findings suggest that maximum entropy derived network models are an important tool for interpreting quantitative proteomics data.
Generalized R\\'enyi Entropy and Structure Detection of Complex Dynamical Systems
Steinbrecher, György
2015-01-01
We study the problem of detecting the structure of a complex dynamical system described by a set of deterministic differential equation that contains a Hamiltonian subsystem, without any information on the explicit form of evolution laws. We suppose that initial conditions are random and the initial conditions of the Hamiltonian subsystem are independent from the initial conditions of the rest of the system. The single numerical information is the probability density function of the system at one or several, finite number of time instants. In the framework of the formalism of the generalized R\\'{e}nyi entropy we find necessary and sufficient conditions that the back reaction of the Hamiltonian subsystem to the rest of the system is negligible.The results can be easily generalized to the case of general, measure preserving subsystem.
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.
Modeling the Mass Action Dynamics of Metabolism with Fluctuation Theorems and Maximum Entropy
Cannon, William; Thomas, Dennis; Baxter, Douglas; Zucker, Jeremy; Goh, Garrett
The laws of thermodynamics dictate the behavior of biotic and abiotic systems. Simulation methods based on statistical thermodynamics can provide a fundamental understanding of how biological systems function and are coupled to their environment. While mass action kinetic simulations are based on solving ordinary differential equations using rate parameters, analogous thermodynamic simulations of mass action dynamics are based on modeling states using chemical potentials. The latter have the advantage that standard free energies of formation/reaction and metabolite levels are much easier to determine than rate parameters, allowing one to model across a large range of scales. Bridging theory and experiment, statistical thermodynamics simulations allow us to both predict activities of metabolites and enzymes and use experimental measurements of metabolites and proteins as input data. Even if metabolite levels are not available experimentally, it is shown that a maximum entropy assumption is quite reasonable and in many cases results in both the most energetically efficient process and the highest material flux.
Scalar-Tensor Theory of Gravity and Generalized Second Law of Thermodynamics on the Event Horizon
Mazumder, Nairwita
2010-01-01
In blackhole physics, the second law of thermodynamics is generally valid whether the blackhole is a static or a non-static one. Considering the universe as a thermodynamical system the second law of blackhole dynamics extends to the non-negativity of the sum of the entropy of the matter and the horizon, known as generalized second law of thermodynamics(GSLT). Here, we have assumed the universe to be bounded by the event-horizon or filled with perfect fluid and holographic dark energy in two cases. Thus considering entropy to be an arbitrary function of the area of the event-horizon, we have tried to find the conditions and the restrictions over the scalar field and equation of state for the validity of the GSLT and both in quintessence-era and in phantom-era in scalar tensor theory.
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.
Gao, Wei; Feng, Shi-Dong; Zhang, Shi-Liang; Qi, Li; Liu, Ri-Ping
2015-12-01
Molecular dynamics simulation is used to investigate the relationship between Voronoi entropy and viscosity for rapid solidification processing of Zr36Cu64 binary alloy melt. The simulation results at different temperatures, cooling rates, and pressures, show that Voronoi entropy is able to accurately describe the relationship of the transition between the cluster structure and the viscosity of Zr36Cu64 binary alloy melt through Voronoi polyhedron analysis. That is, the higher the degree of order of the microstructure, the lower the Voronoi entropy is and the higher the viscosity is. The simulation provides an important reference for studying metallic glass with high glass-forming ability. Project supported by the National Basic Research Program of China (Grant No. 2013CB733000) and the National Natural Science Foundation of China (Grant Nos. 51271161 and 51271162).
Horizon Thermodynamics from Einstein's Equation of State
Hansen, Devin; Mann, Robert
2016-01-01
By regarding the Einstein equations as equation(s) of state, we demonstrate that a full cohomogeneity horizon first law can be derived in horizon thermodynamics. In this approach both the entropy and the free energy are derived concepts, while the standard (degenerate) horizon first law is recovered by a Legendre projection from the more general one we derive. These results readily generalize to higher curvature gravities and establish a way of how to formulate consistent black hole thermodynamics without conserved charges.
The dynamics of information-driven coordination phenomena: A transfer entropy analysis.
Borge-Holthoefer, Javier; Perra, Nicola; Gonçalves, Bruno; González-Bailón, Sandra; Arenas, Alex; Moreno, Yamir; Vespignani, Alessandro
2016-04-01
Data from social media provide unprecedented opportunities to investigate the processes that govern the dynamics of collective social phenomena. We consider an information theoretical approach to define and measure the temporal and structural signatures typical of collective social events as they arise and gain prominence. We use the symbolic transfer entropy analysis of microblogging time series to extract directed networks of influence among geolocalized subunits in social systems. This methodology captures the emergence of system-level dynamics close to the onset of socially relevant collective phenomena. The framework is validated against a detailed empirical analysis of five case studies. In particular, we identify a change in the characteristic time scale of the information transfer that flags the onset of information-driven collective phenomena. Furthermore, our approach identifies an order-disorder transition in the directed network of influence between social subunits. In the absence of clear exogenous driving, social collective phenomena can be represented as endogenously driven structural transitions of the information transfer network. This study provides results that can help define models and predictive algorithms for the analysis of societal events based on open source data.
Adaptive dynamics via Hamilton-Jacobi approach and entropy methods for a juvenile-adult model.
Carrillo, José Antonio; Cuadrado, Sílvia; Perthame, Benoît
2007-01-01
We consider a nonlinear system describing a juvenile-adult population undergoing small mutations. We analyze two aspects: from a mathematical point of view, we use an entropy method to prove that the population neither goes extinct nor blows-up; from an adaptive evolution point of view, we consider small mutations on a long time scale and study how a monomorphic or a dimorphic initial population evolves towards an Evolutionarily Stable State. Our method relies on an asymptotic analysis based on a constrained Hamilton-Jacobi equation. It allows to recover earlier predictions in Calsina and Cuadrado [A. Calsina, S. Cuadrado, Small mutation rate and evolutionarily stable strategies in infinite dimensional adaptive dynamics, J. Math. Biol. 48 (2004) 135; A. Calsina, S. Cuadrado, Stationary solutions of a selection mutation model: the pure mutation case, Math. Mod. Meth. Appl. Sci. 15(7) (2005) 1091.] that we also assert by direct numerical simulation. One of the interests here is to show that the Hamilton-Jacobi approach initiated in Diekmann et al. [O. Diekmann, P.-E. Jabin, S. Mischler, B. Perthame, The dynamics of adaptation: an illuminating example and a Hamilton-Jacobi approach, Theor. Popul. Biol. 67(4) (2005) 257.] extends to populations described by systems.
Directory of Open Access Journals (Sweden)
Timothy R Lezon
2010-06-01
Full Text Available Comparison of elastic network model predictions with experimental data has provided important insights on the dominant role of the network of inter-residue contacts in defining the global dynamics of proteins. Most of these studies have focused on interpreting the mean-square fluctuations of residues, or deriving the most collective, or softest, modes of motions that are known to be insensitive to structural and energetic details. However, with increasing structural data, we are in a position to perform a more critical assessment of the structure-dynamics relations in proteins, and gain a deeper understanding of the major determinants of not only the mean-square fluctuations and lowest frequency modes, but the covariance or the cross-correlations between residue fluctuations and the shapes of higher modes. A systematic study of a large set of NMR-determined proteins is analyzed using a novel method based on entropy maximization to demonstrate that the next level of refinement in the elastic network model description of proteins ought to take into consideration properties such as contact order (or sequential separation between contacting residues and the secondary structure types of the interacting residues, whereas the types of amino acids do not play a critical role. Most importantly, an optimal description of observed cross-correlations requires the inclusion of destabilizing, as opposed to exclusively stabilizing, interactions, stipulating the functional significance of local frustration in imparting native-like dynamics. This study provides us with a deeper understanding of the structural basis of experimentally observed behavior, and opens the way to the development of more accurate models for exploring protein dynamics.
Horizon thermodynamics from Einstein's equation of state
Hansen, Devin; Kubizňák, David; Mann, Robert B.
2017-08-01
By regarding the Einstein equations as equation(s) of state, we demonstrate that a full cohomogeneity horizon first law can be derived in horizon thermodynamics. In this approach both the entropy and the free energy are derived concepts, while the standard (degenerate) horizon first law is recovered by a Legendre projection from the more general one we derive. These results readily generalize to higher curvature gravities where they naturally reproduce a formula for the entropy without introducing Noether charges. Our results thus establish a way of how to formulate consistent black hole thermodynamics without conserved charges.
Entropy of Reissner-Nordstr\\"om-de Sitter black hole
Zhang, Li-Chun; Ma, Meng-Sen
2016-01-01
Based on the consideration that the black hole horizon and the cosmological horizon of Reissner-Nordstr\\"om 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 tends to coincide.
Ma, Haibo
2012-06-07
We perform molecular dynamics simulations of supercritical water (SCW) with a wide range of densities along a near critical isotherm using the simple point charge extended (SPC/E) pair potential in order to study the entropy and the solvation shell structure around a central water molecule. It is shown that both the translational and orientational two-particle correlation entropy terms can serve as the metrics of the translational-orientational structural orders in water and it is revealed that the translational structural order is very sensitive to the density variation in the gas-like and liquid-like region, while the orientational structural order is much more dependent upon compression in the medium-density SCW region. The comparison of the magnitudes of the full thermodynamic excess entropy and two-particle correlation entropy confirms the recent findings that the many-body terms other than two-body ones also present significant and non-neglectable contributions to the full excess entropy for the highly anomalous fluids like water. The analysis of entropy terms as a function of intermolecular distance and the orientational distribution functions as well as the three-dimensional spatial distribution functions indicate that the structural order occurs only in a much more diffused first solvation shell due to the elongated hydrogen bonds under supercritical conditions. It is revealed that no obvious second or higher neighbor shells occur in SCW, in contrast with the feature of normal liquid water that the anomalous decrease of translational order upon compression occurs mainly in the second shell.
Banerjee, Atreyee; Nandi, Manoj Kumar; Sastry, Srikanth; Bhattacharyya, Sarika Maitra
2016-07-01
In this paper, we present a study of supercooled liquids interacting with the Lennard Jones potential and the corresponding purely repulsive (Weeks-Chandler-Andersen) potential, over a range of densities and temperatures, in order to understand the origin of their different dynamics in spite of their structures being similar. Using the configurational entropy as the thermodynamic marker via the Adam Gibbs relation, we show that the difference in the dynamics of these two systems at low temperatures can be explained from thermodynamics. At higher densities both the thermodynamical and dynamical difference between these model systems decrease, which is quantitatively demonstrated in this paper by calculating different parameters. The study also reveals the origin of the difference in pair entropy despite the similarity in the structure. Although the maximum difference in structure is obtained in the partial radial distribution function of the B type of particles, the rdf of AA pairs and AB pairs gives rise to the differences in the entropy and dynamics. This work supports the observation made in an earlier study [A. Banerjee et al., Phys. Rev. Lett. 113, 225701 (2014)] and shows that they are generic in nature, independent of density.
Formation dynamics of subsurface hydrocarbon intrusions following the Deepwater Horizon blowout
Socolofsky, Scott A.; Adams, E. Eric; Sherwood, Christopher R.
2011-01-01
Hydrocarbons released following the Deepwater Horizon (DH) blowout were found in deep, subsurface horizontal intrusions, yet there has been little discussion about how these intrusions formed. We have combined measured (or estimated) observations from the DH release with empirical relationships developed from previous lab experiments to identify the mechanisms responsible for intrusion formation and to characterize the DH plume. Results indicate that the intrusions originate from a stratification-dominated multiphase plume characterized by multiple subsurface intrusions containing dissolved gas and oil along with small droplets of liquid oil. Unlike earlier lab measurements, where the potential density in ambient water decreased linearly with elevation, at the DH site it varied quadratically. We have modified our method for estimating intrusion elevation under these conditions and the resulting estimates agree with observations that the majority of the hydrocarbons were found between 800 and 1200 m.
Callaway, John C.; Cahoon, Donald R.; Lynch, James C.
2014-01-01
Tidal wetlands are highly sensitive to processes that affect their elevation relative to sea level. The surface elevation table–marker horizon (SET–MH) method has been used to successfully measure these processes, including sediment accretion, changes in relative elevation, and shallow soil processes (subsidence and expansion due to root production). The SET–MH method is capable of measuring changes at very high resolution (±millimeters) and has been used worldwide both in natural wetlands and under experimental conditions. Marker horizons are typically deployed using feldspar over 50- by 50-cm plots, with replicate plots at each sampling location. Plots are sampled using a liquid N2 cryocorer that freezes a small sample, allowing the handling and measurement of soft and easily compressed soils with minimal compaction. The SET instrument is a portable device that is attached to a permanent benchmark to make high-precision measurements of wetland surface elevation. The SET instrument has evolved substantially in recent decades, and the current rod SET (RSET) is widely used. For the RSET, a 15-mm-diameter stainless steel rod is pounded into the ground until substantial resistance is achieved to establish a benchmark. The SET instrument is attached to the benchmark and leveled such that it reoccupies the same reference plane in space, and pins lowered from the instrument repeatedly measure the same point on the soil surface. Changes in the height of the lowered pins reflect changes in the soil surface. Permanent or temporary platforms provide access to SET and MH locations without disturbing the wetland surface.
Cavalli, Andrea; Camilloni, Carlo; Vendruscolo, Michele
2013-03-07
In order to characterise the dynamics of proteins, a well-established method is to incorporate experimental parameters as replica-averaged structural restraints into molecular dynamics simulations. Here, we justify this approach in the case of interproton distance information provided by nuclear Overhauser effects by showing that it generates ensembles of conformations according to the maximum entropy principle. These results indicate that the use of replica-averaged structural restraints in molecular dynamics simulations, given a force field and a set of experimental data, can provide an accurate approximation of the unknown Boltzmann distribution of a system.
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.
Computational design of hepatitis C vaccines using maximum entropy models and population dynamics
Hart, Gregory; Ferguson, Andrew
Hepatitis C virus (HCV) afflicts 170 million people and kills 350,000 annually. Vaccination offers the most realistic and cost effective hope of controlling this epidemic. Despite 20 years of research, no vaccine is available. A major obstacle is the virus' extreme genetic variability and rapid mutational escape from immune pressure. Improvements in the vaccine design process are urgently needed. Coupling data mining with spin glass models and maximum entropy inference, we have developed a computational approach to translate sequence databases into empirical fitness landscapes. These landscapes explicitly connect viral genotype to phenotypic fitness and reveal vulnerable targets that can be exploited to rationally design immunogens. Viewing these landscapes as the mutational ''playing field'' over which the virus is constrained to evolve, we have integrated them with agent-based models of the viral mutational and host immune response dynamics, establishing a data-driven immune simulator of HCV infection. We have employed this simulator to perform in silico screening of HCV immunogens. By systematically identifying a small number of promising vaccine candidates, these models can accelerate the search for a vaccine by massively reducing the experimental search space.
A dynamical point of view of Quantum Information: entropy and pressure
Baraviera, A; Lopes, A O; Cunha, M Terra
2011-01-01
Quantum Information is a new area of research which has been growing rapidly since last decade. This topic is very close to potential applications to the so called Quantum Computer. In our point of view it makes sense to develop a more "dynamical point of view" of this theory. We want to consider the concepts of entropy and pressure for "stationary systems" acting on density matrices which generalize the usual ones in Ergodic Theory (in the sense of the Thermodynamic Formalism of R. Bowen, Y. Sinai and D. Ruelle). We consider the operator $\\mathcal{L}$ acting on density matrices $\\rho\\in \\mathcal{M}_N$ over a finite $N$-dimensional complex Hilbert space $\\mathcal{L}(\\rho):=\\sum_{i=1}^k tr(W_i\\rho W_i^*)V_i\\rho V_i^*,$ where $W_i$ and $V_i$, $i=1,2,...k$ are operators in this Hilbert space. $\\mathcal{L}$ is not a linear operator. In some sense this operator is a version of an Iterated Function System (IFS). Namely, the $V_i\\,(.)\\,V_i^*=:F_i(.)$, $i=1,2,...,k$, play the role of the inverse branches (acting on t...
Zunino, Luciano; Bariviera, Aurelio F.; Guercio, M. Belén; Martinez, Lisana B.; Rosso, Osvaldo A.
2016-08-01
In this paper the permutation min-entropy has been implemented to unveil the presence of temporal structures in the daily values of European corporate bond indices from April 2001 to August 2015. More precisely, the informational efficiency evolution of the prices of fifteen sectorial indices has been carefully studied by estimating this information-theory-derived symbolic tool over a sliding time window. Such a dynamical analysis makes possible to obtain relevant conclusions about the effect that the 2008 credit crisis has had on the different European corporate bond sectors. It is found that the informational efficiency of some sectors, namely banks, financial services, insurance, and basic resources, has been strongly reduced due to the financial crisis whereas another set of sectors, integrated by chemicals, automobiles, media, energy, construction, industrial goods & services, technology, and telecommunications has only suffered a transitory loss of efficiency. Last but not least, the food & beverage, healthcare, and utilities sectors show a behavior close to a random walk practically along all the period of analysis, confirming a remarkable immunity against the 2008 financial crisis.
Wang, Fei-Yue; Jin, Ning; Liu, Derong; Wei, Qinglai
2011-01-01
In this paper, we study the finite-horizon optimal control problem for discrete-time nonlinear systems using the adaptive dynamic programming (ADP) approach. The idea is to use an iterative ADP algorithm to obtain the optimal control law which makes the performance index function close to the greatest lower bound of all performance indices within an ε-error bound. The optimal number of control steps can also be obtained by the proposed ADP algorithms. A convergence analysis of the proposed ADP algorithms in terms of performance index function and control policy is made. In order to facilitate the implementation of the iterative ADP algorithms, neural networks are used for approximating the performance index function, computing the optimal control policy, and modeling the nonlinear system. Finally, two simulation examples are employed to illustrate the applicability of the proposed method.
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.
Zhou, C L; Fang, D Q; Zhang, G Q
2013-01-01
Thermodynamic and transport properties of nuclear fireball created in the central region of heavy-ion collisions below 200 MeV/nucleon are investigated within the isospin-dependent quantum molecular dynamic (IQMD) model. These properties include time evolutions of the density, temperature, chemical potential, entropy density ($s$) and shear viscosity ($\\eta$) as well as density and temperature dependencies of the ratio of shear viscosity over entropy density ($\\eta/s$) etc. Based on the shear viscosity parametrization developed by Danilewicz and entropy density which is obtained by a generalized hot Thomas Fermi formalism, the ratio of shear viscosity over entropy density is calculated in the whole collision process as well as in the freeze-out stage. With the collision goes on, a transient minimal $\\eta/s$ with the value around 5/$4\\pi$ occurs in the largest compression stage. While, the relationship of $\\eta/s$ to tempertaure ($T$) in the freeze-out stage displays a local minimum which is about 9-10 times $...
Institute of Scientific and Technical Information of China (English)
ZHANG Hong-lie; ZHANG Guo-yin; YAO Ai-hong
2010-01-01
This paper presents an algorithm that combines the chaos optimization algorithm with the maximum entropy(COA-ME)by using entropy model based on chaos algorithm,in which the maximum entropy is used as the second method of searching the excellent solution.The search direction is improved by chaos optimization algorithm and realizes the selective acceptance of wrong solution.The experimental result shows that the presented algorithm can be used in the partitioning of hardware/software of reconfigurable system.It effectively reduces the local extremum problem,and search speed as well as performance of partitioning is improved.
Entanglement Entropy of Black Holes
Solodukhin, Sergey N.
2011-10-01
The entanglement entropy is a fundamental quantity, which characterizes the correlations between sub-systems in a larger quantum-mechanical system. For two sub-systems separated by a surface the entanglement entropy is proportional to the area of the surface and depends on the UV cutoff, which regulates the short-distance correlations. The geometrical nature of entanglement-entropy calculation is particularly intriguing when applied to black holes when the entangling surface is the black-hole horizon. I review a variety of aspects of this calculation: the useful mathematical tools such as the geometry of spaces with conical singularities and the heat kernel method, the UV divergences in the entropy and their renormalization, the logarithmic terms in the entanglement entropy in four and six dimensions and their relation to the conformal anomalies. The focus in the review is on the systematic use of the conical singularity method. The relations to other known approaches such as 't Hooft's brick-wall model and the Euclidean path integral in the optical metric are discussed in detail. The puzzling behavior of the entanglement entropy due to fields, which non-minimally couple to gravity, is emphasized. The holographic description of the entanglement entropy of the blackhole horizon is illustrated on the two- and four-dimensional examples. Finally, I examine the possibility to interpret the Bekenstein-Hawking entropy entirely as the entanglement entropy.
Entanglement Entropy of Black Holes
Directory of Open Access Journals (Sweden)
Sergey N. Solodukhin
2011-10-01
Full Text Available The entanglement entropy is a fundamental quantity, which characterizes the correlations between sub-systems in a larger quantum-mechanical system. For two sub-systems separated by a surface the entanglement entropy is proportional to the area of the surface and depends on the UV cutoff, which regulates the short-distance correlations. The geometrical nature of entanglement-entropy calculation is particularly intriguing when applied to black holes when the entangling surface is the black-hole horizon. I review a variety of aspects of this calculation: the useful mathematical tools such as the geometry of spaces with conical singularities and the heat kernel method, the UV divergences in the entropy and their renormalization, the logarithmic terms in the entanglement entropy in four and six dimensions and their relation to the conformal anomalies. The focus in the review is on the systematic use of the conical singularity method. The relations to other known approaches such as ’t Hooft’s brick-wall model and the Euclidean path integral in the optical metric are discussed in detail. The puzzling behavior of the entanglement entropy due to fields, which non-minimally couple to gravity, is emphasized. The holographic description of the entanglement entropy of the black-hole horizon is illustrated on the two- and four-dimensional examples. Finally, I examine the possibility to interpret the Bekenstein-Hawking entropy entirely as the entanglement entropy.
Rosser, J. Barkley
2016-12-01
Entropy is a central concept of statistical mechanics, which is the main branch of physics that underlies econophysics, the application of physics concepts to understand economic phenomena. It enters into econophysics both in an ontological way through the Second Law of Thermodynamics as this drives the world economy from its ecological foundations as solar energy passes through food chains in dissipative process of entropy rising and production fundamentally involving the replacement of lower entropy energy states with higher entropy ones. In contrast the mathematics of entropy as appearing in information theory becomes the basis for modeling financial market dynamics as well as income and wealth distribution dynamics. It also provides the basis for an alternative view of stochastic price equilibria in economics, as well providing a crucial link between econophysics and sociophysics, keeping in mind the essential unity of the various concepts of entropy.
Black-hole horizons as probes of black-hole dynamics I: post-merger recoil in head-on collisions
Jaramillo, José Luis; Moesta, Philipp; Rezzolla, Luciano
2011-01-01
The understanding of strong-field dynamics near black-hole horizons is a long-standing and challenging problem in general relativity. Recent advances in numerical relativity and in the geometric characterization of black-hole horizons open new avenues into the problem. In this first paper in a series of two, we focus on the analysis of the recoil occurring in the merger of binary black holes, extending the analysis initiated in [1] with Robinson-Trautman spacetimes. More specifically, we probe spacetime dynamics through the correlation of quantities defined at the black-hole horizon and at null infinity. The geometry of these hypersurfaces responds to bulk gravitational fields acting as test screens in a scattering perspective of spacetime dynamics. Within a 3+1 approach we build an effective-curvature vector from the intrinsic geometry of dynamical-horizon sections and correlate its evolution with the flux of Bondi linear momentum at large distances. We employ this setup to study numerically the head-on coll...
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.
Directory of Open Access Journals (Sweden)
Yu. P. Machekhin
2015-01-01
Full Text Available The article considers the issue of measurement of dynamic variables of open nonlinear dynamical systems. Most of real physical and biological systems in the surrounding world are the nonlinear dynamic systems. The spatial, temporal and spatio-temporal structures are formed in such systems because of dissipation. The collective effects that associated with the processes of self-organization and evolution are possible there too. The objective of this research is a compilation of the Shannon entropy measurement equations for case of nonlinear dynamical systems. It’s proposed to use the interval mathematics methods for this. It is shown that the measurement and measurement results analysis for variables with complex dynamics, as a rule, cannot be described by classical metrological approaches, that metrological documents, for example GUM, contain. The reason of this situation is the mismatch between the classical mathematical and physical approaches on the one hand and processes that occur in real dynamic systems on the other hand. For measurement of nonlinear dynamical systems variables the special measurement model and measurement results analysis model are created. They are based on Open systems theory, Dynamical chaos theory and Information theory. It’s proposed to use the fractal, entropic and temporal scales as tools for evaluation of a systems state. As a result of research the Shannon entropy measurement equations, based on interval representations of measurement results. are created, like for an individual dynamic variable as for nonlinear dynamic system. It is shown that the measurement equations, based on interval mathematics methods, contains the exact solutions and allows take into account full uncertainty. The new results will complement the measurement model and the measurement results analysis model for case of nonlinear dynamic systems.
Cheng, Hao-Chung; Hsieh, Min-Hsiu; Tomamichel, Marco
2017-09-01
In this work, we extend the theory of quantum Markov processes on a single quantum state to a broader theory that covers Markovian evolution of an ensemble of quantum states, which generalizes Lindblad's formulation of quantum dynamical semigroups. Our results establish the equivalence between an exponential decrease of the matrix Φ -entropies and the Φ -Sobolev inequalities, which allows us to characterize the dynamical evolution of a quantum ensemble to its equilibrium. In particular, we study the convergence rates of two special semigroups, namely, the depolarizing channel and the phase-damping channel. In the former, since there exists a unique equilibrium state, we show that the matrix Φ -entropy of the resulting quantum ensemble decays exponentially as time goes on. Consequently, we obtain a stronger notion of monotonicity of the Holevo quantity—the Holevo quantity of the quantum ensemble decays exponentially in time and the convergence rate is determined by the modified log-Sobolev inequalities. However, in the latter, the matrix Φ -entropy of the quantum ensemble that undergoes the phase-damping Markovian evolution generally will not decay exponentially. There is no classical analogy for these different equilibrium situations. Finally, we also study a statistical mixing of Markov semigroups on matrix-valued functions. We can explicitly calculate the convergence rate of a Markovian jump process defined on Boolean hypercubes and provide upper bounds to the mixing time.
Wild, Birgit; Schnecker, Jörg; Knoltsch, Anna; Takriti, Mounir; Mooshammer, Maria; Gentsch, Norman; Mikutta, Robert; Alves, Ricardo J. Eloy; Gittel, Antje; Lashchinskiy, Nikolay; Richter, Andreas
2015-05-01
Soil N availability is constrained by the breakdown of N-containing polymers such as proteins to oligopeptides and amino acids that can be taken up by plants and microorganisms. Excess N is released from microbial cells as ammonium (N mineralization), which in turn can serve as substrate for nitrification. According to stoichiometric theory, N mineralization and nitrification are expected to increase in relation to protein depolymerization with decreasing N limitation, and thus from higher to lower latitudes and from topsoils to subsoils. To test these hypotheses, we compared gross rates of protein depolymerization, N mineralization and nitrification (determined using 15N pool dilution assays) in organic topsoil, mineral topsoil, and mineral subsoil of seven ecosystems along a latitudinal transect in western Siberia, from tundra (67°N) to steppe (54°N). The investigated ecosystems differed strongly in N transformation rates, with highest protein depolymerization and N mineralization rates in middle and southern taiga. All N transformation rates decreased with soil depth following the decrease in organic matter content. Related to protein depolymerization, N mineralization and nitrification were significantly higher in mineral than in organic horizons, supporting a decrease in microbial N limitation with depth. In contrast, we did not find indications for a decrease in microbial N limitation from arctic to temperate ecosystems along the transect. Our findings thus challenge the perception of ubiquitous N limitation at high latitudes, but suggest a transition from N to C limitation of microorganisms with soil depth, even in high-latitude systems such as tundra and boreal forest.
Ansari, Mohammad H
2016-01-01
A common approach to evaluate entropy in quantum systems is to solve a master-Bloch equation to determine density matrix and substitute it in entropy definition. However, this method has been recently understood to lack many energy correlators. The new correlators make entropy evaluation to be different from the substitution method described above. The reason for such complexity lies in the nonlinearity of entropy. In this paper we present a pedagogical approach to evaluate the new correlators and explain their contribution in the analysis. We show that the inherent nonlinearity in entropy makes the second law of thermodynamics to carry new terms associated to the new correlators. Our results show important new remarks on quantum black holes. Our formalism reveals that the notion of degeneracy of states at the event horizon makes an indispensable deviation from black hole entropy in the leading order.
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.
Institute of Scientific and Technical Information of China (English)
Zhang Min-Min; Wang Can-Jun; Mei Dong-Cheng
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 UB(t) of the time derivative of the information entropy.The results show that there is a critical value of T (delay time),and UB(t) presents opposite behaviours on difference sides of the critical value.For the case of the weak additive noise,T can induce a reentrance transition.Delay time T also causes a reversal behaviour in UB(t)-λ plot,where λ denotes the decree of the correlation between the two noises.
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.
Entropy of Quantum Black Holes
Directory of Open Access Journals (Sweden)
Romesh K. Kaul
2012-02-01
Full Text Available In the Loop Quantum Gravity, black holes (or even more general Isolated Horizons are described by a SU(2 Chern-Simons theory. There is an equivalent formulation of the horizon degrees of freedom in terms of a U(1 gauge theory which is just a gauged fixed version of the SU(2 theory. These developments will be surveyed here. Quantum theory based on either formulation can be used to count the horizon micro-states associated with quantum geometry fluctuations and from this the micro-canonical entropy can be obtained. We shall review the computation in SU(2 formulation. Leading term in the entropy is proportional to horizon area with a coefficient depending on the Barbero-Immirzi parameter which is fixed by matching this result with the Bekenstein-Hawking formula. Remarkably there are corrections beyond the area term, the leading one is logarithm of the horizon area with a definite coefficient −3/2, a result which is more than a decade old now. How the same results are obtained in the equivalent U(1 framework will also be indicated. Over years, this entropy formula has also been arrived at from a variety of other perspectives. In particular, entropy of BTZ black holes in three dimensional gravity exhibits the same logarithmic correction. Even in the String Theory, many black hole models are known to possess such properties. This suggests a possible universal nature of this logarithmic correction.
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.
Kolmogorov-Sinai and Bekenstein-Hawking entropies
Ropotenko, K
2007-01-01
It is shown that instability of stringy matter near the event horizon of a black hole (the spreading effect) can be characterized by the Lyapunov exponents. For a homogeneous and isotropic horizon the (average) Lyapunov exponent coincides with the Kolmogorov-Sinai entropy of stringy matter. Due to identity of phase space volume of the string with the area of the horizon the relation between the Kolmogorov-Sinai and Bekenstein-Hawking entropies is established. The Kolmogorov-Sinai entropy measures the rate at which information about the string state is lost as the string spreads over the horizon.
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.
A Dynamic Programming Approach to Finite-horizon Coherent Quantum LQG Control
Vladimirov, Igor G
2011-01-01
The paper considers the coherent quantum Linear Quadratic Gaussian (CQLQG) control problem for time-varying quantum plants governed by linear quantum stochastic differential equations over a bounded time interval. A controller is sought among quantum linear systems satisfying physical realizability (PR) conditions. The latter describe the dynamic equivalence of the system to an open quantum harmonic oscillator and relate its state-space matrices to the free Hamiltonian, coupling and scattering operators of the oscillator. Using the Hamiltonian parameterization of PR controllers, the CQLQG problem is recast into an optimal control problem for a deterministic system governed by a differential Lyapunov equation. The state of this subsidiary system is the symmetric part of the quantum covariance matrix of the plant-controller state vector. The resulting covariance control problem is treated using dynamic programming and Pontryagin's minimum principle. The associated Hamilton-Jacobi-Bellman equation for the minimu...
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.
Pascal, Tod A; Lin, Shiang-Tai; Goddard, William A
2011-01-07
We validate here the Two-Phase Thermodynamics (2PT) method for calculating the standard molar entropies and heat capacities of common liquids. In 2PT, the thermodynamics of the system is related to the total density of states (DoS), obtained from the Fourier Transform of the velocity autocorrelation function. For liquids this DoS is partitioned into a diffusional component modeled as diffusion of a hard sphere gas plus a solid component for which the DoS(υ) → 0 as υ→ 0 as for a Debye solid. Thermodynamic observables are obtained by integrating the DoS with the appropriate weighting functions. In the 2PT method, two parameters are extracted from the DoS self-consistently to describe diffusional contributions: the fraction of diffusional modes, f, and DoS(0). This allows 2PT to be applied consistently and without re-parameterization to simulations of arbitrary liquids. We find that the absolute entropy of the liquid can be determined accurately from a single short MD trajectory (20 ps) after the system is equilibrated, making it orders of magnitude more efficient than commonly used perturbation and umbrella sampling methods. Here, we present the predicted standard molar entropies for fifteen common solvents evaluated from molecular dynamics simulations using the AMBER, GAFF, OPLS AA/L and Dreiding II forcefields. Overall, we find that all forcefields lead to good agreement with experimental and previous theoretical values for the entropy and very good agreement in the heat capacities. These results validate 2PT as a robust and efficient method for evaluating the thermodynamics of liquid phase systems. Indeed 2PT might provide a practical scheme to improve the intermolecular terms in forcefields by comparing directly to thermodynamic properties.
Bernhard, Anne E; Sheffer, Roberta; Giblin, Anne E; Marton, John M; Roberts, Brian J
2016-01-01
The recent oil spill in the Gulf of Mexico had significant effects on microbial communities in the Gulf, but impacts on nitrifying communities in adjacent salt marshes have not been investigated. We studied persistent effects of oil on ammonia-oxidizing archaeal (AOA) and bacterial (AOB) communities and their relationship to nitrification rates and soil properties in Louisiana marshes impacted by the Deepwater Horizon oil spill. Soils were collected at oiled and unoiled sites from Louisiana coastal marshes in July 2012, 2 years after the spill, and analyzed for community differences based on ammonia monooxygenase genes (amoA). Terminal Restriction Fragment Polymorphism and DNA sequence analyses revealed significantly different AOA and AOB communities between the three regions, but few differences were found between oiled and unoiled sites. Community composition of nitrifiers was best explained by differences in soil moisture and nitrogen content. Despite the lack of significant oil effects on overall community composition, we identified differences in correlations of individual populations with potential nitrification rates between oiled and unoiled sites that help explain previously published correlation patterns. Our results suggest that exposure to oil, even 2 years post-spill, led to subtle changes in population dynamics. How, or if, these changes may impact ecosystem function in the marshes, however, remains uncertain.
Madkour, Tarek M; Salem, Sarah A; Miller, Stephen A
2013-04-28
To fully understand the thermodynamic nature of polymer blends and accurately predict their miscibility on a microscopic level, a hybrid model employing both statistical mechanics and molecular dynamics techniques was developed to effectively predict the total free energy of mixing. The statistical mechanics principles were used to derive an expression for the deformational entropy of the chains in the polymeric blends that could be evaluated from molecular dynamics trajectories. Evaluation of the entropy loss due to the deformation of the polymer chains in the case of coiling as a result of the repulsive interactions between the blend components or in the case of swelling due to the attractive interactions between the polymeric segments predicted a negative value for the deformational entropy resulting in a decrease in the overall entropy change upon mixing. Molecular dynamics methods were then used to evaluate the enthalpy of mixing, entropy of mixing, the loss in entropy due to the deformation of the polymeric chains upon mixing and the total free energy change for a series of polar and non-polar, poly(glycolic acid), PGA, polymer blends.
Black hole entropy in loop quantum gravity
Agulló, Iván; Barbero G, J. Fernando; Borja, E. F.; Díaz-Polo, Jacobo; Villaseñor, Eduardo J. S.
2012-05-01
We discuss the recent progress on black hole entropy in loop quantum gravity, focusing in particular on the recently discovered discretization effect for microscopic black holes. Powerful analytical techniques have been developed to perform the exact computation of entropy. A statistical analysis of the structures responsible for this effect shows its progressive damping and eventual disappearance as one increases the considered horizon area.
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.
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
Directory of Open Access Journals (Sweden)
Kai Ziervogel
Full Text Available The Deepwater Horizon oil spill triggered a complex cascade of microbial responses that reshaped the dynamics of heterotrophic carbon degradation and the turnover of dissolved organic carbon (DOC in oil contaminated waters. Our results from 21-day laboratory incubations in rotating glass bottles (roller bottles demonstrate that microbial dynamics and carbon flux in oil-contaminated surface water sampled near the spill site two weeks after the onset of the blowout were greatly affected by activities of microbes associated with macroscopic oil aggregates. Roller bottles with oil-amended water showed rapid formation of oil aggregates that were similar in size and appearance compared to oil aggregates observed in surface waters near the spill site. Oil aggregates that formed in roller bottles were densely colonized by heterotrophic bacteria, exhibiting high rates of enzymatic activity (lipase hydrolysis indicative of oil degradation. Ambient waters surrounding aggregates also showed enhanced microbial activities not directly associated with primary oil-degradation (β-glucosidase; peptidase, as well as a twofold increase in DOC. Concurrent changes in fluorescence properties of colored dissolved organic matter (CDOM suggest an increase in oil-derived, aromatic hydrocarbons in the DOC pool. Thus our data indicate that oil aggregates mediate, by two distinct mechanisms, the transfer of hydrocarbons to the deep sea: a microbially-derived flux of oil-derived DOC from sinking oil aggregates into the ambient water column, and rapid sedimentation of the oil aggregates themselves, serving as vehicles for oily particulate matter as well as oil aggregate-associated microbial communities.
A note on entanglement entropy and quantum geometry
Bodendorfer, Norbert
2014-01-01
It has been argued that the entropy which one is computing 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 generalising these computations to arbitrary spacetime dimensions D+1>2 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.
Multifractals and Entropy Computing
Slomczynski, W; Zyczkowski, K; Slomczynski, Wojciech; Kwapien, Jaroslaw; Zyczkowski, Karol
1998-01-01
We discuss the properties of invariant measures corresponding to iterated function systems (IFSs) with place-dependent probabilities and compute their shown that with certain dynamical systems one can associate the corresponding IFSs in such a way that their generalized entropies are equal. We use this method to compute entropy of some classical and quantum dynamical systems. Numerical techniques are based on integration over fractal measures.
Towards thermodynamics of universal horizons in Einstein-æther theory.
Berglund, Per; Bhattacharyya, Jishnu; Mattingly, David
2013-02-15
Holography grew out of black hole thermodynamics, which relies on the causal structure and general covariance of general relativity. In Einstein-æther theory, a generally covariant theory with a dynamical timelike unit vector, every solution breaks local Lorentz invariance, thereby grossly modifying the causal structure of gravity. However, there are still absolute causal boundaries, called "universal horizons," which are not Killing horizons yet obey a first law of black hole mechanics and must have an entropy if they do not violate a generalized second law. We couple a scalar field to the timelike vector and show via the tunneling approach that the universal horizon radiates as a blackbody at a fixed temperature, even if the scalar field equations also violate local Lorentz invariance. This suggests that the class of holographic theories may be much broader than currently assumed.
Black hole entropy without brick walls
Xiang, L
2002-01-01
The properties of the thermal radiation are discussed by using the new equation of state density motivated by the generalized uncertainty relation in the quantum gravity. There is no burst at the last stage of the emission of a Schwarzshild black hole. When the new equation of state density is utilized to investigate the entropy of a scalar field outside the horizon of a static black hole, the divergence appearing in the brick wall model is removed, without any cutoff. The entropy proportional to the horizon area is derived from the contribution of the vicinity of the horizon.
Black hole entropy without brick walls
Xiang, Li
2002-07-01
The properties of the thermal radiation are discussed by using the new equation of state density motivated by the generalized uncertainty relation in the quantum gravity. There is no burst at the last stage of the emission of a Schwarzschild black hole. When the new equation of state density is utilized to investigate the entropy of a scalar field outside the horizon of a static black hole, the divergence appearing in the brick wall model is removed, without any cutoff. The entropy proportional to the horizon area is derived from the contribution of the vicinity of the horizon.
Polyatomic gases with dynamic pressure: Maximum entropy principle and shock structure
Pavić-Čolić, Milana; Simić, Srboljub
2016-01-01
This paper is concerned with the analysis of polyatomic gases within the framework of kinetic theory. Internal degrees of freedom are modeled using a single continuous variable corresponding to the molecular internal energy. Non-equilibrium velocity distribution function, compatible with macroscopic field variables, is constructed using the maximum entropy principle. A proper collision cross section is constructed which obeys the micro-reversibility requirement. The source term and entropy production rate are determined in the form which generalizes the results obtained within the framework of extended thermodynamics. They can be adapted to appropriate physical situations due to the presence of parameters. They are also compared with the results obtained using BGK approximation. For the proposed model the shock structure problem is thoroughly analyzed.
Dynamics of energy transport and entropy production in ac-driven quantum electron systems
Ludovico, María Florencia; Moskalets, Michael; Sánchez, David; Arrachea, Liliana
2016-07-01
We analyze the time-resolved energy transport and the entropy production in ac-driven quantum coherent electron systems coupled to multiple reservoirs at finite temperature. At slow driving, we formulate the first and second laws of thermodynamics valid at each instant of time. We identify heat fluxes flowing through the different pieces of the device and emphasize the importance of the energy stored in the contact and central regions for the second law of thermodynamics to be instantaneously satisfied. In addition, we discuss conservative and dissipative contributions to the heat flux and to the entropy production as a function of time. We illustrate these ideas with a simple model corresponding to a driven level coupled to two reservoirs with different chemical potentials.
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.
Quantum Hall Effect and Black Hole Entropy in Loop Quantum Gravity
Vaid, Deepak
2012-01-01
In LQG, black hole horizons are described by 2+1 dimensional boundaries of a bulk 3+1 dimensional spacetime. The horizon is endowed with area by lines of gravitational flux which pierce the surface. As is well known, counting of the possible states associated with a given set of punctures allows us to recover the famous Bekenstein-Hawking area law according to which the entropy of a black hole is proportional to the area of the associated horizon $ S_{BH} \\propto A_{Hor} $. It is also known that the dynamics of the horizon degrees of freedom is described by the Chern-Simons action of a $\\mathfrak{su(2)}$ (or $\\mathfrak{u(1)}$ after a certain gauge fixing) valued gauge field $A_{\\mu}^i$. Recent numerical work which performs the state-counting for punctures, from first-principles, reveals a step-like structure in the entropy-area relation. We argue that both the presence of the Chern-Simons action and the step-like structure in the entropy-area curve are indicative of the fact that the effective theory which de...
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.
Stretched horizons, quasiparticles and quasinormal modes
Iizuka, N; Lifschytz, G; Lowe, D A; 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 non-interacting 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, non-extremal 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.
Membrane viewpoint on black holes: Properties and evolution of the stretched horizon
Price, Richard H.; Thorne, Kip S.
1986-02-01
This paper derives the ``membrane formalism'' for black holes. The membrane formalism rewrites the standard mathematical theory of black holes in a language and notation which (we hope) will facilitate research in black-hole astrophysics: The horizon of a black hole is replaced by a surrogate ``stretched horizon,'' which is viewed as a 2-dimensional membrane that resides in 3-dimensional space and evolves in response to driving forces from the external universe. This membrane, following ideas of Damour and Znajek, is regarded as made from a 2-dimensional viscous fluid that is electrically charged and electrically conducting and has finite entropy and temperature, but cannot conduct heat. The interaction of the stretched horizon with the external universe is described in terms of familiar laws for the horizon's fluid, e.g., the Navier-Stokes equation, Ohm's law, a tidal-force equation, and the first and second laws of thermodynamics. Because these laws have familiar forms, they are likely to help astrophysicists understand intuitively and compute quantitatively the behaviors of black holes in complex external environments. Previous papers have developed and elucidated electromagnetic aspects of the membrane formalism for time-independent rotating holes. This paper derives the full formalism for dynamical, evolving holes, with one exception: In its present form the formalism is not equipped to handle horizon caustics, where new generators attach themselves to the horizon.
Vorobeichik, E. L.; Kaigorodova, S. Yu.
2017-08-01
The 23-year-long dynamics of actual acidity (pHwater) and acid-soluble heavy metals (Cu, Pb, Cd, Zn) in the forest litter and humus horizon of soils in spruce-fir forests were studied in the area subjected to the long-term (since 1940) pollution with atmospheric emissions from the Middle Ural Copper Smelter (Revda, Sverdlovsk oblast). For this purpose, 25 permanent sample plots were established on lower slopes at different distances from the enterprise (30, 7, 4, 2, and 1 km; 5 plots at each distance) in 1989. The emissions from the smelter have decreased since the early 1990s. In 2012, the emissions of sulfur dioxide and dust decreased by 100 and 40 times, respectively, as compared with the emissions in 1980. Samples of litter and humus horizons were collected on permanent plots in 1989, 1999, and 2012. The results indicate that the pH of the litter and humus horizons restored to the background level 10 and 23 years after the beginning of the reduction in emissions, respectively. However, these characteristics in the impact zone still somewhat differ from those in the background area. In 2012, the content of Cu in the litter decreased compared to 1989 on all the plots; the content of Cu in the humus horizon decreased only in the close vicinity of the smelter. The contents of other metals in the litter and humus horizons remain constant or increased (probably because of the pH-dependent decrease in migration capacity). The absence of pronounced removal of metals from soils results in the retention of high contamination risk and the conservation of the suppressed state of biota within the impact zone.
Effective first law of thermodynamics of black holes with two horizons
Institute of Scientific and Technical Information of China (English)
Wei Yi-Huan
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.
Energy Technology Data Exchange (ETDEWEB)
Silver, R.N.; Gubernatis, J.E.; Sivia, D.S. (Los Alamos National Lab., NM (USA)); Jarrell, M. (Ohio State Univ., Columbus, OH (USA). Dept. of Physics)
1990-01-01
In this article we describe the results of a new method for calculating the dynamical properties of the Anderson model. QMC generates data about the Matsubara Green's functions in imaginary time. To obtain dynamical properties, one must analytically continue these data to real time. This is an extremely ill-posed inverse problem similar to the inversion of a Laplace transform from incomplete and noisy data. Our method is a general one, applicable to the calculation of dynamical properties from a wide variety of quantum simulations. We use Bayesian methods of statistical inference to determine the dynamical properties based on both the QMC data and any prior information we may have such as sum rules, symmetry, high frequency limits, etc. This provides a natural means of combining perturbation theory and numerical simulations in order to understand dynamical many-body problems. Specifically we use the well-established maximum entropy (ME) method for image reconstruction. We obtain the spectral density and transport coefficients over the entire range of model parameters accessible by QMC, with data having much larger statistical error than required by other proposed analytic continuation methods.
Directory of Open Access Journals (Sweden)
Matthias Weippert
2014-10-01
Full Text Available Nonlinear parameters of heart rate variability (HRV have proven their prognostic value in clinical settings, but their physiological background is not very well established. We assessed the effects of low intensity isometric (ISO and dynamic (DYN exercise of the lower limbs on heart rate matched intensity on traditional and entropy measures of HRV. Due to changes of afferent feedback under DYN and ISO a distinct autonomic response, mirrored by HRV measures, was hypothesized. Five-minute inter-beat interval measurements of 43 healthy males (26.0 ± 3.1 years were performed during rest, DYN and ISO in a randomized order. Blood pressures and rate pressure product were higher during ISO vs. DYN (p < 0.001. HRV indicators SDNN as well as low and high frequency power were significantly higher during ISO (p < 0.001 for all measures. Compared to DYN, sample entropy (SampEn was lower during ISO (p < 0.001. Concluding, contraction mode itself is a significant modulator of the autonomic cardiovascular response to exercise. Compared to DYN, ISO evokes a stronger blood pressure response and an enhanced interplay between both autonomic branches. Non-linear HRV measures indicate a more regular behavior under ISO. Results support the view of the reciprocal antagonism being only one of many modes of autonomic heart rate control. Under different conditions; the identical “end product” heart rate might be achieved by other modes such as sympathovagal co-activation as well.
Entropy of Reissner–Nordström–de Sitter black hole
Directory of Open Access Journals (Sweden)
Li-Chun Zhang
2016-10-01
Full Text Available 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.
Entropy of Reissner-Nordström-de Sitter black hole
Zhang, Li-Chun; Zhao, Ren; Ma, Meng-Sen
2016-10-01
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.
Dynamics enhanced by HCl doping triggers full Pauling entropy release at the ice XII-XIV transition
Köster, K. W.; Fuentes-Landete, V.; Raidt, A.; Seidl, M.; Gainaru, C.; Loerting, T.; Böhmer, R.
2015-06-01
The pressure-temperature phase diagram of ice displays a perplexing variety of structurally distinct phases. In the century-long history of scientific research on ice, the proton-ordered ice phases numbered XIII through XV were discovered only recently. Despite considerable effort, none of the transitions leading from the low-temperature ordered ices VIII, IX, XI, XIII, XIV and XV to their high-temperature disordered counterparts were experimentally found to display the full Pauling entropy. Here we report calorimetric measurements on suitably high-pressure-treated, hydrogen chloride-doped ice XIV that demonstrate just this at the transition to ice XII. Dielectric spectroscopy on undoped and on variously doped ice XII crystals reveals that addition of hydrogen chloride, the agent triggering complete proton order in ice XIV, enhances the precursor dynamics strongest. These discoveries provide new insights into the puzzling observation that different dopants trigger the formation of different proton-ordered ice phases.
Horizon as critical phenomenon
Lee, Sung-Sik
2016-09-01
We show that renormalization group flow can be viewed as a gradual wave function collapse, where a quantum state associated with the action of field theory evolves toward a final state that describes an IR fixed point. The process of collapse is described by the radial evolution in the dual holographic theory. If the theory is in the same phase as the assumed IR fixed point, the initial state is smoothly projected to the final state. If in a different phase, the initial state undergoes a phase transition which in turn gives rise to a horizon in the bulk geometry. We demonstrate the connection between critical behavior and horizon in an example, by deriving the bulk metrics that emerge in various phases of the U( N ) vector model in the large N limit based on the holographic dual constructed from quantum renormalization group. The gapped phase exhibits a geometry that smoothly ends at a finite proper distance in the radial direction. The geometric distance in the radial direction measures a complexity: the depth of renormalization group transformation that is needed to project the generally entangled UV state to a direct product state in the IR. For gapless states, entanglement persistently spreads out to larger length scales, and the initial state can not be projected to the direct product state. The obstruction to smooth projection at charge neutral point manifests itself as the long throat in the anti-de Sitter space. The Poincare horizon at infinity marks the critical point which exhibits a divergent length scale in the spread of entanglement. For the gapless states with non-zero chemical potential, the bulk space becomes the Lifshitz geometry with the dynamical critical exponent two. The identification of horizon as critical point may provide an explanation for the universality of horizon. We also discuss the structure of the bulk tensor network that emerges from the quantum renormalization group.
Entropy and Recurrence Measures of a Financial Dynamic System by an Interacting Voter System
Directory of Open Access Journals (Sweden)
Hong-Li Niu
2015-04-01
Full Text Available A financial time series agent-based model is reproduced and investigated by the statistical physics system, the finite-range interacting voter system. The voter system originally describes the collective behavior of voters who constantly update their positions on a particular topic, which is a continuous-time Markov process. In the proposed model, the fluctuations of stock price changes are attributed to the market information interaction amongst the traders and certain similarities of investors’ behaviors. Further, the complexity of return series of the financial model is studied in comparison with two real stock indexes, the Shanghai Stock Exchange Composite Index and the Hang Seng Index, by composite multiscale entropy analysis and recurrence analysis. The empirical research shows that the simulation data for the proposed model could grasp some natural features of actual markets to some extent.
Hints of quantum gravity from the horizon fluid
Cropp, Bethan; Bhattacharya, Swastik; Shankaranarayanan, S.
2017-01-01
For many years, researchers have tried to glean hints about quantum gravity from black hole thermodynamics. However, black hole thermodynamics suffers from the problem of universality—at leading order, several approaches with different microscopic degrees of freedom lead to Bekenstein-Hawking entropy. We attempt to bypass this issue by using a minimal statistical mechanical model for the horizon fluid based on the Damour-Navier-Stokes (DNS) equation. For stationary asymptotically flat black hole spacetimes in general relativity, we show explicitly that, at equilibrium, the entropy of the horizon fluid is the Bekenstein-Hawking entropy. Further, we show that, for the bulk viscosity of the fluctuations of the horizon fluid to be identical to Damour, a confinement scale exists for these fluctuations, implying quantization of the horizon area. The implications and possible mechanisms from the fluid point of view are discussed.
Hints of quantum gravity from the horizon fluid
Cropp, Bethan; Shankaranarayanan, S
2016-01-01
For many years researchers have tried to glean hints about quantum gravity from black hole thermodynamics. However, black hole thermodynamics suffers from the problem of Universality --- at leading order, several approaches with different microscopic degrees of freedom lead to Bekenstein-Hawking entropy. We attempt to bypass this issue by using a minimal statistical mechanical model for the horizon fluid based on Damour-Navier-Stokes (DNS) equation. For asymptotically flat black hole spacetimes in General Relativity, we show explicitly that at equilibrium the entropy of the horizon fluid is the Bekenstein-Hawking entropy. Further we show that, for the bulk viscosity of the fluctuations of the horizon fluid to be identical to Damour, a confinement scale exists for these fluctuations, implying quantization of the horizon area. The implications and possible mechanisms from the fluid point of view are discussed.
Horizon Thermodynamics and Gravitational Tension
Widom, A; Srivastava, Y N
2016-01-01
We consider the thermodynamics of a horizon surface from the viewpoint of the vacuum tension $\\tau =(c^4/4G )$. Numerically, $\\tau \\approx 3.026\\times 10^{43}$ Newton. In order of magnitude, this is the tension that has been proposed for microscopic string models of gravity. However, after decades of hard work on string theory models of gravity, there is no firm scientific evidence that such models of gravity apply empirically. Our purpose is thereby to discuss the gravitational tension in terms of the conventional Einstein general theory of relativity that apparently does explain much and maybe all of presently known experimental gravity data. The central result is that matter on the horizon surface is bound by the entropy-area law by tension in the closely analogous sense that the Wilson action-area law also describes a surface confinement.
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
Entanglement entropy of round spheres
Energy Technology Data Exchange (ETDEWEB)
Solodukhin, Sergey N., E-mail: Sergey.Solodukhin@lmpt.univ-tours.f [Laboratoire de Mathematiques et Physique Theorique, Universite Francois-Rabelais Tours Federation Denis Poisson - CNRS, Parc de Grandmont, 37200 Tours (France)
2010-10-18
We propose that the logarithmic term in the entanglement entropy computed in a conformal field theory for a (d-2)-dimensional round sphere in Minkowski spacetime is identical to the logarithmic term in the entanglement entropy of extreme black hole. The near horizon geometry of the latter is H{sub 2}xS{sub d-2}. For a scalar field this proposal is checked by direct calculation. We comment on relation of this and earlier calculations to the 'brick wall' model of 't Hooft. The case of generic 4d conformal field theory is discussed.
Gravity and the Thermodynamics of Horizons
Padmanabhan, T
2003-01-01
Spacetimes with horizons show a resemblance to thermodynamic systems and it is possible to associate the notions of temperature and entropy with them. Several aspects of this connection are reviewed in a manner appropriate for broad readership. The approach uses two essential principles: (a) the physical theories must be formulated for each observer entirely in terms of variables any given observer can access and (b) consistent formulation of quantum field theory requires analytic continuation to the complex plane. These two principles, when used together in spacetimes with horizons, are powerful enough to provide several results in a unified manner. Since spacetimes with horizons have a generic behaviour under analytic continuation, standard results of quantum field theory in curved spacetimes with horizons can be obtained directly (Sections III to VII). The requirements (a) and (b) also put strong constraints on the action principle describing the gravity and, in fact, one can obtain the Einstein-Hilbert ac...
Thermodynamics of the Apparent Horizon in FRW Universe with Massive Gravity
Institute of Scientific and Technical Information of China (English)
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 dS,where the heat flow 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/(2π(r)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 Hc → 0,which recovers the Minkowski reference metric solution in the flat case,the generalized second law of thermodynamics holds if α3 + 4α4 ＜ 0.Without this condition,even for the simplest model of dRGT massive cosmology with α3 =α4 =0,the generalized second law of thermodynamics could be violated.
A note on entropy of de Sitter black holes
Bhattacharya, Sourav
2015-01-01
A de Sitter black hole or a black hole spacetime endowed with a positive cosmological constant has two Killing horizons -- a black hole horizon 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 first use a suitable general geometric set up for 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 the horizons in an equal footing and to obtain the total entropy. We show that in order get the total entropy, the near horizon mode functions for the diffeomorphism generating vector fields has to be restricted in a certain manner, compared to the single horizon spacetimes. We nex...
Black holes, entropies, and semiclassical spacetime in quantum gravity
Nomura, Yasunori; Weinberg, Sean J.
2014-10-01
We present a coherent picture of the quantum mechanics of black holes. The picture does not require the introduction of any drastically new physical effect beyond what is already known; it arises mostly from synthesizing and (re)interpreting existing results in appropriate manners. We identify the Bekenstein-Hawking entropy as the entropy associated with coarse-graining performed to obtain semiclassical field theory from a fundamental microscopic theory of quantum gravity. This clarifies the issues around the unitary evolution, the existence of the interior spacetime, and the thermodynamic nature in black hole physics — any result in semiclassical field theory is a statement about the maximally mixed ensemble of microscopic quantum states consistent with the specified background, within the precision allowed by quantum mechanics. We present a detailed analysis of information transfer in Hawking emission and black hole mining processes, clarifying what aspects of the underlying dynamics are (not) visible in semiclassical field theory. We also discuss relations between the black hole entropy and the entanglement entropy across the horizon. We then extend our discussions to more general contexts in quantum gravity. The subjects include extensions to de Sitter and Minkowski spaces and implications for complementarity and cosmology, especially the eternally inflating multiverse.
Thermodynamics Properties of the Inner Horizon of a Kerr-Newman Black Hole
Ren, Jun
2009-07-01
In this paper, we study the thermal properties of the inner horizon of a Kerr-Newman black hole. By adopting Damour-Ruffini method and the thin film model which is developed on the base of brick wall model suggested by ’t Hooft, we calculate the temperature and the entropy of the inner horizon of a Kerr-Newman black hole. We conclude that the temperature of inner horizon is positive and the entropy of the inner horizon is proportional to the area of the inner horizon. The cut-off factor is same as it in calculation of the entropy of the outer horizon, 90 β. In addition, we write the integral and differential Bekenstein-Smarr formula as the parameters of the inner horizon. Then, we discuss that if the contribution of the inner horizon is taken into account to the total entropy of the black hole, the Nernst theorem can be satisfied. At last, We calculate the tunneling rate of the outer horizon Γ+ and the inner horizon Γ-. The total tunneling rate Γ should be the product of the rates of the outer and inner horizon, Γ=Γ+ṡΓ-. We find that the total tunneling rate is in agreement with the Parikh’s standard result, Γ→exp (Δ S BH ), and there is no information loss.
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.
Black hole entropy without brick walls
Xiang, Li
2002-01-01
The properties of the thermal radiation are discussed by using the new equation of state density motivated by the generalized uncertainty relation in the quantum gravity. There is no burst at the last stage of the emission of a Schwarzshild black hole. When the new equation of state density is utilized to investigate the entropy of a scalar field outside the horizon of a static black hole, the divergence appearing in the brick wall model is removed, without any cutoff. The entropy proportiona...
Euclidean Approach for Entropy of Black Shells
S., J Robel Arenas
2016-01-01
We introduce the concept of black shell, consisting on a massive thin spherical shell contracting toward its gravitational radius from the point of view of an external observer far from the shell, in order to effectively model the gravitational collapse. Considering complementary description of entanglement entropy of a black shell and according to Gibbons-Hawking Euclidean approach, we calculate the Bekenstein-Hawking entropy retrieving horizon integral and discarding boundary at infinity.
Configurational entropy of glueball states
Bernardini, Alex E.; Braga, Nelson R. F.; da Rocha, Roldão
2017-02-01
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.
Conditional entropy of glueball states
Bernardini, Alex E; da Rocha, Roldao
2016-01-01
The conditional 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 conditional entropy is studied as a function of the glueball spin and of the mass, providing information about the stability of the glueball states.
Salimi, S.; Haseli, S.; Khorashad, A. S.; Adabi, F.
2016-09-01
The interaction between system and environment is a fundamental concept in the theory of open quantum systems. As a result of the interaction, an amount of correlation (both classical and quantum) emerges between the system and the environment. In this work, we recall the quantity that will be very useful to describe the emergence of the correlation between the system and the environment, namely, the total entropy production. Appearance of total entropy production is due to the entanglement production between the system and the environment. In this work, we discuss about the role of the total entropy production for detecting the non-Markovianity. By utilizing the relation between the total entropy production and total correlation between subsystems, one can see a temporary decrease of total entropy production is a signature of non-Markovianity. We apply our criterion for the special case, where the composite system has initial correlation with environment.
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)
Strange Horizons: Understanding Causal Barriers Beyond General Relativity
Cropp, Bethan
2016-01-01
This thesis explores two avenues into understanding the physics of black holes and horizons beyond general relativity, via analogue models and Lorentz violating theories. Analogue spacetimes have wildly different dynamics to general relativity; this allows the possibility of non-Killing horizons in stationary solutions. In the case of non-Killing horizons different definitions of surface gravity are truly different quantities. This also has application to modified theories of gravity, where there is no reason to expect all horizons to be Killing horizons. In Lorentz violating theories, the situation becomes even stranger, as Killing horizons are at best low energy barriers, but for superluminal dispersion relations a true causal barrier, the universal horizon, may be present. We investigate the nature of these universal horizons via a ray tracing study, and delve into what happens near both the universal and Killing horizons. From this study we determine the surface gravity of universal horizons by the peelin...
Cortical Entropy, Mutual Information and Scale-Free Dynamics in Waking Mice
Fagerholm, Erik D.; Scott, Gregory; Shew, Woodrow L.; Song, Chenchen; Leech, Robert; Knöpfel, Thomas; Sharp, David J.
2016-01-01
Some neural circuits operate with simple dynamics characterized by one or a few well-defined spatiotemporal scales (e.g. central pattern generators). In contrast, cortical neuronal networks often exhibit richer activity patterns in which all spatiotemporal scales are represented. Such “scale-free” cortical dynamics manifest as cascades of activity with cascade sizes that are distributed according to a power-law. Theory and in vitro experiments suggest that information transmission among cortical circuits is optimized by scale-free dynamics. In vivo tests of this hypothesis have been limited by experimental techniques with insufficient spatial coverage and resolution, i.e., restricted access to a wide range of scales. We overcame these limitations by using genetically encoded voltage imaging to track neural activity in layer 2/3 pyramidal cells across the cortex in mice. As mice recovered from anesthesia, we observed three changes: (a) cortical information capacity increased, (b) information transmission among cortical regions increased and (c) neural activity became scale-free. Our results demonstrate that both information capacity and information transmission are maximized in the awake state in cortical regions with scale-free network dynamics. PMID:27384059
Logarithmic Black Hole Entropy Corrections and Holographic R\\'enyi Entropy
Mahapatra, Subhash
2016-01-01
The entanglement and R\\'{e}nyi 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 horizon area. With the corrected black hole entropy expression, we then find corrections to the R\\'{e}nyi entropies. We calculate these corrections for both Einstein as well as Gauss-Bonnet gravity duals. Corrections with logarithmic dependence on the area of the entangling surface naturally occur at the order $G_{D}^0$ and it seems to be a general feature of entanglement and R\\'{e}nyi entropies for CFTs with gravity duals. In particular, there is...
Davies, T.; Fry, H.; Wilson, A.; Palmisano, A; Altaweel, M.; Radner, K.
2014-01-01
We present a spatial interaction entropy maximizing and structural dynamics model of settlements from the Middle Bronze (MBA) and Iron Ages (IA) in the Khabur Triangle (KT) region within Syria. The model addresses factors that make locations attractive for trade and settlement, affecting settlement growth and change. We explore why some sites become relatively major settlements, while others diminish in the periods discussed. We assess how political and geographic constraints affect regional ...
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
[Objective] The aim was to study the coupling relationship between economic development and ecological environment. [Method] Firstly, the evaluation index system for the coupling system of economic development and ecological environment in Xi'an City was established, then the dynamic variation of coupling relationship between economic development and ecological environment in Xi'an City from 2001 to 2010 was analyzed by using entropy method, finally some corresponding suggestions were put forward according ...
Emergent horizon, Hawking radiation and chaos in the collapsed polymer model of a black hole
Brustein, Ram
2016-01-01
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 a...
Directory of Open Access Journals (Sweden)
Gustavo M. Souza
2004-09-01
Full Text Available Approximate Entropy (ApEn, a model-independent statistics to quantify serial irregularities, was used to evaluate changes in sap flow temporal dynamics of two tropical species of trees subjected to water deficit. Water deficit induced a decrease in sap flow of G. ulmifolia, whereas C. legalis held stable their sap flow levels. Slight increases in time series complexity were observed in both species under drought condition. This study showed that ApEn could be used as a helpful tool to assess slight changes in temporal dynamics of physiological data, and to uncover some patterns of plant physiological responses to environmental stimuli.Entropia Aproximada (ApEn, um modelo estatístico independente para quantificar irregularidade em séries temporais, foi utilizada para avaliar alterações na dinâmica temporal do fluxo de seiva em duas espécies arbóreas tropicais submetidas à deficiência hídrica. A deficiência hídrica induziu uma grande redução no fluxo de seiva em G. ulmifolia, enquanto que na espécie C. legalis manteve-se estável. A complexidade das séries temporais foi levemente aumentada sob deficiência hídrica. O estudo mostrou que ApEn pode ser usada como um método para detectar pequenas alterações na dinâmica temporal de dados fisiológicos, e revelar alguns padrões de respostas fisiológicas a estímulos ambientais.
The information entropy of a static dilaton black hole
Institute of Scientific and Technical Information of China (English)
LIU ChengZhou
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.
Logarithmic corrections to gravitational entropy and the null energy condition
Parikh, Maulik; Svesko, Andrew
2016-10-01
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.
Logarithmic corrections to gravitational entropy and the null energy condition
Directory of Open Access Journals (Sweden)
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.
Astuti, Valerio; Rovelli, Carlo
2016-01-01
Building on a technical result by Brunnemann and Rideout on the spectrum of the Volume operator in Loop Quantum Gravity, we show that the dimension of the space of the quadrivalent states --with finite-volume individual nodes-- describing a region with total volume smaller than $V$, has \\emph{finite} dimension, bounded by $V \\log V$. This allows us to introduce the notion of "volume entropy": the von Neumann entropy associated to the measurement of volume.
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.
Unexpectedly Large Surface Gravities for Acoustic Horizons?
Liberati, S; Visser, M; Liberati, Stefano; Sonego, Sebastiano; Visser, Matt
2000-01-01
Acoustic black holes are fluid dynamic analogs of general relativistic black holes, wherein the behaviour of sound waves in a moving fluid acts as an analog for scalar fields propagating in a gravitational background. Acoustic horizons possess many of the properties more normally associated with the event horizons of general relativity, up to and including Hawking radiation. They have received much attention because it would seem to be much easier to experimentally create an acoustic horizon than to create an event horizon. We wish to point out some potential difficulties (and opportunities) in actually setting up an experiment that possesses an acoustic horizon. We show that in zero-viscosity, stationary fluid flow with generic boundary conditions, the creation of an acoustic horizon is accompanied by a formally infinite ``surface gravity'', and a formally infinite Hawking flux. Only by applying a suitable non-constant external body force, and for very specific boundary conditions on the flow, can these quan...
The entropy of a hole in spacetime
Balasubramanian, Vijay; Chowdhury, Borun D; de Boer, Jan
2013-01-01
We compute the gravitational entropy of 'spherical Rindler space', a time-dependent, spherically symmetric generalization of ordinary Rindler space, defined with reference to a family of observers traveling along non-parallel, accelerated trajectories. All these observers are causally disconnected from a spherical region H (a 'hole') located at the origin of Minkowski space. The entropy evaluates to S = A/4G, where A is the area of the spherical acceleration horizon, which coincides with the boundary of H. We propose that S is the entropy of entanglement between quantum gravitational degrees of freedom supporting the interior and the exterior of the sphere H.
Thermality and heat content of horizons from infinitesimal coordinate transformations
Energy Technology Data Exchange (ETDEWEB)
Majhi, Bibhas Ranjan; Padmanabhan, T. [IUCAA, Pune (India)
2013-12-15
Thermal properties of a static horizon (like the entropy S, heat content TS, etc.) can be obtained either from the surface term of the Einstein-Hilbert action or by evaluating the Noether charge, corresponding to the diffeomorphisms generated by the timelike Killing vector field. We show that, for a wide class of geometries, the same results can be obtained using the vector field which produces an infinitesimal coordinate transformation between two physically relevant reference frames, viz. the freely falling frame near the horizon and the static, accelerated, frame. In particular, the infinitesimal coordinate transformation from inertial coordinates to a uniformly accelerated frame can be used to obtain the heat content and entropy of the Rindler horizon. This result offers insight into the observer-dependent degrees of freedom which contribute to the entropy of null surfaces. (orig.)
Entropy and topology of the Kerr-de Sitter black hole
Institute of Scientific and Technical Information of China (English)
陈松柏; 荆继良
2002-01-01
By using the path integral method of Gibbons and Hawking, the entropy of the Kerr-de Sitter black hole isinvestigated under the microcanonical ensemble. We find that the entropy is one eighth the sum of the products of theEuler number of its cosmological horizon and event horizon with their respective areas. It is shown that the origin ofthe entropy of the black hole is related to the topology of its instanton.
Directory of Open Access Journals (Sweden)
Wei Xu
2015-03-01
Full Text Available Based on entropy relations, we derive the thermodynamic bound for entropy and the area of horizons for a Schwarzschild–dS black hole, including the event horizon, Cauchy horizon, and negative horizon (i.e., the horizon with negative value, which are all geometrically bound and comprised by the cosmological radius. We consider the first derivative of the entropy relations to obtain the first law of thermodynamics for all horizons. We also obtain the Smarr relation for the horizons using the scaling discussion. For the thermodynamics of all horizons, the cosmological constant is treated as a thermodynamic variable. In particular, the thermodynamics of the negative horizon are defined well in the r<0 side of space–time. This formula appears to be valid for three-horizon black holes. We also generalize the discussion to thermodynamics for the event horizon and Cauchy horizon of Gauss–Bonnet charged flat black holes because the Gauss–Bonnet coupling constant is also considered to be thermodynamic variable. These results provide further insights into the crucial role played by the entropy relations of multi-horizons in black hole thermodynamics as well as improving our understanding of entropy at the microscopic level.
Equivalence of Variations of Statistical and Wald's Entropies
Hadad, Merav
2010-01-01
We calculate the variation of the statistical entropy of a black hole with a bifurcate Killing horizon in generalized theories of gravity due to variation of the matter Lagrangian. Using the classical generalized gravity equations, we find that this exactly equals the variation of Wald's entropy. Since this is proved for any generalized theory of gravity, it indicates that the two entropies have a natural connection and that they may have the same physical origin.
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.
Loop quantum gravity and black hole entropy quantization
Institute of Scientific and Technical Information of China (English)
LI ChuanAn; JIANG JiJian; SU JiuQing
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.
Uncertainty relation and black hole entropy of Kerr spacetime
Institute of Scientific and Technical Information of China (English)
Hu Shuang-Qi; Zhao Ren
2005-01-01
The properties of thermal radiation are discussed by using a new equation of state density, which is motivated by the generalized uncertainty relation in the quantum gravity. There is no burst at the last stage of the emission of Kerr black hole. When the new equation of state density is utilized to investigate the entropy of a Bosonic field and Fermionic field outside the horizon of a static Kerr black hole, the divergence appearing in the brick wall model is removed, without any cutoff. The entropy proportional to the horizon area is derived from the contribution of the vicinity of the horizon.
Horowitz-Strominger Black Hole Entropy Without Brick Wall
Institute of Scientific and Technical Information of China (English)
ZHANG Li-Chun; ZHAO Ren; LIN Hai
2004-01-01
@@ A Horowitz-Strominger black hole is discussed through a new equation of state density motivated by the generalized uncertainty relation in quantum gravity. There is no burst in the last stage of emission from a HorowitzStrominger black hole. When the new equation of state density is used to investigate the entropy of bosonic field and fermionic field outside the horizon of a static Horowitz-Strominger black hole, the divergence that appears in the brick-wall model is removed without any cutoff. The entropy proportional to the horizon area is derived from the contribution in the vicinity of the horizon.
Uncertainty relation and black hole entropy of Kerr spacetime
Hu, Shuang-Qi; Zhao, Ren
2005-07-01
The properties of thermal radiation are discussed by using a new equation of state density, which is motivated by the generalized uncertainty relation in the quantum gravity. There is no burst at the last stage of the emission of Kerr black hole. When the new equation of state density is utilized to investigate the entropy of a Bosonic field and Fermionic field outside the horizon of a static Kerr black hole, the divergence appearing in the brick wall model is removed, without any cutoff. The entropy proportional to the horizon area is derived from the contribution of the vicinity of the horizon.
Spherically symmetric black-hole entropy without brick walls
Ren, Zhao; Yue-Qin, Wu; Li-Chun, Zhang
2003-11-01
Properties of the thermal radiation of black holes are discussed using a new equation of state density motivated by the generalized uncertainty relation in quantum gravity. There is no burst at the last stage of emission from a spherically symmetric black hole. When the new equation of state density is used to investigate the entropy of a bosonic field and fermionic field outside the horizon of a static spherically symmetric black hole, the divergence that appears in the brick-wall model is removed without any cutoff. The entropy proportional to the horizon area is derived from the contribution from the vicinity of the horizon.
Letter: Dilatonic Black Hole Entropy Without Brick Walls
Ren, Zhao; Sheng-Li, Zhang
2004-09-01
The properties of the thermal radiation are discussed by using the new equation of state density motivated by the generalized uncertainty relation in the quantum gravity. There is no burst at the last stage of the emission of dilatonic black hole. When the new equation of state density is utilized to investigate the entropy of a bosonic field and fermionic field outside the horizon of a static dilatonic black hole, the divergence appearing in the brick wall model is removed, without any cutoff. It is derived from the contribution of the vicinity of the horizon that the entropy is proportional to the horizon area.
Weakly isolated horizon information loss paradox
Chen, Ge-Rui
2014-01-01
In this paper we investigate the information loss paradox of weakly isolated horizon(WIH) based on the Parikh and Wilczek's tunneling spectrum. We find that there are correlations among Hawking radiations from weakly isolated horizon, the information can be carried out in terms of correlations between sequential emissions, and the radiation is an entropy conservation process. We generalize Refs.[11-13]' results to a more general spacetime. Through revisiting the calculation of tunneling of weakly isolated horizon, we find that Ref.[12]'s requirement that radiating particles have the same angular momenta of unit mass as that of black hole is not needed, and the energy and angular momenta of emitting particles are very arbitrary, which should be restricted only by keeping the cosmic censorship of black hole.
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.
Super-translations and super-rotations at the horizon
Donnay, Laura; Gonzalez, Hernan A; Pino, Miguel
2015-01-01
We show that the asymptotic symmetries close to non-extremal black hole horizons are generated by an extension of super-translations. This group is generated by a semi-direct sum of Virasoro and abelian currents. The charges associated to the asymptotic Killing symmetries satisfy the same algebra. When considering the special case of the stationary black hole, the zero mode charges correspond to the angular momentum and the entropy at the horizon.
Falling through the black hole horizon
Energy Technology Data Exchange (ETDEWEB)
Brustein, Ram [Department of Physics, Ben-Gurion University,Beer-Sheva 84105 (Israel); Medved, A.J.M. [Department of Physics & Electronics, Rhodes University,Grahamstown 6140 (South Africa); National Institute for Theoretical Physics (NITheP),Matieland, Western Cape 7602 (South Africa)
2015-06-15
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.
Holography of 3d Flat Cosmological Horizons
Bagchi, Arjun; Fareghbal, Reza; Simon, Joan
2013-01-01
We provide a first derivation of the Bekenstein-Hawking entropy of 3d flat cosmological horizons in terms of the counting of states in a dual field theory. These horizons appear in the shifted-boost orbifold of R^{1,2}, the flat limit of non-extremal rotating BTZ black holes. These 3d geometries carry non-zero charges under the asymptotic symmetry algebra of R^{1,2}, the 3d Bondi-Metzner-Sachs (BMS3) algebra. The dual theory has the symmetries of the 2d Galilean Conformal Algebra, a contraction of two copies of the Virasoro algebra, which is isomorphic to BMS3. We study flat holography as a limit of AdS3/CFT2 to semi-classically compute the density of states in the dual, exactly reproducing the bulk entropy in the limit of large charges. Our flat horizons, remnants of the BTZ inner horizons also satisfy a first law of thermodynamics. We comment on how the dual theory reproduces the bulk first law and how cosmological bulk excitations are matched with boundary quantum numbers.
Charge Expulsion from Black Brane Horizons, and Holographic Quantum Criticality in the Plane
D'Hoker, Eric
2012-01-01
Quantum critical behavior in 2+1 dimensions is established via holographic methods in a 5+1-dimensional Einstein gravity theory with gauge potential form fields of rank 1 and 2. These fields are coupled to one another via a tri-linear Chern-Simons term with strength k. The quantum phase transition is physically driven by the expulsion of the electric charge from inside the black brane horizon to the outside, where it gets carried by the gauge fields which acquire charge thanks to the Chern-Simons interaction. At a critical value k=k_c, zero temperature, and any finite value of the magnetic field, the IR behavior is governed by a near-horizon Lifshitz geometry. The associated dynamical scaling exponent depends on the magnetic field. For k k_c, the IR flow is towards the purely magnetic brane in AdS_6. Its near-horizon geometry is AdS_4 \\times R^2, so that the entropy density vanishes quadratically with temperature, and all charge is carried by the gauge fields outside of the horizon.
D'Sa, Eurico J; Overton, Edward B; Lohrenz, Steven E; Maiti, Kanchan; Turner, R Eugene; Freeman, Angelina
2016-05-17
The characteristics of fluorescent components of dissolved organic matter (DOM) were examined using excitation emission matrix (EEM) fluorescence spectroscopy combined with parallel-factor analysis (PARAFAC) for seawater samples obtained from the northern Gulf of Mexico (NGoM) before, during, and after the 2010 Deepwater Horizon (DwH) oil spill. An EEMs PARAFAC modeling of samples collected within 16 km of the wellhead during the oil spill in May 2010, which included one typical subsurface sample with a PAH concentration of 1.09 μg/L, identified two humic-like and two previously reported oil-like components. Compared to prespill levels, however, there were order-of-magnitude higher fluorescence intensities associated with these components that are consistent with an oil-spill source. The spectral decomposition of the EEMs data using individual and combined data sets from coastal and offshore waters impacted by the DwH spill further revealed the changing nature of fluorescent DOM composition. Although the PAHs concentrations were at prespill conditions after the spill in 2012 and 2013 near the DwH site, the variable and anomalous levels of fluorescence intensities and DOC concentrations three years after the spill suggest the potential long-term persistence of the oil in the DOC pool in the NGoM.
Soft hairy horizons in three spacetime dimensions
Afshar, Hamid; Merbis, Wout; Perez, Alfredo; Tempo, David; Troncoso, Ricardo
2016-01-01
We discuss some aspects of soft hairy black holes and a new kind of "soft hairy cosmologies", including a detailed derivation of the metric formulation, results on flat space, and novel observations concerning the entropy. Remarkably, like in the case with negative cosmological constant, we find that the asymptotic symmetries for locally flat spacetimes with a horizon are governed by infinite copies of the Heisenberg algebra that generate soft hair descendants. It is also shown that the generators of the three-dimensional Bondi-Metzner-Sachs algebra arise from composite operators of the affine u(1) currents through a twisted Sugawara-like construction. We then discuss entropy macroscopically, thermodynamically and microscopically and discover that a microscopic formula derived recently for boundary conditions associated to the Korteweg-de Vries hierarchy fits perfectly our results for entropy and ground state energy. We conclude with a comparison to related approaches.
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.
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.
Gravitational surface Hamiltonian and entropy quantization
Bakshi, Ashish; Majhi, Bibhas Ranjan; Samanta, Saurav
2017-02-01
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.
Halyo, Edi
2015-01-01
We generalize the concept of complexity near horizons to all nondegenerate black holes. For Schwarzschild black holes, we show that Rindler observers see a complexity change of $S$ during proper time $1/\\kappa$ which corresponds to the creation of a causal patch with proper length $1/\\kappa$ inside the horizon. We attempt to describe complexity in the horizon CFT and the Euclidean picture.
"Nowhere" differentiable horizons
Chrúsciel, P T
1996-01-01
It is folklore knowledge amongst general relativists that horizons are well behaved, continuously differentiable hypersurfaces except perhaps on a negligible subset one needs not to bother with. We show that this is not the case, by constructing a Cauchy horizon, as well as a black hole event horizon, which contain no open subset on which they are differentiable.
Indian Academy of Sciences (India)
K B Athreya
2009-09-01
It is shown that (i) every probability density is the unique maximizer of relative entropy in an appropriate class and (ii) in the class of all pdf that satisfy $\\int fh_id_=_i$ for $i=1,2,\\ldots,\\ldots k$ the maximizer of entropy is an $f_0$ that is proportional to $\\exp(\\sum c_i h_i)$ for some choice of $c_i$. An extension of this to a continuum of constraints and many examples are presented.
Wang, Zhankun; DiMarco, Steven F.; Socolofsky, Scott A.
2016-03-01
An integrated observational field effort that makes simultaneous and collocated measurements of turbulence and fine-scale parameters has been conducted near the Deepwater Horizon oil spill site in the northern Gulf of Mexico (GOM). Full water column profiles are collected across the continental slope in July 2013. The observational results suggest that strong turbulence is patchy and mostly measured in the thermocline and deepwater when using the buoyancy Reynolds number, Reb=200 criterion, the boundary between weak and strong turbulence. Bottom enhanced turbulence is often seen on the continental slope. Using the ratio of the turbulent velocity scale and the oil droplets rising velocity, we develop criteria for when turbulence will dominate the movement of oil droplets and when turbulence can be ignored. Based on the data collected, for oil droplets with rising velocity greater than 6×10-3 m s-1, the turbulence effect can be ignored on the continental slope of the northern GOM. For oil droplets with rising speed less than 10-4 m s-1, their motions will be affected by the turbulent flow at all depths. For oil droplets with rising speed between 10-4 and 6×10-3 m s-1, the role of turbulence will depend on the strength of the local turbulence and water stratification. We also relate turbulent velocity to the size and density of oil droplets by estimating the rising velocity of different size oil droplets due to balance between buoyancy and drag force. Droplet size and density difference are the two critical parameters in determining the role of turbulence.
Black Hole Entropy, Marginal Stability and Mirror Symmetry
Energy Technology Data Exchange (ETDEWEB)
Aspinwall, Paul S.; Maloney, Alexander; Simons, Aaron
2006-10-06
We consider the superconformal quantum mechanics associated to BPS black holes in type IIB Calabi-Yau compactifications. This quantum mechanics describes the dynamics of D-branes in the near-horizon attractor geometry of the black hole. In many cases, the black hole entropy can be found by counting the number of chiral primaries in this quantum mechanics. Both the attractor mechanism and notions of marginal stability play important roles in generating the large number of microstates required to explain this entropy. We compute the microscopic entropy explicitly in a few different cases, where the theory reduces to quantum mechanics on the moduli space of special Lagrangians. Under certain assumptions, the problem may be solved by implementing mirror symmetry as three T-dualities: this is essentially the mirror of a calculation by Gaiotto, Strominger and Yin. In some simple cases, the calculation may be done in greater generality without resorting to conjectures about mirror symmetry. For example, the K3 x T{sub 2} case may be studied precisely using the Fourier-Mukai transform.
Energy Technology Data Exchange (ETDEWEB)
Harrison, Sarah; Kachru, Shamit; Wang, Huajia; /Stanford U., ITP /Stanford U., Phys. Dept. /SLAC
2012-04-24
Via the AdS/CFT correspondence, ground states of field theories at finite charge density are mapped to extremal black brane solutions. Studies of simple gravity + matter systems in this context have uncovered wide new classes of extremal geometries. The Lifshitz metrics characterizing field theories with non-trivial dynamical critical exponent z {ne} 1 emerge as one common endpoint in doped holographic toy models. However, the Lifshitz horizon exhibits mildly singular behaviour - while curvature invariants are finite, there are diverging tidal forces. Here we show that in some of the simplest contexts where Lifshitz metrics emerge, Einstein-Maxwell-dilaton theories, generic corrections lead to a replacement of the Lifshitz metric, in the deep infrared, by a re-emergent AdS{sub 2} x R{sup 2} geometry. Thus, at least in these cases, the Lifshitz scaling characterizes the physics over a wide range of energy scales, but the mild singularity is cured by quantum or stringy effects.
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.)
Entropy computing via integration over fractal measures.
Słomczynski, Wojciech; Kwapien, Jarosław; Zyczkowski, Karol
2000-03-01
We discuss the properties of invariant measures corresponding to iterated function systems (IFSs) with place-dependent probabilities and compute their Renyi entropies, generalized dimensions, and multifractal spectra. It is shown that with certain dynamical systems, one can associate the corresponding IFSs in such a way that their generalized entropies are equal. This provides a new method of computing entropy for some classical and quantum dynamical systems. Numerical techniques are based on integration over the fractal measures. (c) 2000 American Institute of Physics.
Covariant Entropy Bound and Padmanabhan's Emergent Paradigm
Hadi, H; Darabi, F
2016-01-01
The covariant entropy conjecture is invariant under time reversal and consequently its origin must be statistical rather than thermodynamical. This may impose a fundamental constraint on the number of degrees of freedom in nature. Indeed, the covariant entropy bound imposes an upper entropy bound for any physical system. Considering a cosmological system, we show that Padmanabhan's emergent paradigm, which indicates that the emergence of cosmic space is due to the discrepancy between the surface and bulk degrees of freedom, leads to a lower entropy bound. The lower and upper entropy bounds may coincide on the apparent horizon for the radiation field and dark energy with the equations of state $\\omega=\\frac{1}{3}$ and $\\omega=-1$, respectively. Moreover, the maximal entropy inside the apparent horizon occurs when it is filled completely by the radiation field or dark energy. It turns out that for dark energy case (pure de Sitter space)\\ the holographic principle is satisfied in the sense that the number of deg...
Entanglement entropy converges to classical entropy around periodic orbits
Energy Technology Data Exchange (ETDEWEB)
Asplund, Curtis T., E-mail: ca2621@columbia.edu [Department of Physics, Columbia University, 538 West 120th Street, New York, NY 10027 (United States); Berenstein, David, E-mail: dberens@physics.ucsb.edu [Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom)
2016-03-15
We consider oscillators evolving subject to a periodic driving force that dynamically entangles them, and argue that this gives the linearized evolution around periodic orbits in a general chaotic Hamiltonian dynamical system. We show that the entanglement entropy, after tracing over half of the oscillators, generically asymptotes to linear growth at a rate given by the sum of the positive Lyapunov exponents of the system. These exponents give a classical entropy growth rate, in the sense of Kolmogorov, Sinai and Pesin. We also calculate the dependence of this entropy on linear mixtures of the oscillator Hilbert-space factors, to investigate the dependence of the entanglement entropy on the choice of coarse graining. We find that for almost all choices the asymptotic growth rate is the same.
Quasiparticle picture of black holes and the entropy--area relation
Iizuka, N; Lifschytz, G; Lowe, D A; Iizuka, Norihiro; Kabat, Daniel; Lifschytz, Gilad; Lowe, David A.
2003-01-01
We propose an effective description of 0-brane black holes, in which the black hole is modeled as a gas of non-interacting quasi-particles in the dual quantum mechanics. This simple model is shown to account for many of the static thermodynamic properties of the black hole. It also accounts for dynamical properties, such as the rate at which energy gets thermalized by the black hole. We use the model to show that the entropy of the quantum mechanics is proportional to the black hole horizon area in Planck units.
Production and decay of evolving horizons
Visser, M; Nielsen, Alex; Visser, Matt
2006-01-01
We consider a simple physical model for an evolving horizon that is strongly interacting with its environment, exchanging arbitrarily large quantities of matter with its environment in the form of both infalling material and outgoing Hawking radiation. We permit fluxes of both lightlike and timelike particles to cross the horizon, and ask how the horizon grows and shrinks in response to such flows. We place a premium on providing a clear and straightforward exposition with simple formulae. To be able to handle such a highly dynamical situation in a simple manner we make one significant physical restriction, that of spherical symmetry, and two technical mathematical restrictions: (1) We choose to slice the spacetime in such a way that the space-time foliations (and hence the horizons) are always spherically symmetric. (2) Furthermore we adopt Painleve-Gullstrand coordinates (which are well suited to the problem because they are nonsingular at the horizon) in order to simplify the relevant calculations. We find...
Institute of Scientific and Technical Information of China (English)
Fu-qi Yin; Sheng-fan Zhou
2006-01-01
In this paper, we establish the existence of a global attractor for a coupled k-dimensional lattice dynamical system governed by a discrete version of the Klein-Gordon-Schrodinger Equation. An estimate of the upper bound of the Kolmogorov ε-entropy of the global attractor is made by a method of element decomposition and the covering property of a polyhedron by balls of radii ε in a finite dimensional space. Finally, a scheme to approximate the global attractor by the global attractors of finite-dimensional ordinary differential systems is presented .
Åqvist, Johan; Kazemi, Masoud; Isaksen, Geir Villy; Brandsdal, Bjørn Olav
2017-02-21
The role played by entropy for the enormous rate enhancement achieved by enzymes has been debated for many decades. There are, for example, several confirmed cases where the activation free energy is reduced by around 10 kcal/mol due to entropic effects, corresponding to a rate enhancement of ∼10(7) compared to the uncatalyzed reaction. However, despite substantial efforts from both the experimental and theoretical side, no real consensus has been reached regarding the origin of such large entropic contributions to enzyme catalysis. Another remarkable instance of entropic effects is found in enzymes that are adapted by evolution to work at low temperatures, near the freezing point of water. These cold-adapted enzymes invariably show a more negative entropy and a lower enthalpy of activation than their mesophilic orthologs, which counteracts the exponential damping of reaction rates at lower temperature. The structural origin of this universal phenomenon has, however, remained elusive. The basic problem with connecting macroscopic thermodynamic quantities, such as activation entropy and enthalpy derived from Arrhenius plots, to the 3D protein structure is that the underlying detailed (microscopic) energetics is essentially inaccessible to experiment. Moreover, attempts to calculate entropy contributions by computer simulations have mostly focused only on substrate entropies, which do not provide the full picture. We have recently devised a new approach for accessing thermodynamic activation parameters of both enzyme and solution reactions from computer simulations, which turns out to be very successful. This method is analogous to the experimental Arrhenius plots and directly evaluates the temperature dependence of calculated reaction free energy profiles. Hence, by extensive molecular dynamics simulations and calculations of up to thousands of independent free energy profiles, we are able to extract activation parameters with sufficient precision for making
Tawfik, Abdel Nasser
2015-01-01
Recently, there has been much attention devoted to resolving the quantum corrections to the Bekenstein-Hawking (black hole) entropy, which relates the entropy to the cross-sectional area of the black hole horizon. Using generalized uncertainty principle (GUP), corrections to the geometric entropy and thermodynamics of black hole will be introduced. The impact of GUP on the entropy near the horizon of three types of black holes; Schwarzschild, Garfinkle-Horowitz-Strominger and Reissner-Nordstr\\"om is determined. It is found that the logarithmic divergence in the entropy-area relation turns to be positive. The entropy $S$, which is assumed to be related to horizon's two-dimensional area, gets an additional terms, for instance $2\\, \\sqrt{\\pi}\\, \\alpha\\, \\sqrt{S}$, where $\\alpha$ is the GUP parameter.
Xu, Wei; Meng, Xin-he
2015-01-01
Based on the entropy relations, we derive thermodynamic bound for entropy and area of horizons of Schwarzschild-dS black hole, including the event horizon, Cauchy horizon and negative horizon (i.e. the horizon with negative value), which are all geometrical bound and made up of the cosmological radius. Consider the first derivative of entropy relations together, we get the first law of thermodynamics for all horizons. We also obtain the Smarr relation of horizons by using the scaling discussion. For thermodynamics of all horizons, the cosmological constant is treated as a thermodynamical variable. Especially for thermodynamics of negative horizon, it is defined well in the $r<0$ side of spacetime. The validity of this formula seems to work well for three-horizons black holes. We also generalize the discussion to thermodynamics for event horizon and Cauchy horizon of Gauss-Bonnet charged flat black holes, as the Gauss-Bonnet coupling constant is also considered as thermodynamical variable. These give furthe...
The Entropy of a Vacuum: What Does the Covariant Entropy Count?
Nomura, Yasunori
2013-01-01
We argue that a unitary description of the formation and evaporation of a black hole implies that the Bekenstein-Hawking entropy is the "entropy of a vacuum": the logarithm of the number of possible independent ways in which quantum field theory on a fixed classical spacetime background can emerge in a full quantum theory of gravity. In many cases, the covariant entropy counts this entropy--the degeneracy of emergent quantum field theories in full quantum gravity--with the entropy of particle excitations in each quantum field theory giving only a tiny perturbation. In the Rindler description of a (black hole) horizon, the relevant vacuum degrees of freedom manifest themselves as an extra hidden quantum number carried by the states representing the second exterior region; this quantum number is invisible in the emergent quantum field theory. In a distant picture, these states arise as exponentially degenerate ground and excited states of the intrinsically quantum gravitational degrees of freedom on the stretch...
Holographic avatars of entanglement entropy
Energy Technology Data Exchange (ETDEWEB)
Barbon, J.L.F. [Instituto de Fisica Teorica IFT UAM/CSIC, Ciudad Universitaria de Cantoblanco 28049, Madrid (Spain)
2009-07-15
This is a rendering of the blackboard lectures at the 2008 Cargese summer school, discussing some elementary facts regarding the application of AdS/CFT techniques to the computation of entanglement entropy in strongly coupled systems. We emphasize the situations where extensivity of the entanglement entropy can be used as a crucial criterion to characterize either nontrivial dynamical phenomena at large length scales, or nonlocality in the short-distance realm.
Generalized gravitational entropy of interacting scalar field and Maxwell field
Directory of Open Access Journals (Sweden)
Wung-Hong Huang
2014-12-01
Full Text Available The generalized gravitational entropy proposed recently by Lewkowycz and Maldacena is extended to the interacting real scalar field and Maxwell field system. Using the BTZ geometry we first investigate the case of free real scalar field and then show a possible way to calculate the entropy of the interacting scalar field. Next, we investigate the Maxwell field system. We exactly solve the wave equation and calculate the analytic value of the generalized gravitational entropy. We also use the Einstein equation to find the effect of backreaction of the Maxwell field on the area of horizon. The associated modified area law is consistent with the generalized gravitational entropy.
Generalized gravitational entropy of interacting scalar field and Maxwell field
Huang, Wung-Hong
2014-12-01
The generalized gravitational entropy proposed recently by Lewkowycz and Maldacena is extended to the interacting real scalar field and Maxwell field system. Using the BTZ geometry we first investigate the case of free real scalar field and then show a possible way to calculate the entropy of the interacting scalar field. Next, we investigate the Maxwell field system. We exactly solve the wave equation and calculate the analytic value of the generalized gravitational entropy. We also use the Einstein equation to find the effect of backreaction of the Maxwell field on the area of horizon. The associated modified area law is consistent with the generalized gravitational entropy.
Generalized gravitational entropy of interacting scalar field and Maxwell field
Energy Technology Data Exchange (ETDEWEB)
Huang, Wung-Hong, E-mail: whhwung@mail.ncku.edu.tw
2014-12-12
The generalized gravitational entropy proposed recently by Lewkowycz and Maldacena is extended to the interacting real scalar field and Maxwell field system. Using the BTZ geometry we first investigate the case of free real scalar field and then show a possible way to calculate the entropy of the interacting scalar field. Next, we investigate the Maxwell field system. We exactly solve the wave equation and calculate the analytic value of the generalized gravitational entropy. We also use the Einstein equation to find the effect of backreaction of the Maxwell field on the area of horizon. The associated modified area law is consistent with the generalized gravitational entropy.
The new thermodynamic relations of multi-horizons black holes
Xu, Wei; Meng, Xin-he
2014-01-01
We present some general entropy and temperature relations of multi-horizons, even of the "virtual" horizon. These relations are related to product, division and sum of entropy and temperature of multi-horizons. We obtain the additional thermodynamic relations for Schwarzschild-(A)dS black holes and Reissner-Nordstr{\\"o}m-(A)dS black holes, which are found to be held for both AdS and dS black holes. Besides, a new dimensionless, mass-independence and $T_+S_+=T_-S_-$ like relation is presented. It seems to be more universal and does not depend on the mass, electric charge and cosmological constant, as it is a constant in both Schwarzschild-(A)dS black holes and Reissner-Nordstr{\\"o}m-(A)dS black holes. This new relation can be expected to link entropy relations via thermodynamics law and Smarr relation of each horizons and be helpful of understanding microscopically the black hole entropy.
Accelerated Observers, Thermal Entropy, and Spacetime Curvature
Kothawala, Dawood
2016-01-01
Assuming that an accelerated observer with four-velocity ${\\bf u}_{\\rm R}$ in a curved spacetime attributes the standard Bekenstein-Hawking entropy and Unruh temperature to his "local Rindler horizon", we show that the $\\rm \\it change$ in horizon area under parametric displacements of the horizon has a very specific thermodynamic structure. Specifically, it entails information about the time-time component of the Einstein tensor: $\\bf G({\\bf u}_{\\rm R}, {\\bf u}_{\\rm R})$. Demanding that the result holds for all accelerated observers, this actually becomes a statement about the full Einstein tensor, $\\rm \\bf G$. We also present some perspectives on the free fall with four-velocity ${\\bf u}_{\\rm ff}$ across the horizon that leads to such a loss of entropy for an accelerated observer. Motivated by results for some simple quantum systems at finite temperature $T$, we conjecture that at high temperatures, there exists a universal, system-independent curvature correction to partition function and thermal entropy of...
Scalar field reconstruction of power-law entropy-corrected holographic dark energy
Energy Technology Data Exchange (ETDEWEB)
Ebrahimi, Esmaeil [Department of Physics, Shahid Bahonar University, PO Box 76175, Kerman (Iran, Islamic Republic of); Sheykhi, Ahmad, E-mail: eebrahimi@uk.ac.ir, E-mail: sheykhi@uk.ac.ir [Department of Physics, Kerman Branch, Islamic Azad University, Kerman (Iran, Islamic Republic of)
2011-10-15
A so-called 'power-law entropy-corrected holographic dark energy' (PLECHDE) was recently proposed to explain the dark energy (DE)-dominated universe. This model is based on the power-law corrections to black hole entropy that appear when dealing with the entanglement of quantum fields between the inside and the outside of the horizon. In this paper, we suggest a correspondence between the interacting PLECHDE and the tachyon, quintessence, K-essence and dilaton scalar field models of DE in a non-flat Friedmann-Robertson-Walker universe. Then, we reconstruct the potential terms accordingly, and present the dynamical equations that describe the evolution of the scalar field DE models.
Black-hole dynamics in BHT massive gravity
Maeda, Hideki
2011-02-01
Using an exact Vaidya-type null-dust solution, we study the area and entropy laws for dynamical black holes defined by a future outer trapping horizon in (2 + 1) dimensional Bergshoeff-Hohm-Townsend (BHT) massive gravity. We consider the theory admitting a degenerate (anti-)de Sitter vacuum and pure BHT gravity. It is shown that, while the area of a black hole decreases by the injection of a null dust with positive energy density in several cases, the Wald-Kodama dynamical entropy always increases.
You, Wanli; Huang, Yu-Ming M; Kizhake, Smitha; Natarajan, Amarnath; Chang, Chia-En A
2016-08-01
Inhibition of the protein-protein interaction (PPI) mediated by breast-cancer-gene 1 C-terminal (BRCT) is an attractive strategy to sensitize breast and ovarian cancers to chemotherapeutic agents that induce DNA damage. Such inhibitors could also be used for studies to understand the role of this PPI in DNA damage response. However, design of BRCT inhibitors is challenging because of the inherent flexibility associated with this domain. Several studies identified short phosphopeptides as tight BRCT binders. Here we investigated the thermodynamic properties of 18 phosphopeptides or peptide with phosphate mimic and three compounds with phosphate groups binding to BRCT to understand promiscuous molecular recognition and guide inhibitor design. We performed molecular dynamics (MD) simulations to investigate the interactions between inhibitors and BRCT and their dynamic behavior in the free and bound states. MD simulations revealed the key role of loops in altering the shape and size of the binding site to fit various ligands. The mining minima (M2) method was used for calculating binding free energy to explore the driving forces and the fine balance between configuration entropy loss and enthalpy gain. We designed a rigidified ligand, which showed unfavorable experimental binding affinity due to weakened enthalpy. This was because it lacked the ability to rearrange itself upon binding. Investigation of another phosphate group containing compound, C1, suggested that the entropy loss can be reduced by preventing significant narrowing of the energy well and introducing multiple new compound conformations in the bound states. From our computations, we designed an analog of C1 that introduced new intermolecular interactions to strengthen attractions while maintaining small entropic penalty. This study shows that flexible compounds do not always encounter larger entropy penalty, compared with other more rigid binders, and highlights a new strategy for inhibitor design.
An Improved Thin Film Brick-Wall Model of Black Hole Entropy
Institute of Scientific and Technical Information of China (English)
LIU Wen-Biao; ZHAO Zheng
2001-01-01
We 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 us 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 L3 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.
Suárez, Dimas; Díaz, Natalia
2017-01-04
Herein, we report the results of 5.0 μs molecular dynamics simulations of native α-, β- and γ-cyclodextrins (CDs) in explicit water solvent that are useful to describe, in a comparative manner, the distorted geometry of the CD molecules in aqueous solution, the width and fluctuations of their cavities, and the number of cavity waters. By discretizing the time evolution of the dihedral angles, the rate of conformational change of the torsional motions and the conformational entropy are calculated for the three CDs, thus allowing the analysis of the extent of the MD sampling and the entropic significance of the CD flexibility. To obtain a first estimation of the conformational and entropy changes in the host molecule upon ligand binding, the inclusion complex formed between β-CD and nabumetone is also studied. Overall, the simulations complement previous experimental results on the structure and dynamics of native CDs, and together with the results obtained for the inclusion complex, provide insight into the entropic effects at work on the binding equilibria between CDs and guest ligands.
Gravitational Black Hole Hair from Event Horizon Supertranslations
Averin, Artem; Gomez, Cesar; Lust, Dieter
2016-01-01
We discuss BMS supertranslations both at null-infinity and on the horizon 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 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 these quotient transformations 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 geo...
Thermodynamics of Horizons from a Dual Quantum System
Directory of Open Access Journals (Sweden)
T. Padmanabhan
2007-08-01
Full Text Available It was shown recently that, in the case of Schwarschild black hole, one can obtainthe correct thermodynamic relations by studying a model quantum system and using a partic-ular duality transformation. We study this approach further for the case a general sphericallysymmetric horizon. We show that the idea works for a general case only if we define the en-tropy S as a congruence (Ã¢Â€ÂœobserverÃ¢Â€Â dependent quantity and the energy E as the integral overthe source of the gravitational acceleration for the congruence. In fact, in this case, one recov-ers the relation S = E/2T between entropy, energy and temperature previously proposed byone of us in gr-qc/0308070. This approach also enables us to calculate the quantum correc-tions of the Bekenstein-Hawking entropy formula for all spherically symmetric horizons.
Entropy production and wave packet dynamics in the Fock space of closed chaotic many-body systems
Flambaum, V V
2001-01-01
Highly excited many-particle states in quantum systems such as nuclei, atoms, quantum dots, spin systems, quantum computers etc., can be considered as ``chaotic'' superpositions of mean-field basis states (Slater determinants, products of spin or qubit states). This is due to a very high level density of many-body states that are easily mixed by a residual interaction between particles (quasi-particles). For such systems, we have derived simple analytical expressions for the time dependence of energy width of wave packets, as well as for the entropy, number of principal basis components and inverse participation ratio, and tested them in numerical experiments. It is shown that the energy width $\\Delta (t)$ increases linearly and very quickly saturates. The entropy of a system increases quadratically, $S(t) \\sim t^2$ at small times, and after, can grow linearly, $S(t) \\sim t$, before the saturation. Correspondingly, the number of principal components determined by the entropy, $N_{pc} \\sim exp{(S(t))}$, or by ...
The concept of entropy. Relation between action and entropy
Directory of Open Access Journals (Sweden)
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.
Black hole radiation spectrum in loop quantum gravity: isolated horizon framework
Energy Technology Data Exchange (ETDEWEB)
Diaz-Polo, Jacobo [Departamento de Astronomia y Astrofisica, Universidad de Valencia, Burjassot-46100, Valencia (Spain); Fernandez-Borja, Enrique [Departamento de Fisica Teorica and IFIC, Centro Mixto Universidad de Valencia-CSIC. Universidad de Valencia, Burjassot-46100, Valencia (Spain)], E-mail: Jacobo.Diaz@uv.es, E-mail: Enrique.Fernandez@uv.es
2008-05-21
Recent detailed analysis within the loop quantum gravity calculation of black hole entropy shows a stair-like structure in the behavior of entropy as a function of horizon area. The non-trivial distribution of the degeneracy of the black hole horizon area eigenstates is at the origin of this behavior. This degeneracy distribution is analyzed and a phenomenological model is put forward to study the implications of this distribution in the black hole radiation spectrum. Some qualitative quantum effects are obtained within the isolated horizon framework. This result provides us with a possible observational test of this model for quantum black holes.
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.
Cao, Ning; Zhang, Huaguang; Luo, Yanhong; Feng, Dezhi
2012-09-01
In this article, a novel iteration algorithm named two-stage approximate dynamic programming (TSADP) is proposed to seek the solution of nonlinear switched optimal control problem. At each iteration of TSADP, a multivariate optimal control problem is transformed to be a certain number of univariate optimal control problems. It is shown that the value function at each iteration can be characterised pointwisely by a set of smooth functions recursively obtained from TSADP, and the associated control policy, continuous control and switching control law included, is explicitly provided in a state-feedback form. Moreover, the convergence and optimality of TSADP is strictly proven. To implement this algorithm efficiently, neural networks, critic and action networks, are utilised to approximate the value function and continuous control law, respectively. Thus, the value function is expressed by the weights of critic networks pointwise. Besides, redundant weights are ruled out at each iteration to simplify the exponentially increasing computation burden. Finally, a simulation example is provided to demonstrate its effectiveness.
Entropy of Open Lattice Systems
Derrida, B.; Lebowitz, J. L.; Speer, E. R.
2007-03-01
We investigate the behavior of the Gibbs-Shannon entropy of the stationary nonequilibrium measure describing a one-dimensional lattice gas, of L sites, with symmetric exclusion dynamics and in contact with particle reservoirs at different densities. In the hydrodynamic scaling limit, L → ∞, the leading order ( O( L)) behavior of this entropy has been shown by Bahadoran to be that of a product measure corresponding to strict local equilibrium; we compute the first correction, which is O(1). The computation uses a formal expansion of the entropy in terms of truncated correlation functions; for this system the k th such correlation is shown to be O( L - k+1). This entropy correction depends only on the scaled truncated pair correlation, which describes the covariance of the density field. It coincides, in the large L limit, with the corresponding correction obtained from a Gaussian measure with the same covariance.
Holographic Entropy Bound of a Nonstationary Black Hole
Institute of Scientific and Technical Information of China (English)
LIU Cheng-Zhou
2006-01-01
@@ In accordance with the holographic principle, by counting the states of the scalar field just at the event horizon of the Vaidya-Bonner black hole, the holographic entropy bound of the black hole is calculated and the BekensteinHawking formula is obtained. With the generalized uncertainty principle, the divergence of statedensity at event horizon in the ordinary quantum field theory is removed. With the residue theorem, the integral trouble in the calculation is overcome. The present result is quantitatively tenable and the holographic principle is realized by applying the quantum field theory to the black hole entropy problem. Compared with some previous works, it is suggested that the quantum states contributing to black hole entropy should be restricted on the event horizon.
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.
VMware horizon view essentials
von Oven, Peter
2014-01-01
If you are a desktop administrator or an end user of a computing project team looking to speed up to the latest VMware Horizon View solution, then this book is perfect for you. It is your ideal companion to deploy a solution to centrally manage and virtualize your desktop estate using Horizon View 6.0.
Energy Technology Data Exchange (ETDEWEB)
Batic, Davide, E-mail: dbatic@uniandes.edu.c [Departamento de Matematica, Universidad de los Andes, Cra 1E, No. 18A-10, Bogota, Colombia Department of Mathematics, University of West Indies, Kingston (Jamaica); Nicolini, Piero, E-mail: nicolini@th.physik.uni-frankfurt.d [Frankfurt Institute for Advanced Studies (FIAS), Institut fuer Theoretische Physik, Johann Wolfgang Goethe-Universitaet, Ruth-Moufang-Strasse 1, 60438 Frankfurt am Main (Germany)
2010-08-16
We study the stability of the noncommutative Schwarzschild black hole interior by analysing the propagation of a massless scalar field between the two horizons. We show that the spacetime fuzziness triggered by the field higher momenta can cure the classical exponential blue-shift divergence, suppressing the emergence of infinite energy density in a region nearby the Cauchy horizon.
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.
Apparent horizons in Clifton-Mota-Barrow inhomogeneous universe
Vitagliano, Vincenzo; Sotiriou, Thomas P; Liberati, Stefano
2013-01-01
We analyze the apparent horizon dynamics in the inhomogeneous Clifton-Mota-Barrow solution of Brans-Dicke theory. This solution models a central matter configuration embedded in a cosmological background. In certain regions of the parameter space we find solutions exhibiting dynamical creation or merging of two horizons.
Anomaly corrected heterotic horizons
Fontanella, A.; Gutowski, J. B.; Papadopoulos, G.
2016-10-01
We consider supersymmetric near-horizon geometries in heterotic supergravity up to two loop order in sigma model perturbation theory. We identify the conditions for the horizons to admit enhancement of supersymmetry. We show that solutions which undergo supersymmetry enhancement exhibit an {s}{l}(2,{R}) symmetry, and we describe the geometry of their horizon sections. We also prove a modified Lichnerowicz type theorem, incorporating α' corrections, which relates Killing spinors to zero modes of near-horizon Dirac operators. Furthermore, we demonstrate that there are no AdS2 solutions in heterotic supergravity up to second order in α' for which the fields are smooth and the internal space is smooth and compact without boundary. We investigate a class of nearly supersymmetric horizons, for which the gravitino Killing spinor equation is satisfied on the spatial cross sections but not the dilatino one, and present a description of their geometry.
Anomaly Corrected Heterotic Horizons
Fontanella, A; Papadopoulos, G
2016-01-01
We consider supersymmetric near-horizon geometries in heterotic supergravity up to two loop order in sigma model perturbation theory. We identify the conditions for the horizons to admit enhancement of supersymmetry. We show that solutions which undergo supersymmetry enhancement exhibit an sl(2,R) symmetry, and we describe the geometry of their horizon sections. We also prove a modified Lichnerowicz type theorem, incorporating $\\alpha'$ corrections, which relates Killing spinors to zero modes of near-horizon Dirac operators. Furthermore, we demonstrate that there are no AdS2 solutions in heterotic supergravity up to second order in $\\alpha'$ for which the fields are smooth and the internal space is smooth and compact without boundary. We investigate a class of nearly supersymmetric horizons, for which the gravitino Killing spinor equation is satisfied on the spatial cross sections but not the dilatino one, and present a description of their geometry.
Extended Symmetries at the Black Hole Horizon
Donnay, Laura; González, Hernán A; Pino, Miguel
2016-01-01
We prove that non-extremal black holes in four-dimensional general relativity exhibit an infinite-dimensional symmetry in their near horizon region. By prescribing a physically sensible set of boundary conditions at the horizon, we derive the algebra of asymptotic Killing vectors, which is shown to be infinite-dimensional and includes, in particular, two sets of supertranslations and two mutually commuting copies of the Virasoro algebra. We define the surface charges associated to the asymptotic diffeomorphisms that preserve the boundary conditions and discuss the subtleties of this definition, such as the integrability conditions and the correct definition of the Dirac brackets. When evaluated on the stationary solutions, the only non-vanishing charges are the zero-modes. One of them reproduces the Bekenstein-Hawking entropy of Kerr black holes. We also study the extremal limit, recovering the NHEK geometry. In this singular case, where the algebra of charges and the integrability conditions get modified, we...
Inner and outer horizons of time experience.
Wackermann, Jirí
2007-05-01
Human experience of temporal durations exhibits a multi-regional structure, with more or less distinct boundaries, or horizons, on the scale of physical duration. The inner horizons are imposed by perceptual thresholds for simultaneity (approximately equal to 3 ms) and temporal order (approximatly equal to 30 ms), and are determined by the dynamical properties of the neural substrate integrating sensory information. Related to the inner horizon of experienced time are perceptual or cognitive "moments." Comparative data on autokinetic times suggest that these moments may be relatively invariant (approximately equal to 10(2) ms) across a wide range of species. Extension of the "sensible present" (approximately equal to 3 s) defines an intermediate horizon, beyond which the generic experience of duration develops. The domain of immediate duration experience is delimited by the ultimate outer horizon at about = 10(2) s, as evidenced by analysis of duration reproduction experiments (reproducibility horizon), probably determined by relaxation times of "neural accumulators." Beyond these phenomenal horizons, time is merely cognitively (re)constructed, not actually experienced or "perceived," a fact that is frequently ignored by contemporary time perception research. The nyocentric organization of time experience shows an interesting analogy with the egocentric organization of space, suggesting that structures of subjective space and time are derived from active motion as a common experiential basis.
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.
Entanglement, Tensor Networks and Black Hole Horizons
Molina-Vilaplana, Javier
2014-01-01
We elaborate on a previous proposal by Hartman and Maldacena on a tensor network which accounts for the scaling of the entanglement entropy in a system at a finite temperature. In this construction, the ordinary entanglement renormalization flow given by the class of tensor networks known as the Multi Scale Entanglement Renormalization Ansatz (MERA), is supplemented by an additional entanglement structure at the length scale fixed by the temperature. The network comprises two copies of a MERA circuit with a fixed number of layers and a pure matrix product state which joins both copies by entangling the infrared degrees of freedom of both MERA networks. The entanglement distribution within this bridge state defines reduced density operators on both sides which cause analogous effects to the presence of a black hole horizon when computing the entanglement entropy at finite temperature in the AdS/CFT correspondence. The entanglement and correlations during the thermalization process of a system after a quantum q...
Leydesdorff, Loet
2009-01-01
Can change in citation patterns among journals be used as an indicator of structural change in the organization of the sciences? Aggregated journal-journal citations for 1999 are compared with similar data in the Journal Citation Reports 1998 of the Science Citation Index. In addition to indicating local change, probabilistic entropy measures enable us to analyze changes in distributions at different levels of aggregation. The results of various statistics are discussed and compared by elaborating the journal-journal mappings. The relevance of this indicator for science and technology policies is further specified.
Phase transitions near black hole horizons
Gubser, S S
2005-01-01
The Reissner-Nordstrom black hole in four dimensions can be made unstable without violating the dominant energy condition by introducing a real massive scalar with non-renormalizable interactions with the gauge field. New stable black hole solutions then exist with greater entropy for fixed mass and charge than the Reissner-Nordstrom solution. In these new solutions, the scalar condenses to a non-zero value near the horizon. Various generalizations of these hairy black holes are discussed, and an attempt is made to characterize when black hole hair can occur.
Kruglikov, Boris; Rypdal, Martin
2005-01-01
The topological entropy of piecewise affine maps is studied. It is shown that singularities may contribute to the entropy only if there is angular expansion and we bound the entropy via the expansion rates of the map. As a corollary we deduce that non-expanding conformal piecewise affine maps have zero topological entropy. We estimate the entropy of piecewise affine skew-products. Examples of abnormal entropy growth are provided.
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.
Energy Technology Data Exchange (ETDEWEB)
Harrison, Sarah; Kachru, Shamit; Wang, Huajia [Stanford Institute for Theoretical Physics, Department of Physics, Stanford University,Stanford, CA 94305 (United States); Theory Group, SLAC National Accelerator Laboratory,Menlo Park, CA 94309 (United States)
2014-02-20
Via the AdS/CFT correspondence, ground states of field theories at finite charge density are mapped to extremal black brane solutions. Studies of simple gravity + matter systems in this context have uncovered wide new classes of extremal geometries. The Lifshitz metrics characterising field theories with non-trivial dynamical critical exponent z≠1 emerge as one common endpoint in doped holographic toy models. However, the Lifshitz horizon exhibits mildly singular behaviour - while curvature invariants are finite, there are diverging tidal forces. Here we show that in some of the simplest contexts where Lifshitz metrics emerge, Einstein-Maxwell-dilaton theories, toy models of generic corrections can lead (presumably as one possibility among many) to a replacement of the Lifshitz metric, in the deep infrared, by a re-emergent AdS{sub 2}×R{sup 2} geometry. Thus, at least in these cases, the Lifshitz scaling characterises the physics over a wide range of energy scales, but the mild singularity is cured by quantum or stringy effects.
Entropy in spin foam models: the statistical calculation
Energy Technology Data Exchange (ETDEWEB)
Garcia-Islas, J Manuel, E-mail: jmgislas@leibniz.iimas.unam.m [Instituto de Investigaciones en Matematicas Aplicadas y en Sistemas, Universidad Nacional Autonoma de Mexico, UNAM, A. Postal 20-726, 01000, Mexico DF (Mexico)
2010-07-21
Recently an idea for computing the entropy of black holes in the spin foam formalism has been introduced. Particularly complete calculations for the three-dimensional Euclidean BTZ black hole were performed. The whole calculation is based on observables living at the horizon of the black hole universe. Departing from this idea of observables living at the horizon, we now go further and compute the entropy of the BTZ black hole in the spirit of statistical mechanics. We compare both calculations and show that they are very interrelated and equally valid. This latter behaviour is certainly due to the importance of the observables.
Logarithmic Corrections to the Black Hole Entropy Product of ${\\cal H}^{\\pm}$ via Cardy Formula
Pradhan, Parthapratim
2016-01-01
We compute the logarithmic corrections to the black hole (BH) entropy product of ${\\cal H}^{\\pm}$ \\footnote{ ${\\cal H}^{+}$ and ${\\cal H}^{-}$ denote outer (event) horizon and inner (Cauchy) horizons} by using \\emph{Cardy prescription}. We particularly apply this formula for BTZ BH. We show that logarithmic corrections to the entropy product of ${\\cal H}^{\\pm}$ when computed \\emph{via Cardy formula} it does not mass-independent (universal) nor does it quantized.
Distributed Fusion Receding Horizon Filtering in Linear Stochastic Systems
Directory of Open Access Journals (Sweden)
Il Young Song
2009-01-01
Full Text Available This paper presents a distributed receding horizon filtering algorithm for multisensor continuous-time linear stochastic systems. Distributed fusion with a weighted sum structure is applied to local receding horizon Kalman filters having different horizon lengths. The fusion estimate of the state of a dynamic system represents the optimal linear fusion by weighting matrices under the minimum mean square error criterion. The key contribution of this paper lies in the derivation of the differential equations for determining the error cross-covariances between the local receding horizon Kalman filters. The subsequent application of the proposed distributed filter to a linear dynamic system within a multisensor environment demonstrates its effectiveness.
Saha, Subhajit
2016-01-01
Thermodynamics on the cosmological apparent horizon of a flat Friedmann-Lemaitre-Robertson-Walker metric has been investigated with Bekenstein entropy and Hawking temperature on the horizon, and Unruh temperature for the fluid inside the horizon. This temperature is experienced by a radial comoving observer infinitesimally close to the horizon due to the pressure exerted by the fluid bounded by the horizon. An expression for the entropy of the fluid has been obtained which is found to be proportional to the volume of the thermodynamic system which implies that the Unruh temperature of the fluid is inconsistent with the holographic principle. Further, we have been able to find an expression for the effective entropy of the system. Finally, assuming a barotropic equation of state $p=w\\rho$ ($w$ constant) for the fluid, it has been shown that the generalized second law holds good for a non-phantom w, while thermodynamic equilibrium is never possible for such a scenario.
BTZ black hole entropy: a spin foam model description
Energy Technology Data Exchange (ETDEWEB)
Garcia-Islas, J Manuel [Instituto de Investigaciones en Matematicas Aplicadas y en Sistemas, Universidad Nacional Autonoma de Mexico, UNAM, A Postal 20-726, 01000, Mexico DF (Mexico)], E-mail: jmgislas@leibniz.iimas.unam.mx
2008-12-21
We present a microscopical explanation of the entropy of the BTZ black hole using discrete spin foam models of quantum gravity. The entropy of a black hole is given in geometrical terms which led us to think that its statistical description must be given in terms of a quantum geometry. In this paper we present it in terms of spin foam geometrical observables at the horizon of the black hole.
Chemical potential in the first law for holographic entanglement entropy
Kastor, David; Ray, Sourya; Traschen, Jennie
2014-01-01
Entanglement entropy in conformal field theories is known to satisfy a first law. For spherical entangling surfaces, this has been shown to follow via the AdS/CFT correspondence and the holographic prescription for entanglement entropy from the bulk first law for Killing horizons. The bulk first law can be extended to include variations in the cosmological constant $\\Lambda$, which we established in earlier work. Here we show that this implies an extension of the boundary first law to include...
Statistical entropy of Calabi-Yau black holes
Iofa, Mikhail Z.; Pando Zayas, Leopoldo A.
1999-03-01
We compute the statistical entropy of nonextremal 4D and extremal 5D Calabi-Yau black holes and find exact agreement with the Bekenstein-Hawking entropy. The computation is based on the fact that the near-horizon geometry of equivalent representations contains as a factor the Bañados-Teitelboim-Zanelli black hole and on subsequent use of Strominger's proposal generalizing the statistical count of microstates of the BTZ black hole due to Carlip.
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…
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…
Directory of Open Access Journals (Sweden)
Yaman Arkun
Full Text Available An optimization model is introduced in which proteins try to evade high energy regions of the folding landscape, and prefer low entropy loss routes during folding. We make use of the framework of optimal control whose convenient solution provides practical and useful insight into the sequence of events during folding. We assume that the native state is available. As the protein folds, it makes different set of contacts at different folding steps. The dynamic contact map is constructed from these contacts. The topology of the dynamic contact map changes during the course of folding and this information is utilized in the dynamic optimization model. The solution is obtained using the optimal control theory. We show that the optimal solution can be cast into the form of a Gaussian Network that governs the optimal folding dynamics. Simulation results on three examples (CI2, Sso7d and Villin show that folding starts by the formation of local clusters. Non-local clusters generally require the formation of several local clusters. Non-local clusters form cooperatively and not sequentially. We also observe that the optimal controller prefers "zipping" or small loop closure steps during folding. The folding routes predicted by the proposed method bear strong resemblance to the results in the literature.
Ishimaru, Shin'ichi; Saito, Kazuya; Ikeuchi, Satoaki; Massalska-Arodz, Maria; Witko, Waclaw
2005-05-26
Molecular dynamics and resulting disorder in the soft crystal, smectic E (SmE) phase, were studied in detail for the title compound, 4-butyl-4'-isothiocyano-1,1'-biphenyl (4TCB), by (1)H NMR spectroscopy and adiabatic calorimetry. The ordered crystal phase of 4TCB was realized for the first time under ambient pressure after long two-step annealing and used as the reference state in the analysis of the experimental results. Four motional modes were identified in the SmE phase through the analysis of the (1)H NMR T(1). The residual entropy was determined as ca. 6 J K(-1) mol(-1). This magnitude implies that most of the disorder in the SmE phase at high temperatures is removed on cooling except for the head-to-tail disorder of the rod-shaped 4TCB molecule. Standard thermodynamic functions are tabulated below 375 K.
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.
Deepwater Horizon - Baseline Dataset
National Oceanic and Atmospheric Administration, Department of Commerce — In 2010, the Deepwater Horizon oil spill occurred in the Gulf of Mexico and the Natural Resources Damage Assessment (NRDA) was initiated to determine the extent of...
The dynamical model and quantization of the Schwarzschild black hole
Institute of Scientific and Technical Information of China (English)
2008-01-01
The mass of the Schwarzschild black hole, an observable quantity, is defined as a dynamical variable, while the corresponding conjugate is considered as a general- ized momentum. Then a two-dimensional phase space is composed of the two variables. In the two-dimensional phase space, a harmonic oscillator model of the Schwarzschild black hole is obtained by a canonical transformation. By this model, the mass spectrum of the Schwarzschild black hole is firstly obtained. Further the horizon area operator, quantum area spectrum and entropy are obtained in the Fock representation. Lastly, the wave function of the horizon area is derived also.
Quantum-corrected two-dimensional Horava-Lifshitz black hole entropy
Anacleto, M A; Brito, F A; Mota-Silva, J C
2015-01-01
In this paper we focus on the Halmiton-Jacobi method to determine the temperature and the entropy of a two-dimensional Horava-Lifshitz black hole by using the generalized uncertainty principles (GUP). We also address the product of horizons, mainly concerning the event, Cauchy, cosmological and virtual horizons.
Quantum-Corrected Two-Dimensional Horava-Lifshitz Black Hole Entropy
Directory of Open Access Journals (Sweden)
M. A. Anacleto
2016-01-01
Full Text Available We focus on the Hamilton-Jacobi method to determine several thermodynamic quantities such as temperature, entropy, and specific heat of two-dimensional Horava-Lifshitz black holes by using the generalized uncertainty principles (GUP. We also address the product of horizons, mainly concerning the event, Cauchy, and cosmological and virtual horizons.
Quantum geometry and microscopic black hole entropy
Energy Technology Data Exchange (ETDEWEB)
Corichi, Alejandro [Instituto de Matematicas, Universidad Nacional Autonoma de Mexico, A Postal 61-3, Morelia, Michoacan 58090 (Mexico); DIaz-Polo, Jacobo [Departamento de AstronomIa y AstrofIsica, Universidad de Valencia, Burjassot-46100, Valencia (Spain); Fernandez-Borja, Enrique [Departamento de Fisica Teorica and IFIC, Centro Mixto Universidad de Valencia-CSIC, Universidad de Valencia, Burjassot-46100, Valencia (Spain)
2007-01-07
Quantum black holes within the loop quantum gravity (LQG) framework are considered. The number of microscopic states that is consistent with a black hole of a given horizon area A{sub 0} are counted and the statistical entropy, as a function of the area, is obtained for A{sub 0} up to 550l{sup 2}{sub Pl}. The results are consistent with an asymptotic linear relation and a logarithmic correction with a coefficient equal to -1/2. The Barbero-Immirzi parameter that yields the asymptotic linear relation compatible with the Bekenstein-Hawking entropy is shown to coincide with a value close to {gamma} = 0.274, which has been previously obtained analytically. However, a new and oscillatory functional form for the entropy is found for small, Planck size, black holes that calls for a physical interpretation.
Disordered quivers and cold horizons
Energy Technology Data Exchange (ETDEWEB)
Anninos, Dionysios [School of Natural Sciences, Institute for Advanced Study,Princeton, NJ, 08540 (United States); Anous, Tarek [Center for Theoretical Physics, Massachusetts Institute of Technology,77 Massachusetts Avenue, Cambridge, MA, 02139 (United States); Denef, Frederik [Department of Physics, Columbia University,538 West 120th Street, New York, New York, 10027 (United States)
2016-12-15
We analyze the low temperature structure of a supersymmetric quiver quantum mechanics with randomized superpotential coefficients, treating them as quenched disorder. These theories describe features of the low energy dynamics of wrapped branes, which in large number backreact into extremal black holes. We show that the low temperature theory, in the limit of a large number of bifundamentals, exhibits a time reparametrization symmetry as well as a specific heat linear in the temperature. Both these features resemble the behavior of black hole horizons in the zero temperature limit. We demonstrate similarities between the low temperature physics of the random quiver model and a theory of large N free fermions with random masses.
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
Darabi, F; Setare, M R
2016-01-01
We study the inflation via logarithmic entropy-corrected holographic dark energy LECHDE model with future event horizon, particle horizon and Hubble horizon cut-offs, and compare the results with those of obtained in the study of inflation by holographic dark energy HDE model. In comparison, the spectrum of primordial scalar power spectrum in the LECHDE model becomes redder than the spectrum in HDE model. Moreover, the consistency with the observational data in 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.
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.
Entropy Product Formula for spinning BTZ Black Hole
Pradhan, Parthapratim
2015-01-01
We investigate the thermodynamic properties of inner and outer horizons in the background of spinning BTZ(Ba\\~{n}ados,Teitelboim and Zanelli) black hole. We compute the \\emph{horizon radii product, the entropy product, the surface temperature product, the Komar energy product and the specific heat product} for both the horizons. We observe that the entropy product is \\emph{universal}(mass-independent), whereas the surface temperature product, Komar energy product and specific heat product are \\emph{not universal} because they all depends on mass parameter. We also show that the \\emph{First law} of black hole thermodynamics and \\emph {Smarr-Gibbs-Duhem } relations hold for inner horizon as well as outer horizon. The Christodoulou-Ruffini mass formula is derived for both the horizons. We further study the \\emph{stability} of such black hole by computing the specific heat for both the horizons. It has been observed that under certain condition the black hole possesses \\emph{second order phase transition}.
Comment on Hawking radiation and trapping horizons
Baier, Rudolf
2015-01-01
We consider dynamical black hole formation from a collapsing fluid described by a symmetric and flat FRW metric. Using the Hamilton-Jacobi method the local Hawking temperature for the formed trapping/apparent horizon is calculated. The local Hawking temperature depends on the tunneling path, which we take to be along a null direction $(\\Delta s=0)$. We find that the local Hawking temperature depends directly on the equation of state of the collapsing fluid. We argue that Hawking radiation by quantum tunnelling from future inner and future outer trapping horizons is possible. However, only radiation from a space-like dynamical horizon has a chance to be observed by an external observer. Some comparison to existing literature is made.
First quantum correction to entropy of Vaidya-Bonner black holes due to arbitrary spin fields
Institute of Scientific and Technical Information of China (English)
高长军; 沈有根
2002-01-01
Using the improved brick-wall model, we have calculated the first quantum correction to the entropy of non-staticblack holes, Vaidya-Bonner black holes, due to the gravitational, electro-magnetic and neutrino fields. The result showsthat both bosonic entropy and fermionic entropy are exactly proportional to the area of the event horizon. Thus, theentropy-area law still holds in such a non-static case.
Reissner-Nordström black-hole entropy without brick walls
Ren, Zhao; Shuangqi, Hu
2004-02-01
The properties of the thermal radiation are discussed by using the new equation of state density motivated by the generalized uncertainty relation in the quantum gravity. There is no burst at the last stage of the emission of the Reissner-Nordström black hole. When the new equation of state density is utilized to investigate the entropy of a bosonic field and a fermionic field outside the horizon of a static Reissner-Nordström black hole, the divergence appearing in the brick wall model is removed, without any cut-off. The entropy proportional to the horizon area is derived from the contribution of the vicinity of the horizon.
Bekenstein-Hawking Entropy as Entanglement Entropy
Feng, Yu-Lei
2015-01-01
We show that the Bekenstein-Hawking entropy $S_{BH}$ should be treated as an entanglement entropy, provided that the formation and evaporation of a black hole can be described by quantum unitary evolutions. To confirm this statement, we derive statistical mechanics from quantum mechanics effectively by means of open quantum systems. Then a new definition of Boltzmann entropy for a quantum closed system is given to count microstates in a way consistent with the superposition principle. In particular, this new Boltzmann entropy is a constant that depends only on the dimension of the system's relevant Hilbert subspace. Based on this new definition, some kind of "detailed balance" condition is obtained to stabilize the thermal equilibrium between two macroscopic subsystems within a larger closed system. However, the required "detailed balance" condition between black hole and matter would be broken, if the Bekenstein-Hawking entropy was treated as Boltzmann entropy together with the Hawking temperature as thermal...
Connecting horizon pixels and interior voxels of a black hole
Energy Technology Data Exchange (ETDEWEB)
Nicolini, Piero, E-mail: nicolini@fias.uni-frankfurt.de [Frankfurt Institute for Advanced Studies (FIAS), Ruth-Moufang-Str. 1, 60438 Frankfurt am Main (Germany); Institut für Theoretische Physik, J.W. Goethe-Universität, Max-von-Laue-Str. 1, 60438 Frankfurt am Main (Germany); Singleton, Douglas, E-mail: dougs@csufresno.edu [Department of Physics, California State University, Fresno, CA 93740-8031 (United States); Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apartado Postal 70-543, Distrito Federal, 04510 (Mexico)
2014-11-10
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.
Connecting horizon pixels and interior voxels of a black hole
Nicolini, Piero
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.
A Proposed Absolute Entropy of Near Extremal Kerr-Newman Black Hole
Lin, H
2001-01-01
Some problems have been found as to the definition of entropy of black hole being applied to the extremal Kerr-Newman case, which has conflicts with the third law of thermodynamics. We have proposed a new modification for the near extremal one, which not only obeys the third law, but also does not conflict with other results in black hole thermodynamics. Then we proved that the inner horizon has temperature and proposed that the inner horizon contributes to the entropy of the near extremal one so that the entropy of it has a modified form and vanishes at absolute zero temperature.
Beretta, G P
2001-01-01
In view 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, in this paper, together with a review of the general features of the nonlinear quantum (thermo)dynamics I proposed in a series of papers [see references in G.P. Beretta, Found.Phys. 17, 365 (1987)], I show its exact equivalence with the maximal-entropy-production variational-principle formulation recently derived in S. Gheorghiu-Svirschevski, Phys.Rev. A 63, 022105 (2001). In addition, based on the formalism of general interest I developed for the analysis of composite systems, I show how the variational derivation can be extended to the case of a composite system to obtain the general form of my equation of motion, that turns out to be consistent with the demanding requirements of strong separability. Moreover, I propose a new intriguing fundamental ansat...
Ren, Huilong; Cai, Yongchang; Rabczuk, Timon
2015-01-01
In this paper we develop a new Peridynamic approach that naturally includes varying horizon sizes and completely solves the "ghost force" issue. Therefore, the concept of dual-horizon is introduced to consider the unbalanced interactions between the particles with different horizon sizes. The present formulation is proved to fulfill both the balances of linear momentum and angular momentum. Neither the "partial stress tensor" nor the "`slice" technique are needed to ameliorate the ghost force issue in \\cite{Silling2014}. The consistency of reaction forces is naturally fulfilled by a unified simple formulation. The method can be easily implemented to any existing peridynamics code with minimal changes. A simple adaptive refinement procedure is proposed minimizing the computational cost. The method is applied here to the three Peridynamic formulations, namely bond based, ordinary state based and non-ordinary state based Peridynamics. Both two- and three- dimensional examples including the Kalthof-Winkler experi...
Evolving Horava Cosmological Horizons
Fathi, Mohsen
2016-01-01
Several sets of radially propagating null congruence generators are exploited in order to form 3-dimensional marginally trapped surfaces, referred to as black hole and cosmological apparent horizons in a Horava universe. Based on this method, we deal with the characteristics of the 2-dimensional space-like spheres of symmetry and the peculiarities of having trapping horizons. Moreover, we apply this method in standard expanding and contracting FLRW cosmological models of a Horava universe to investigate the conditions under which the extra parameters of the theory may lead to trapped/anti-trapped surfaces both in the future and in the past. We also include the cases of negative time, referred to as the finite past, and discuss the formation of anti-trapped surfaces inside the cosmological apparent horizons.
Dirty black holes Entropy as a surface term
Visser, M
1993-01-01
It is by now clear that the naive rule for the entropy of a black hole, {entropy} = 1/4 {area of event horizon}, is violated in many interesting cases. Indeed, several authors have recently conjectured that in general the entropy of a dirty black hole might be given purely in terms of some surface integral over the event horizon of that black hole. A formal proof of this conjecture, using Lorentzian signature techniques, has recently been provided by Wald. This note performs two functions. Firstly, a rather different proof of this result is presented --- a proof based on Euclidean signature techniques. The total entropy is S = 1/4 {k A_H / l_P^2} + \\int_H {S} \\sqrt{g} d^2x. The integration runs over a spacelike cross-section of the event horizon H. The surface entropy density, {S}, is related to the behaviour of the matter Lagrangian under time dilations. Secondly, I shall consider the specific case of Einstein-Hilbert gravity coupled to an effective Lagrangian that is an arbitrary function of the Riemann ten...
VMware Horizon Workspace essentials
von Oven, Peter; Lindberg, Joel
2014-01-01
This book uses a step-by-step approach to teach you how to design, deploy, and manage a Horizon Workspace based on real world experience. Written in an easy-to-follow style, this book explains the terminology in a clear and concise manner. Each feature is explained starting at a high level and then drilling down into the technical detail, using diagrams and screenshots.This book is perfect for IT administrators who want to deploy a solution to centrally manage access to corporate applications, data, and virtual desktops using Horizon Workspace. You need to have some experience in delivering BY
Bootstrap, universality and horizons
Energy Technology Data Exchange (ETDEWEB)
Chang, Chi-Ming [Center for Theoretical Physics and Department of Physics,University of California, Berkeley, CA 94704 (United States); Lin, Ying-Hsuan [Jefferson Physical Laboratory, Harvard University,Cambridge, MA 02138 (United States)
2016-10-13
We present a closed form expression for the semiclassical OPE coefficients that are universal for all 2D CFTs with a “weak” light spectrum, by taking the semiclassical limit of the fusion kernel. We match this with a properly regularized and normalized bulk action evaluated on a geometry with three conical defects, analytically continued in the deficit angles beyond the range for which a metric with positive signature exists. The analytically continued geometry has a codimension-one coordinate singularity surrounding the heaviest conical defect. This singularity becomes a horizon after Wick rotating to Lorentzian signature, suggesting a connection between universality and the existence of a horizon.
Oven, Peter von
2015-01-01
If you are working as a desktop admin, part of a EUC team, an architect, or a consultant on a desktop virtualization project and you are looking to use VMware's Horizon solution, this book is for you. This book will demonstrate the new capabilities of Horizon 6. You should have experience in desktop management using Windows and Microsoft Office, and be familiar with Active Directory, SQL, Windows Remote Desktop Session Hosting, and VMware vSphere infrastructure (ESXi and vCenter Server) technology.
Dirty black holes Entropy versus area
Visser, M
1993-01-01
Considerable interest has recently been expressed in the entropy versus area relationship for ``dirty'' black holes --- black holes in interaction with various classical matter fields, distorted by higher derivative gravity, or infested with various forms of quantum hair. In many cases it is found that the entropy is simply related to the area of the event horizon: S = k A_H/(4\\ell_P^2). For example, the ``entropy = (1/4) area'' law *holds* for: Schwarzschild, Reissner--Nordstrom, Kerr--Newman, and dilatonic black holes. On the other hand, the ``entropy = (1/4) area'' law *fails* for: various types of (Riemann)^n gravity, Lovelock gravity, and various versions of quantum hair. The pattern underlying these results is less than clear. This paper systematizes these results by deriving a general formula for the entropy: S = {k A_H/(4\\ell_P^2)} + {1/T_H} \\int_\\Sigma [rho - {L}_E ] K^\\mu d\\Sigma_\\mu + \\int_\\Sigma s V^\\mu d\\Sigma_\\mu. (K^\\mu is the timelike Killing vector, V^\\mu the four velocity of a co--rotating o...
Area Bound of Horizons for Ho\\v{r}ava Lifshitz Black Hole
Pradhan, Parthapratim
2016-01-01
We discuss various thermodynamic properties of the inner and outer horizons in the background of Ho\\v{r}ava Lifshitz black hole. We compute \\emph{area sum, area minus and area division} of black hole horizons. We find that they all are not universal quantities whereas the product is an universal quantity. Based on these relations, we derive the area bound of all horizons. From area bound we derive entropy bound and irreducible mass bound for both the horizons. We also observe that the \\emph{First law} of black hole thermodynamics and \\emph {Smarr-Gibbs-Duhem } relations do not hold for this black hole. The underlying reason behind this failure due to the scale invariance of the coupling constant. All these calculations might be help us to understanding the nature of black hole entropy both \\emph{interior} and exterior at the microscopic level.
A discussion of a possible corrected black hole entropy
He, Miao; Fang, Chao; Sun, Dao-Quan; Deng, Jian-Bo
2016-01-01
Einstein's equation could be interpreted as the first law of thermodynamic near the spherically symmetric horizon. By using this method, we investigate the Eddington-inspired Born-Infeld (EiBI) gravity. Without matter field, the EiBI gravity can also derive the first law. With an electromagnetic field, as the field equations have a more general spherically symmetric solution in EiBI gravity, we find that the entropy would have a correction. Through recalling the Einstein gravity with a more general static spherical symmetric, this correction of the entropy might be generalized to Einstein 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.
Black hole entropy divergence and the uncertainty principle
Brustein, Ram
2011-01-01
Black hole entropy has been shown by 't Hooft to diverge at the horizon. The region near the horizon is in a thermal state, so entropy is linear to energy which consequently also diverges. We find a similar divergence for the energy of the reduced density matrix of relativistic and non-relativistic field theories, extending previous results in quantum mechanics. This divergence is due to an infinitely sharp boundary, and it stems from the position/momentum uncertainty relation in the same way that the momentum fluctuations of a precisely localized quantum particle diverge. We show that when the boundary is smoothed the divergence is tamed. We argue that the divergence of black hole entropy can also be interpreted as a consequence of position/momentum uncertainty, and that 't Hooft's brick wall tames the divergence in the same way, by smoothing the boundary.
Gravitational Entropy of Static Spacetimes and Microscopic Density of States
Padmanabhan, T
2003-01-01
A general definition for gravitational entropy can be provided using the criterion that, any patch of area which acts as a horizon for a suitably defined accelerated observer, must have an entropy proportional to its area. In any static spacetime with a horizon and associated temperature $\\beta^{-1}$, this entropy satisfies the relation $S=(1/2)\\beta E$ where $E$ is the energy source for gravitational acceleration, obtained as an integral of $(T_{ab}-(1/2)Tg_{ab})u^au^b$. With this definition of $S$, the minimisation of Einstein-Hilbert action is equivalent to minimising the free energy $F$ with $\\beta F=\\beta U-S$ where $U$ is the integral of $T_{ab}u^au^b$. We discuss the conditions under which these results imply $S\\propto E^2$ and/or $S\\propto U^2$. This approach links with several other known results, especially the holographic views of spacetime.
Transplanckian dispersion relation and entanglement entropy of blackhole
Energy Technology Data Exchange (ETDEWEB)
Chang, D. [Department of Physics, National Tsing-Hua University, Hsin-Chu (Taiwan); Chu, C.S.; Lin, F.L. [Physics Division, National Center for Theoretical Sciences, National Tsing-Hua University, Hsin-Chu (Taiwan)
2004-06-01
The quantum correction to the entanglement entropy of the event horizon is plagued by the UV divergence due to the infinitely blue-shifted near horizon modes. The resolution of this UV divergence provides an excellent window to a better understanding and control of the quantum gravity effects. We claim that the key to resolve this UV puzzle is the transplanckian dispersion relation. We calculate the entanglement entropy using a very general type of transplanckian dispersion relation such that high energy modes above a certain scale are cutoff, and show that the entropy is rendered UV finite. We argue that modified dispersion relation is a generic feature of string theory, and this boundedness nature of the dispersion relation is a general consequence of the existence of a minimal distance in string theory. (Abstract Copyright [2004], Wiley Periodicals, Inc.)
Mechanics of universal horizons
Berglund, Per; Mattingly, David
2012-01-01
Modified gravity models such as Ho\\v{r}ava-Lifshitz gravity or Einstein-{\\ae}ther theory violate local Lorentz invariance and therefore destroy the notion of a universal light cone. Despite this, in the infrared limit both models above possess static, spherically symmetric solutions with "universal horizons" - hypersurfaces that are causal boundaries between an interior region and asymptotic spatial infinity. In other words, there still exist black hole solutions. We construct a Smarr formula (the relationship between the total energy of the spacetime and the area of the horizon) for such a horizon in Einstein-{\\ae}ther theory. We further show that a slightly modified first law of black hole mechanics still holds with the relevant area now a cross-section of the universal horizon. We construct new analytic solutions for certain Einstein-{\\ae}ther Lagrangians and illustrate how our results work in these exact cases. Our results suggest that holography may be extended to these theories despite the very differen...
Visser, M
1997-01-01
The ``reliability horizon'' for semi-classical quantum gravity quantifies the extent to which we should trust semi-classical quantum gravity, and gives a handle on just where the ``Planck regime'' resides. The key obstruction to pushing semi-classical quantum gravity into the Planck regime is often the existence of large metric fluctuations, rather than a large back-reaction.
Lee, Jeongseog; Safdi, Benjamin R
2014-01-01
Entanglement entropy in even dimensional conformal field theories (CFTs) contains well-known universal terms arising from the conformal anomaly. Renyi entropies are natural generalizations of the entanglement entropy that are much less understood. Above two spacetime dimensions, the universal terms in the Renyi entropies are unknown for general entangling geometries. We conjecture a new structure in the dependence of the four-dimensional Renyi entropies on the intrinsic and extrinsic geometry of the entangling surface. We provide evidence for this conjecture by direct numerical computations in the free scalar and fermion field theories. The computation involves relating the four-dimensional free massless Renyi entropies across cylindrical entangling surfaces to corresponding three-dimensional massive Renyi entropies across circular entangling surfaces. Our numerical technique also allows us to directly probe other interesting aspects of three-dimensional Renyi entropy, including the massless renormalized Reny...
Gagie, Travis
2007-01-01
We trace the history of empirical entropy, touching briefly on its relation to Markov processes, normal numbers, Shannon entropy, the Chomsky hierarchy, Kolmogorov complexity, Ziv-Lempel compression, de Bruijn sequences and stochastic complexity.
Singh, Priti; Chakraborty, Abhishek; Manoj, B. S.
2017-01-01
In this paper we propose a new metric, Link Influence Entropy (LInE), which describes importance of each node based on the influence of each link present in a network. Influence of a link can neither be effectively estimated using betweenness centrality nor using degree based probability measures. The proposed LInE metric which provides an effective way to estimate the influence of a link in the network and incorporates this influence to identify nodal characteristics, performs better compared to degree based entropy. We found that LInE can differentiate various network types which degree-based or betweenness centrality based node influence metrics cannot. Our findings show that spatial wireless networks and regular grid networks, respectively, have lowest and highest LInE values. Finally, performance analysis of LInE is carried out on a real-world network as well as on a wireless mesh network testbed to study the influence of our metric as well as influence stability of nodes in dynamic networks.
Black Hole Thermodynamics from Near-Horizon Conformal Quantum Mechanics
Camblong, H E; Camblong, Horacio E.; Ordonez, Carlos R.
2004-01-01
The thermodynamics of black holes is shown to be directly induced by their near-horizon conformal invariance. This behavior is exhibited using a scalar field as a probe of the black hole gravitational background, for a general class of metrics in D spacetime dimensions (with $D \\geq 4$). The ensuing analysis is based on conformal quantum mechanics, within a hierarchical near-horizon expansion. In particular, the leading conformal behavior provides the correct quantum statistical properties for the Bekenstein-Hawking entropy, with the near-horizon physics governing the thermodynamic properties from the outset. Most importantly: (i) this treatment reveals the emergence of holographic properties; (ii) the conformal coupling parameter is shown to be related to the Hawking temperature; and (iii) Schwarzschild-like coordinates, despite their ``coordinate singularity,''can be used self-consistently to describe the thermodynamics of black holes.
Black Hole Horizons and Thermodynamics: A Quantum Approach
Directory of Open Access Journals (Sweden)
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.
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
Averin, Artem; Dvali, Gia; Gomez, Cesar; Lüst, Dieter
2016-06-01
We discuss BMS supertranslations both at null-infinity BMS- and on the horizon {BMS}^{mathscr{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 mathcal{A}equiv {BMS}^{mathscr{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 mathcal{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.
A q-parameter bound for particle spectra based on black hole thermodynamics with Rényi entropy
Energy Technology Data Exchange (ETDEWEB)
Biró, Tamás S., E-mail: biro.tamas@wigner.mta.hu [HAS Wigner Research Centre for Physics, Institute for Particle and Nuclear Physics, H-1525 Budapest, P.O. Box 49 (Hungary); Czinner, Viktor G., E-mail: czinner.viktor@wigner.mta.hu [HAS Wigner Research Centre for Physics, Institute for Particle and Nuclear Physics, H-1525 Budapest, P.O. Box 49 (Hungary); Centro de Matemática, Universidade do Minho, Campus de Gualtar, 4710-057 Braga (Portugal)
2013-11-04
By regarding the Hawking–Bekenstein entropy of Schwarzschild black hole horizons as a non-extensive Tsallis entropy, its formal logarithm, the Rényi entropy, is considered. The resulting temperature – horizon radius relation has the same form as the one obtained from a (3+1)-dimensional black hole in anti-de Sitter space using the original entropy formula. In both cases the temperature has a minimum. A semi-classical estimate of the horizon radius at this minimum leads to a Bekenstein bound for the q-parameter in the Rényi entropy of micro black holes (q⩾1+2/π{sup 2}), which is surprisingly close to fitted q-parameters of cosmic ray spectra and power-law distribution of quarks coalescing to hadrons in high energy accelerator experiments.
Instability of enclosed horizons
Kay, Bernard S.
2015-03-01
We point out that there are solutions to the scalar wave equation on dimensional Minkowski space with finite energy tails which, if they reflect off a uniformly accelerated mirror due to (say) Dirichlet boundary conditions on it, develop an infinite stress-energy tensor on the mirror's Rindler horizon. We also show that, in the presence of an image mirror in the opposite Rindler wedge, suitable compactly supported arbitrarily small initial data on a suitable initial surface will develop an arbitrarily large stress-energy scalar near where the two horizons cross. Also, while there is a regular Hartle-Hawking-Israel-like state for the quantum theory between these two mirrors, there are coherent states built on it for which there are similar singularities in the expectation value of the renormalized stress-energy tensor. We conjecture that in other situations with analogous enclosed horizons such as a (maximally extended) Schwarzschild black hole in equilibrium in a (stationary spherical) box or the (maximally extended) Schwarzschild-AdS spacetime, there will be similar stress-energy singularities and almost-singularities—leading to instability of the horizons when gravity is switched on and matter and gravity perturbations are allowed for. All this suggests it is incorrect to picture a black hole in equilibrium in a box or a Schwarzschild-AdS black hole as extending beyond the past and future horizons of a single Schwarzschild (/Schwarzschild-AdS) wedge. It would thus provide new evidence for 't Hooft's brick wall model while seeming to invalidate the picture in Maldacena's ` Eternal black holes in AdS'. It would thereby also support the validity of the author's matter-gravity entanglement hypothesis and of the paper ` Brick walls and AdS/CFT' by the author and Ortíz.
2016-01-01
We propose an entropy function for simplicial complices. Its value gives the expected cost of the optimal encoding of sequences of vertices of the complex, when any two vertices belonging to the same simplex are indistinguishable. We show that the proposed entropy function can be computed efficiently. By computing the entropy of several complices consisting of hundreds of simplices, we show that the proposed entropy function can be used in the analysis of the large sequences of simplicial com...
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.
Balian, Roger
We review at a tutorial level the many aspects of the concept of entropy and their interrelations, in thermodynamics, information theory, probability theory and statistical physics. The consideration of relevant entropies and the identification of entropy with missing information enlighten the paradoxes of irreversibility and of Maxwell's demon.
Chirikjian, Gregory S
2011-01-01
Proteins fold from a highly disordered state into a highly ordered one. Traditionally, the folding problem has been stated as one of predicting "the" tertiary structure from sequential information. However, new evidence suggests that the ensemble of unfolded forms may not be as disordered as once believed, and that the native form of many proteins may not be described by a single conformation, but rather an ensemble of its own. Quantifying the relative disorder in the folded and unfolded ensembles as an entropy difference may therefore shed light on the folding process. One issue that clouds discussions of "entropy" is that many different kinds of entropy can be defined: entropy associated with overall translational and rotational Brownian motion, configurational entropy, vibrational entropy, conformational entropy computed in internal or Cartesian coordinates (which can even be different from each other), conformational entropy computed on a lattice, each of the above with different solvation and solvent models, thermodynamic entropy measured experimentally, etc. The focus of this work is the conformational entropy of coil/loop regions in proteins. New mathematical modeling tools for the approximation of changes in conformational entropy during transition from unfolded to folded ensembles are introduced. In particular, models for computing lower and upper bounds on entropy for polymer models of polypeptide coils both with and without end constraints are presented. The methods reviewed here include kinematics (the mathematics of rigid-body motions), classical statistical mechanics, and information theory.
Entropy Is Simple, Qualitatively.
Lambert, Frank L.
2002-01-01
Suggests that qualitatively, entropy is simple. Entropy increase from a macro viewpoint is a measure of the dispersal of energy from localized to spread out at a temperature T. Fundamentally based on statistical and quantum mechanics, this approach is superior to the non-fundamental "disorder" as a descriptor of entropy change. (MM)
Ben-Naim, Arieh
2011-01-01
Changes in entropy can "sometimes" be interpreted in terms of changes in disorder. On the other hand, changes in entropy can "always" be interpreted in terms of changes in Shannon's measure of information. Mixing and demixing processes are used to highlight the pitfalls in the association of entropy with disorder. (Contains 3 figures.)
Entropy/information flux in Hawking radiation
Alonso-Serrano, Ana
2015-01-01
Blackbody radiation contains (on average) an entropy of $3.9\\pm2.5$ bits per photon. This applies not only to the proverbial case of "burning a lump of coal", but also to the Hawking radiation from both analogue black holes and general relativistic black holes. The flip side of this observation is the information budget: If the emission process is unitary, (as it certainly is for normal physical/chemical burning, and also for the Hawking emission from analogue black holes), then this entropy is exactly compensated by the "hidden information" in the correlations. We shall now extend this argument to the Hawking radiation from general relativistic black holes, (where previous discussion is both heated and inconclusive), demonstrating that the assumption of unitarity leads to a perfectly reasonable entropy/information budget without any hint of a "firewall". The assumption of unitarity instead has a different implication --- the horizon (if present) cannot be an *event* horizon, it must be an *apparent/trapping*...
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.
Entropy of a generic null surface from its associated Virasoro algebra
Chakraborty, Sumanta; Bhattacharya, Sourav; Padmanabhan, T.
2016-12-01
Null surfaces act as one-way membranes, blocking information from those observers who do not cross them (e.g., in the black hole and the Rindler spacetimes) and these observers associate an entropy (and temperature) with the null surface. The black hole entropy can be computed from the central charge of an appropriately defined, local, Virasoro algebra on the horizon. We show that one can extend these ideas to a general class of null surfaces, all of which possess a Virasoro algebra and a central charge, leading to an entropy density (i.e., per unit area) which is just (1 / 4). All the previously known results of associating entropy with horizons arise as special cases of this very general property of null surfaces demonstrated here and we believe this work represents the derivation of the entropy-area law in the most general context. The implications are discussed.
Quasilocal rotating conformal Killing horizons
Chatterjee, Ayan
2015-01-01
The formulation of quasi-local conformal Killling horizons(CKH) is extended to include rotation. This necessitates that the horizon be foliated by 2-spheres which may be distorted. Matter degrees of freedom which fall through the horizon is taken to be a real scalar field. We show that these rotating CKHs also admit a first law in differential form.
Trapping Horizons as inner boundary conditions for black hole spacetimes
Jaramillo, J L; Cordero-Carrion, I; Ibáñez, J M
2007-01-01
We present a set of inner boundary conditions for the numerical construction of dynamical black hole space-times, when employing a 3+1 constrained evolution scheme and an excision technique. These inner boundary conditions are heuristically motivated by the dynamical trapping horizon framework and are enforced in an elliptic subsystem of the full Einstein equation. In the stationary limit they reduce to existing isolated horizon boundary conditions. A characteristic analysis completes the discussion of inner boundary conditions for the radiative modes.
Bell, Iris R; Howerter, Amy; Jackson, Nicholas; Aickin, Mikel; Bootzin, Richard R; Brooks, Audrey J
2012-07-01
Investigators of homeopathy have proposed that nonlinear dynamical systems (NDS) and complex systems science offer conceptual and analytic tools for evaluating homeopathic remedy effects. Previous animal studies demonstrate that homeopathic medicines alter delta electroencephalographic (EEG) slow wave sleep. The present study extended findings of remedy-related sleep stage alterations in human subjects by testing the feasibility of using two different NDS analytic approaches to assess remedy effects on human slow wave sleep EEG. Subjects (N=54) were young adult male and female college students with a history of coffee-related insomnia who participated in a larger 4-week study of the polysomnographic effects of homeopathic medicines on home-based all-night sleep recordings. Subjects took one bedtime dose of a homeopathic remedy (Coffea cruda or Nux vomica 30c). We computed multiscale entropy (MSE) and the correlation dimension (Mekler-D2) for stages 3 and 4 slow wave sleep EEG sampled in artifact-free 2-min segments during the first two rapid-eye-movement (REM) cycles for remedy and post-remedy nights, controlling for placebo and post-placebo night effects. MSE results indicate significant, remedy-specific directional effects, especially later in the night (REM cycle 2) (CC: remedy night increases and post-remedy night decreases in MSE at multiple sites for both stages 3 and 4 in both REM cycles; NV: remedy night decreases and post-remedy night increases, mainly in stage 3 REM cycle 2 MSE). D2 analyses yielded more sporadic and inconsistent findings. Homeopathic medicines Coffea cruda and Nux vomica in 30c potencies alter short-term nonlinear dynamic parameters of slow wave sleep EEG in healthy young adults. MSE may provide a more sensitive NDS analytic method than D2 for evaluating homeopathic remedy effects on human sleep EEG patterns. Copyright © 2012 The Faculty of Homeopathy. Published by Elsevier Ltd. All rights reserved.
Brissaud, Jean-Bernard
2005-03-01
Entropy is a basic physical quantity that led to various, and sometimes apparently conflicting interpretations. It has been successively assimilated to different concepts such as disorder and information. In this paper we're going to revisit these conceptions, and establish the three following results: Entropy measures lack of information; it also measures information. These two conceptions are complementary. Entropy measures freedom, and this allows a coherent interpretation of entropy formulas and of experimental facts. To associate entropy and disorder implies defining order as absence of freedom. Disorder or agitation is shown to be more appropriately linked with temperature.
Directory of Open Access Journals (Sweden)
Jean-Bernard Brissaud
2005-02-01
Full Text Available Abstract: Entropy is a basic physical quantity that led to various, and sometimes apparently conflicting interpretations. It has been successively assimilated to different concepts such as disorder and information. In this paper we're going to revisit these conceptions, and establish the three following results: Entropy measures lack of information; it also measures information. These two conceptions are complementary. Entropy measures freedom, and this allows a coherent interpretation of entropy formulas and of experimental facts. To associate entropy and disorder implies defining order as absence of freedom. Disorder or agitation is shown to be more appropriately linked with temperature.
Component analysis of the protein hydration entropy
Chong, Song-Ho; Ham, Sihyun
2012-05-01
We report the development of an atomic decomposition method of the protein solvation entropy in water, which allows us to understand global change in the solvation entropy in terms of local changes in protein conformation as well as in hydration structure. This method can be implemented via a combined approach based on molecular dynamics simulation and integral-equation theory of liquids. An illustrative application is made to 42-residue amyloid-beta protein in water. We demonstrate how this method enables one to elucidate the molecular origin for the hydration entropy change upon conformational transitions of protein.
1976-06-01
If two reversible Q-conservative curves could intersect, it would be possible to violate the axiom by performing the cycle if 1 f 2 i. b. Integrability...is one that makes. a complete cyclic transformation in a completely reversible way. The cyclic process of a Carnot engine is, illustrated in Figure...etialdynamics 2.A§SS"CT (Canuw an reverse side It m....ay and fdsnetl 6y Week& sumber) It is shown that the laws of particle dynamics can be formulated
Horizon Scanning for Pharmaceuticals
DEFF Research Database (Denmark)
Lepage-Nefkens, Isabelle; Douw, Karla; Mantjes, GertJan
will collect country-specific information, liaise between the central HS unit and country-specific clinical and other experts, coordinate the national prioritization process (to select products for early assessment), and communicate the output of the HSS to national decision makers. The outputs of the joint...... for a joint horizon scanning system (HSS). We propose to create a central “horizon scanning unit” to perform the joint HS activities (a newly established unit, an existing HS unit, or a third party commissioned and financed by the collaborating countries). The unit will be responsible for the identification...... and filtration of new and emerging pharmaceutical products. It will maintain and update the HS database, organise company pipeline meetings, and disseminate the HSS’s outputs. The HS unit works closely together with the designated national HS experts in each collaborating country. The national HS experts...
Guica, Monica; Ross, Simon F.
2015-03-01
We explore the Papadodimas-Raju prescription for reconstructing the region behind the horizon of one-sided black holes in AdS/CFT in the case of the {R}{{P}2} geon—a simple, analytic example of a single-sided, asymptotically AdS3 black hole, which corresponds to a pure CFT state that thermalizes at late times. We show that in this specific example, the mirror operators involved in the reconstruction of the interior have a particularly simple form: the mirror of a single trace operator at late times is just the corresponding single trace operator at early times. We use some explicit examples to explore how changes in the state modify the geometry inside the horizon.
Guica, Monica
2014-01-01
We explore the Papadodimas-Raju prescription for reconstructing the region behind the horizon of one-sided black holes in AdS/CFT in the case of the RP^2 geon - a simple, analytic example of a single-sided, asymptotically AdS_3 black hole, which corresponds to a pure CFT state that thermalises at late times. We show that in this specific example, the mirror operators involved in the reconstruction of the interior have a particularly simple form: the mirror of a single trace operator at late times is just the corresponding single trace operator at early times. We use some explicit examples to explore how changes in the state modify the geometry inside the horizon.
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.
Schaefer, Bradley E.; Liller, William
1990-01-01
Variations in astronomical refraction near the horizon are examined. Sunset timings, a sextant mounted on a tripod, and a temperature profile are utilized to derive the variations in refraction data, collected from 7 locations. It is determined that the refraction ranges from 0.234 to 1.678 deg with an rms deviation of 0.16, and it is observed that the variation is larger than previously supposed. Some applications for the variation of refraction value are discussed.
Horizons of cybernetical physics
Fradkov, Alexander L.
2017-03-01
The subject and main areas of a new research field-cybernetical physics-are discussed. A brief history of cybernetical physics is outlined. The main areas of activity in cybernetical physics are briefly surveyed, such as control of oscillatory and chaotic behaviour, control of resonance and synchronization, control in thermodynamics, control of distributed systems and networks, quantum control. This article is part of the themed issue 'Horizons of cybernetical physics'.
Doria, Alaric
2015-01-01
We derive the metric of an accelerating observer moving with non-constant proper acceleration in flat spacetime. With the exception of a limiting case representing a Rindler observer, there are no horizons. In our solution, observers can accelerate to any desired terminal speed $v_{\\infty} < c$. The motion of the accelerating observer is completely determined by the distance of closest approach and terminal velocity or, equivalently, by an acceleration parameter and terminal velocity.
Horizons of cybernetical physics
2017-01-01
The subject and main areas of a new research field—cybernetical physics—are discussed. A brief history of cybernetical physics is outlined. The main areas of activity in cybernetical physics are briefly surveyed, such as control of oscillatory and chaotic behaviour, control of resonance and synchronization, control in thermodynamics, control of distributed systems and networks, quantum control. This article is part of the themed issue ‘Horizons of cybernetical physics’. PMID:28115620
Liu, Hang; Meng, Xin-he
2016-08-01
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.
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.
Topological entropy of continuous functions on topological spaces
Energy Technology Data Exchange (ETDEWEB)
Liu Lei [Department of Mathematics, Northwest University, Xian, Shaanxi 710069 (China)], E-mail: liugh105@163.com; Wang Yangeng [Department of Mathematics, Northwest University, Xian, Shaanxi 710069 (China)], E-mail: ygwang62@163.com; Wei Guo [Department of Mathematics and Computer Science, University of North Carolina at Pembroke, Pembroke, NC 28372 (United States)], E-mail: guo.wei@uncp.edu
2009-01-15
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.
Entropy production in systems with long range interactions
Pakter, Renato; Levin, Yan
2017-04-01
On a fine grained scale the Gibbs entropy of an isolated system remains constant throughout its dynamical evolution. This is a consequence of Liouville’s theorem for Hamiltonian systems and appears to contradict the second law of thermodynamics. In reality, however, there is no problem since the thermodynamic entropy should be associated with the Boltzmann entropy, which for non-equilibrium systems is different from Gibbs entropy. The Boltzmann entropy accounts for the microstates which are not accessible from a given initial condition, but are compatible with a given macrostate. In a sense the Boltzmann entropy is a coarse grained version of the Gibbs entropy and will not decrease during the dynamical evolution of a macroscopic system. In this paper we will explore the entropy production for systems with long range interactions. Unlike for short range systems, in the thermodynamic limit, the probability density function for these systems decouples into a product of one particle distribution functions and the coarse grained entropy can be calculated explicitly. We find that the characteristic time for the entropy production scales with the number of particles as {{N}α} , with α >0 , so that in the thermodynamic limit entropy production takes an infinite amount of time.
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
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
Joannah Caborn Wengler
2012-01-01
Every tenth member of the CERN personnel participates in an EU-funded project – a strong indication of CERN’s successful relations with the European Commission (EC), coordinated by the CERN EU projects office. The EC director in charge of preparing “Horizon 2020”, the new EU funding programme for research and innovation (2014-2020), will be giving a presentation at CERN on 8 May. He will reveal more about what the new programme has in store. “It’s a very interesting time in the development of Horizon 2020, which is focusing the attention of all research communities in Europe,” explains Svetlomir Stavrev, head of the EU projects office. “After a long public consultation and drafting process, the Horizon 2020 proposal documents are now being reviewed by the European Parliament and Council.” CERN already participated in the consultation, making good use of the opportunity to contribute to the shaping of wh...
Flandera, Aleš
2016-01-01
While the formalism of isolated horizons is known for some time, only quite recently the near horizon solution of Einstein's equations has been found in the Bondi-like coordinates by Krishnan in 2012. In this framework, the space-time is regarded as the characteristic initial value problem with the initial data given on the horizon and another null hypersurface. It is not clear, however, what initial data reproduce the simplest physically relevant black hole solution, namely that of Kerr-Newman which describes stationary, axisymmetric black hole with charge. Moreover, Krishnan's construction employs the non-twisting null geodesic congruence and the tetrad which is parallelly propagated along this congruence. While the existence of such tetrad can be easily established in general, its explicit form can be very difficult to find and, in fact it has not been provided for the Kerr-Newman metric. The goal of this thesis was to fill this gap and provide a full description of the Kerr-Newman metric in the framework ...
Black hole entropy off-shell vs on-shell
Frolov, V P; Zelnikov, A I
1996-01-01
Different methods of calculation of quantum corrections to the thermodynamical characteristics of a black hole are discussed and compared. The relation between on-shell and off-shell approaches is established. The off-shell methods are used to explicitly demonstrate that the thermodynamical entropy S^{TD} of a black hole, defined by the first thermodynamical law, differs from the statistical-mechanical entropy S^{SM}, determined as S^{SM}=-\\mbox{Tr}(\\hat{\\rho}^H\\ln\\hat{\\rho}^H) for the density matrix \\hat{\\rho}^H of a black hole. It is shown that the observable thermodynamical black hole entropy can be presented in the form S^{TD}=\\pi {\\bar r}_+^2+S^{SM}-S^{SM}_{Rindler}. Here {\\bar r}_+ is the radius of the horizon shifted because of the quantum backreaction effect, and S^{SM}_{Rindler} is the statistical-mechanical entropy calculated in the Rindler space.
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.
Thermodynamics of Coherent States and Black Hole Entropy
Bashkirov, A G
2001-01-01
Mean values of any observable variable are always calculated in a coherent state as in a mixed state because the coherent state is an eigenstate of non-Hermitian operator. Thus, we propose the concept of a coherent ensemble closely resemble the canonical ensemble. The entropy and temperature are naturally defined for the coherent ensemble. As an example, entropy and temperature are evaluated for coherent states of a harmonic oscillator and quantum field described by the Klein-Gordon-Fock equation with a source term. It is shown, in particular, that the temperature of the coherent oscillator coincides with the effective temperature of a harmonic oscillator being in contact with a heath bath (Bloch formula) when the bath temperature tends to zero. The Bekenstein-Hawking entropy and temperature of a black hole can also be interpreted as an entropy and temperature of coherent states of a physical vacuum in the vicinity of a horizon surface.
Thermodynamic Interpretation of Field Equations at Horizon of BTZ Black Hole
Institute of Scientific and Technical Information of China (English)
M. Akbar
2007-01-01
A spacetime horizon comprising with a black hole singularity acts like a boundary of a thermal system associated with the notions of temperature and entropy. In the case of static metric of Banados-Teitelboim-Zanelli (BTZ) black hole, the Reid equations near the horizon boundary can be expressed as a thermal identity dE = TdS+PrdA, where E = M is the mass of BTZ black hole, dA is the change in the area of the black hole horizon when the horizon is displaced innnitesimally small, Pr is the radial pressure provided by the source of Einstein equations, S = 4πa is the entropy and T = κ/2π is the Hawking temperature associated with the horizon. This approach is studied further to generalize it for non-static BTZ black hole, showing that it is also possible to interpret the field equation near horizon as a thermodynamic identity dE = TdS + PrdA + Ω+dJ, where Ω+ is the angular velocity and J is the angular momentum of BTZ black hole. These results indicate that the Geld equations for BTZ black hole possess intrinsic thermodynamic properties near the horizon.
Entropy of a rotating and charged black string to all orders in the Planck length
Institute of Scientific and Technical Information of China (English)
Zhao Ren; Wu Yue-Qin; Zhang Li-Chun
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.
Entanglement entropy in three dimensional gravity
Maxfield, Henry
2014-01-01
The Ryu-Takayanagi and covariant Hubeny-Rangamani-Takayanagi proposals relate entanglement entropy in CFTs with holographic duals to the areas of minimal or extremal surfaces in the bulk geometry. We show how, in three dimensional pure gravity, the relevant regulated geodesic lengths can be obtained by writing a spacetime as a quotients of AdS3, with the problem reduced to a simple purely algebraic calculation. We explain how this works in both Lorentzian and Euclidean formalisms, before illustrating its use to obtain novel results in a number of examples, including rotating BTZ, the RP2 geon, and several wormhole geometries. This includes spatial and temporal dependence of single-interval entanglement entropy, despite these symmetries being broken only behind an event horizon. We also discuss considerations allowing HRT to be derived from analytic continuation of Euclidean computations in certain contexts, and a related class of complexified extremal surfaces.
Entropy Correction for Kerr Black Hole
Institute of Scientific and Technical Information of China (English)
ZHAO Ren; ZHANG Sheng-Li
2005-01-01
In this paper, we discuss leading-order corrections to the entropy of Kerr black hole due to thermal fluctuations in the finite cavity. Then temperature is constant, the solution of the black hole is obtained within a cavity, that is, the solution of the spacetime after considering the radiation of the black hole. Therefore, we derive that the location of the black hole horizon and specific heat are the functions of temperature and the radius of the cavity.Corrections to entropy also are related to the radius of the cavity. Through calculation, we obtain conditions of taking the value of the cavity's radius. We provide a new way for studying the corrections of complicated spacetimes.
Entanglement entropy in three dimensional gravity
Energy Technology Data Exchange (ETDEWEB)
Maxfield, Henry [Centre for Particle Theory & Department of Mathematical Sciences, Durham University,South Road, Durham DH1 3LE (United Kingdom)
2015-04-07
The Ryu-Takayanagi (RT) and covariant Hubeny-Rangamani-Takayanagi (HRT) proposals relate entanglement entropy in CFTs with holographic duals to the areas of minimal or extremal surfaces in the bulk geometry. We show how, in three dimensional pure gravity, the relevant regulated geodesic lengths can be obtained by writing a spacetime as a quotient of AdS{sub 3}, with the problem reduced to a simple purely algebraic calculation. We explain how this works in both Lorentzian and Euclidean formalisms, before illustrating its use to obtain novel results in a number of examples, including rotating BTZ, the ℝℙ{sup 2} geon, and several wormhole geometries. This includes spatial and temporal dependence of single-interval entanglement entropy, despite these symmetries being broken only behind an event horizon. We also discuss considerations allowing HRT to be derived from analytic continuation of Euclidean computations in certain contexts, and a related class of complexified extremal surfaces.
Relative entropy equals bulk relative entropy
Jafferis, Daniel L; Maldacena, Juan; Suh, S Josephine
2015-01-01
We consider the gravity dual of the modular Hamiltonian associated to a general subregion of a boundary theory. We use it to argue that the relative entropy of nearby states is given by the relative entropy in the bulk, to leading order in the bulk gravitational coupling. We also argue that the boundary modular flow is dual to the bulk modular flow in the entanglement wedge, with implications for entanglement wedge reconstruction.
Effects of closed topology of black hole horizon
Majhi, Abhishek
2014-01-01
Considering the quantum description of equilibrium black holes, given by the quantum isolated horizon framework in loop quantum gravity, the effect of closed topology of the horizon is studied. Black hole entropy is now given by $S=A_{cl}/4\\ell_p^2+4\\pi\\rho(A_{cl})$, where $\\rho(A_{cl})$ is a complicated function of the classical area of the horizon$(A_{cl})$. The expression is valid for any finite positive value of the Barbero-Immirzi parameter. The expression for the equilibrium temperature appearing in the first law of black hole mechanics (generalized for isolated horizons in present day literature) gets modified as a consequence. Furthermore, two very interesting predictions are made : i) there is a possible upper bound on the amount of holographic information that can be stored on the horizon of a black hole ii) the mass of a black hole is bounded above (which is at par with recent astrophysical observations based on experimental data).
Black hole evaporation without an event horizon
Bardeen, James M
2014-01-01
A reformulation of the calculation of the semi-classical energy-momentum tensor on a Schwarzschild background, the Bousso covariant entropy bound, and the ER=EPR conjecture of Maldacena and Susskind taken together suggest a scenario for the evaporation of a large spherically symmetric black hole formed in gravitational collapse in which 1) the classical r = 0 singularity is replaced by an initially small non-singular core inside an inner apparent horizon, 2) the radius of the core grows with time due to the increasing entanglement between Hawking radiation quanta outside the black hole and the Hawking partner quanta in the core contributing to the quantum back-reaction, and 3) by the Page time the trapped surfaces disappear and all quantum information stored in the interior is free to escape. The scenario preserves unitarity without any need for a "firewall" in the vicinity of the outer apparent horizon. Qbits in the Hawking radiation are never mutually entangled, and their number never exceeds the Bekenstein...
Entanglement, tensor networks and black hole horizons
Molina-Vilaplana, J.; Prior, J.
2014-11-01
We elaborate on a previous proposal by Hartman and Maldacena on a tensor network which accounts for the scaling of the entanglement entropy in a system at a finite temperature. In this construction, the ordinary entanglement renormalization flow given by the class of tensor networks known as the Multi Scale Entanglement Renormalization Ansatz (MERA), is supplemented by an additional entanglement structure at the length scale fixed by the temperature. The network comprises two copies of a MERA circuit with a fixed number of layers and a pure matrix product state which joins both copies by entangling the infrared degrees of freedom of both MERA networks. The entanglement distribution within this bridge state defines reduced density operators on both sides which cause analogous effects to the presence of a black hole horizon when computing the entanglement entropy at finite temperature in the AdS/CFT correspondence. The entanglement and correlations during the thermalization process of a system after a quantum quench are also analyzed. To this end, a full tensor network representation of the action of local unitary operations on the bridge state is proposed. This amounts to a tensor network which grows in size by adding succesive layers of bridge states. Finally, we discuss on the holographic interpretation of the tensor network through a notion of distance within the network which emerges from its entanglement distribution.
Hubeny, Veronika E
2014-01-01
A recently explored interesting quantity in AdS/CFT, dubbed 'residual entropy', characterizes the amount of collective ignorance associated with either boundary observers restricted to finite time duration, or bulk observers who lack access to a certain spacetime region. However, the previously-proposed expression for this quantity involving variation of boundary entanglement entropy (subsequently renamed to 'differential entropy') works only in a severely restrictive context. We explain the key limitations, arguing that in general, differential entropy does not correspond to residual entropy. Given that the concept of residual entropy as collective ignorance transcends these limitations, we identify two correspondingly robust, covariantly-defined constructs: a 'strip wedge' associated with boundary observers and a 'rim wedge' associated with bulk observers. These causal sets are well-defined in arbitrary time-dependent asymptotically AdS spacetimes in any number of dimensions. We discuss their relation, spec...
Information Entropy of Fullerenes.
Sabirov, Denis Sh; Ōsawa, Eiji
2015-08-24
The reasons for the formation of the highly symmetric C60 molecule under nonequilibrium conditions are widely discussed as it dominates over numerous similar fullerene structures. In such conditions, evolution of structure rather than energy defines the processes. We have first studied the diversity of fullerenes in terms of information entropy. Sorting 2079 structures from An Atlas of Fullerenes [ Fowler , P. W. ; Manolopoulos , D. E. An Atlas of Fullerenes ; Oxford : Clarendon , 1995 . ], we have found that the information entropies of only 14 fullerenes (entropy, i.e., an exclusive compound among the other members of the fullerene family. Such an efficient sorting demonstrates possible relevance of information entropy to chemical processes. For this reason, we have introduced an algorithm for calculating changes in information entropy at chemical transformations. The preliminary calculations of changes in information entropy at the selected fullerene reactions show good agreement with thermochemical data.
Modified $f(R)$ Gravity and Thermodynamics of Time-Dependent Wormholes at Event Horizon
Saiedi, H
2016-01-01
In the context of modified $f(R)$ gravity theory, we study time-dependent wormhole spacetimes in the radiation background. In this framework, we attempt to generalize the thermodynamic properties of time-dependent wormholes in $f(R)$ gravity. Finally, at event horizon, the rate of change of total entropy has been discussed.
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.
VMware Horizon Mirage essentials
Von Oven, Peter
2013-01-01
This book provides a practical, step-by-step approach to teach you how to build a successful infrastructure.This book is perfect for desktop administrators who want to deploy a solution to centrally manage their endpoint images across their entire estate using VMware Horizon Mirage. You need to have some experience in desktop image management using Microsoft Windows operating systems and Windows applications, as well as be familiar with Active Directory, SQL, IIS, and general server infrastructure relating to supporting end users.
Kaltenhauser, Kristin
2015-01-01
Expanding your horizons is a bi-annual “Science Day” for girls aged 11 to 14, held at the University of Geneva on 14 November. The girls had the opportunity to take part in hands-on workshops held by local professional women in the field of science, mathematics, engineering and technology. For the fourth time, CERN was part of this event, offering three workshops as well as a booth at the Discovery Fair, including Higgnite, an interactive visualization of the Higgs Field.
Silk, Joseph
2011-01-01
Horizons of Cosmology: Exploring Worlds Seen and Unseen is the fourth title published in the Templeton Science and Religion Series, in which scientists from a wide range of fields distill their experience and knowledge into brief tours of their respective specialties. In this volume, highly esteemed astrophysicist Joseph Silk explores the vast mysteries and speculations of the field of cosmology in a way that balances an accessible style for the general reader and enough technical detail for advanced students and professionals. Indeed, while the p
2015-09-29
understanding of high entropy alloys from phase diagram calculations. Calphad 45, 1–10 (2014). 29. Santodonato, L. et al. Deviation from high-entropy...exist, which exhibit them. Inspired by research activities in the metal alloy communities and fundamental principles of thermodynamics we extend the...yields a single- phase material. The second experiment uses five individual phase diagrams to explore the configurational entropy versus composition trend
Special Issue: Tsallis Entropy
Anastasios Anastasiadis
2012-01-01
One of the crucial properties of the Boltzmann-Gibbs entropy in the context of classical thermodynamics is extensivity, namely proportionality with the number of elements of the system. The Boltzmann-Gibbs entropy satisfies this prescription if the subsystems are statistically (quasi-) independent, or typically if the correlations within the system are essentially local. In such cases the energy of the system is typically extensive and the entropy is additive. In general, however, the situati...
The Homological Nature of Entropy
Directory of Open Access Journals (Sweden)
Pierre Baudot
2015-05-01
Full Text Available We propose that entropy is a universal co-homological class in a theory associated to a family of observable quantities and a family of probability distributions. Three cases are presented: (1 classical probabilities and random variables; (2 quantum probabilities and observable operators; (3 dynamic probabilities and observation trees. This gives rise to a new kind of topology for information processes, that accounts for the main information functions: entropy, mutual-informations at all orders, and Kullback–Leibler divergence and generalizes them in several ways. The article is divided into two parts, that can be read independently. In the first part, the introduction, we provide an overview of the results, some open questions, future results and lines of research, and discuss briefly the application to complex data. In the second part we give the complete definitions and proofs of the theorems A, C and E in the introduction, which show why entropy is the first homological invariant of a structure of information in four contexts: static classical or quantum probability, dynamics of classical or quantum strategies of observation of a finite system.
P. Mitra
1994-01-01
In the talk different definitions of the black hole entropy are discussed and compared. It is shown that the Bekenstein-Hawking entropy $S^{BH}$ (defined by the response of the free energy of a system containing a black hole on the change of the temperature) differs from the statistical- mechanical entropy $S^{SM}=-\\mbox{Tr}(\\hat{\\rho}\\ln \\hat{\\rho})$ (defined by counting internal degrees of freedom of a black hole). A simple explanation of the universality of the Bekenstein-Hawking entropy (...
Frolov, V
1994-01-01
In the talk different definitions of the black hole entropy are discussed and compared. It is shown that the Bekenstein-Hawking entropy S^{BH} (defined by the response of the free energy of a system containing a black hole on the change of the temperature) differs from the statistical- mechanical entropy S^{SM}=-\\mbox{Tr}(\\hat{\\rho}\\ln \\hat{\\rho}) (defined by counting internal degrees of freedom of a black hole). A simple explanation of the universality of the Bekenstein-Hawking entropy (i.e. its independence of the number and properties of the fields which might contribute to S^{SM}) is given.
The gravity dual of Rényi entropy
Dong, Xi
2016-08-01
A remarkable yet mysterious property of black holes is that their entropy is proportional to the horizon area. This area law inspired the holographic principle, which was later realized concretely in gauge-gravity duality. In this context, entanglement entropy is given by the area of a minimal surface in a dual spacetime. However, discussions of area laws have been constrained to entanglement entropy, whereas a full understanding of a quantum state requires Rényi entropies. Here we show that all Rényi entropies satisfy a similar area law in holographic theories and are given by the areas of dual cosmic branes. This geometric prescription is a one-parameter generalization of the minimal surface prescription for entanglement entropy. Applying this we provide the first holographic calculation of mutual Rényi information between two disks of arbitrary dimension. Our results provide a framework for efficiently studying Rényi entropies and understanding entanglement structures in strongly coupled systems and quantum gravity.
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.
Universal canonical entropy for gravitating systems
Indian Academy of Sciences (India)
Ashok Chatterjee; Parthasarathi Majumdar
2004-10-01
The thermodynamics of general relativistic systems with boundary, obeying a Hamiltonian constraint in the bulk, is determined solely by the boundary quantum dynamics, and hence by the area spectrum. Assuming, for large area of the boundary, (a) an area spectrum as determined by non-perturbative canonical quantum general relativity (NCQGR), (b) an energy spectrum that bears a power law relation to the area spectrum, (c) an area law for the leading order microcanonical entropy, leading thermal fluctuation corrections to the canonical entropy are shown to be logarithmic in area with a universal coefficient. Since the microcanonical entropy also has universal logarithmic corrections to the area law (from quantum space-time fluctuations, as found earlier) the canonical entropy then has a universal form including logarithmic corrections to the area law. This form is shown to be independent of the index appearing in assumption (b). The index, however, is crucial in ascertaining the domain of validity of our approach based on thermal equilibrium.
Probabilistic solution of relative entropy weighted control
Bierkens, Joris
2012-01-01
We show that stochastic control problems with a particular cost structure involving a relative entropy term admit a purely probabilistic solution, without the necessity of applying the dynamic programming principle. The argument is as follows. Minimization of the expectation of a random variable with respect to the underlying probability measure, penalized by relative entropy, may be solved exactly. In the case where the randomness is generated by a standard Brownian motion, this exact solution can be written as a Girsanov density. The stochastic process appearing in the Girsanov exponent has the role of control process, and the relative entropy of the change of probability measure is equal to the integral of the square of this process. An explicit expression for the control process may be obtained in terms of the Malliavin derivative of the density process. The theory is applied to the problem of minimizing the maximum of a Brownian motion (penalized by the relative entropy), leading to an explicit expressio...
Partial Transfer Entropy on Rank Vectors
Kugiumtzis, Dimitris
2013-01-01
For the evaluation of information flow in bivariate time series, information measures have been employed, such as the transfer entropy (TE), the symbolic transfer entropy (STE), defined similarly to TE but on the ranks of the components of the reconstructed vectors, and the transfer entropy on rank vectors (TERV), similar to STE but forming the ranks for the future samples of the response system with regard to the current reconstructed vector. Here we extend TERV for multivariate time series, and account for the presence of confounding variables, called partial transfer entropy on ranks (PTERV). We investigate the asymptotic properties of PTERV, and also partial STE (PSTE), construct parametric significance tests under approximations with Gaussian and gamma null distributions, and show that the parametric tests cannot achieve the power of the randomization test using time-shifted surrogates. Using simulations on known coupled dynamical systems and applying parametric and randomization significance tests, we s...
Generalized second law of thermodynamics for non-canonical scalar field model with corrected-entropy
Das, Sudipta; Debnath, Ujjal; Mamon, Abdulla Al
2015-10-01
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.
Generalized Second Law of Thermodynamics for Non-canonical Scalar Field Model with Corrected-Entropy
Das, Sudipta; Mamon, Abdulla Al
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.
Generalized second law of thermodynamics for non-canonical scalar field model with corrected-entropy
Energy Technology Data Exchange (ETDEWEB)
Das, Sudipta; Mamon, Abdulla Al [Visva-Bharati, Department of Physics, Santiniketan (India); Debnath, Ujjal [Indian Institute of Engineering Science and Technology, Department of Mathematics, Shibpur, Howrah (India)
2015-10-15
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.)
Black hole entropy from non-perturbative gauge theory
Kabat, D; Lowe, D A; Kabat, Daniel; Lifschytz, Gilad; Lowe, David A.
2001-01-01
We present the details of a mean-field approximation scheme for the quantum mechanics of N D0-branes at finite temperature. The approximation can be applied at strong 't Hooft coupling. We find that the resulting entropy is in good agreement with the Bekenstein-Hawking entropy of a ten-dimensional non-extremal black hole with 0-brane charge. This result is in accord with the duality conjectured by Itzhaki, Maldacena, Sonnenschein and Yankielowicz. We discuss ways of resolving the black hole horizon, and also study the spectrum of single-string excitations within the quantum mechanics.
Statistical Entropy of Horowitz-Strominger Black Hole
Institute of Scientific and Technical Information of China (English)
ZHAO Ren; ZHANG Jun-Fang; ZHANG Li-Chun
2002-01-01
The partition functions of bosonic and fermionic fields in Horowitz Strominger black hole are deriveddirectly by quantum statistical method. Then via the improved brick-wall method (membrane model), the statisticalentropy of black hole is obtained. If a proper parameter is chosen in our result, it is found out that the entropy isproportional to the area of horizon. The stripped term and the divergent logarithmic term in the original brick-wallmethod no longer exist. The difficulty in solving the wave equations of scalar and Dirac fields is avoided. A new neatway of calculating the entropy of various complicated black holes is offered.
A Comparative Study of Different Entropies in Fractal Universe
Haldar, Sourav; Chakraborty, Subenoy
2016-01-01
Here we make an attempt to extend the idea of generalized Hawking temperature and modified Bekenstein entropy at event horizon in fractal universe. The modified Hawking temperature and Bekenstein entropy is considered in the governing Friedmann equations, which is modified in the background of a fractal universe. The validity of the Generalised second law of thermodynamics (GSLT) and Thermodynamic Equilibrium (TE) have been examined in a fractal universe filled with perfect fluid having constant equation of state in four different generalized Bekenstein system. Finally both laws are examined and compared numerically in all four cases.
The scaling of black hole entropy in loop quantum gravity
Ghosh, Amit
2012-01-01
We discuss some general properties of black hole entropy in loop quantum gravity from the perspective of local stationary observers at distance l from the horizon. The present status of the theory indicates that black hole entropy differs from the low energy (IR) expected value A/(4G) (in natural units) in the deep Planckian regime (UV). The partition function is well defined if the number of non-geometric degrees of freedom g_M (encoding the degeneracy of the area a_p eigenvalue at a puncture p) satisfy the holographic bound g_M S_IR=A/(4 G) as the scale l flows.
Near-Horizon Conformal Structure of Black Holes
Birmingham, Daniel; Sen, S; Birmingham, Danny; Gupta, Kumar S.; Sen, Siddhartha
2001-01-01
The near-horizon properties of a black hole are studied within an algebraic framework, using a scalar field as a simple probe to analyze the geometry. The operator H governing the near-horizon dynamics of the scalar field contains an inverse square interaction term. It is shown that the operators appearing in the corresponding algebraic description belong to the representation space of the Virasoro algebra. The operator H is studied using the representation theory of the Virasoro algebra. We observe that the wave functions exhibit scaling behaviour in a band-like region near the horizon of the black hole.
Can a particle detector cross a Cauchy horizon?
Juárez-Aubry, Benito A
2015-01-01
Cauchy horizons are well known to exhibit instabilities in classical spacetime dynamics and singularities in quantum field theory. We analyse the response of an Unruh-DeWitt particle detector that falls towards a Cauchy horizon, in terms of the specifics of the horizon, the choice of the quantum state and the specifics of the detector's trajectory. As a prototype, we study in detail the case for the $1+1$ Reissner-Nordstr\\"om black hole with a scalar field in the Hartle-Hawking state. Comparisons are made with the response of a detector that falls into a Schwarzschild-like singularity.
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.
Fountain, Glen H; Hersman, Christopher B; Herder, Timothy S; Coughlin, Thomas B; Gibson, William C; Clancy, Deborah A; DeBoy, Christopher C; Hill, T Adrian; Kinnison, James D; Mehoke, Douglas S; Ottman, Geffrey K; Rogers, Gabe D; Stern, S Alan; Stratton, James M; Vernon, Steven R; Williams, Stephen P
2007-01-01
The New Horizons spacecraft was launched on 19 January 2006. The spacecraft was designed to provide a platform for seven instruments that will collect and return data from Pluto in 2015. The design drew on heritage from previous missions developed at The Johns Hopkins University Applied Physics Laboratory (APL) and other missions such as Ulysses. The trajectory design imposed constraints on mass and structural strength to meet the high launch acceleration needed to reach the Pluto system prior to the year 2020. The spacecraft subsystems were designed to meet tight mass and power allocations, yet provide the necessary control and data handling finesse to support data collection and return when the one-way light time during the Pluto flyby is 4.5 hours. Missions to the outer solar system require a radioisotope thermoelectric generator (RTG) to supply electrical power, and a single RTG is used by New Horizons. To accommodate this constraint, the spacecraft electronics were designed to operate on less than 200 W....
Instability of enclosed horizons
Kay, Bernard S
2013-01-01
We study the classical massless scalar wave equation on the region of 1+1-dimensional Minkowski space between the two branches of the hyperbola $x^2-t^2=1$ with vanishing boundary conditions on it. We point out that there are initially finite-energy initially, say, right-going waves for which the stress-energy tensor becomes singular on the null-line $t+x=0$. We also construct the quantum theory of this system and show that, while there is a regular Hartle-Hawking-Israel-like state, there are coherent states built on this for which there is a similar singularity in the expectation value of the renormalized stress-energy tensor. We conjecture that in 1+3-dimensional situations with 'enclosed horizons' such as a (maximally extended) Schwarzschild black hole in equilibrium in a stationary box or the (maximally extended) Schwarzschild-AdS spacetime, there will be a similar singularity at the horizon and that would signal an instability when matter perturbations and/or gravity are switched on. Such an instability ...
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)
2016-10-28
We show that the spectrum of normalizable states on a Euclidean SL(2, R)/U(1) black hole exhibits a duality between oscillator states and wound strings. This duality generalizes the identification between a normalizable mode of dilaton gravity on the cigar and a mode of the tachyon with winding number one around the Euclidean time circle, which plays an important role in the FZZ correspondence. It implies that normalizable states on a large Euclidean black hole have support at widely separated scales. In particular, localized states that are extended over the cap of the cigar (the Euclidian analog of the black hole atmosphere) have a component that is localized near the tip of the cigar (the analog of the stretched horizon). As a consequence of this duality, the states exhibit a transition as a function of radial excitation level. From the perspective of a low energy probe, low lying states are naturally thought of as oscillator states in the black hole atmosphere, while at large excitation level they are naturally described as wound strings. As the excitation level increases, the size of the states first decreases and then increases. This behavior is expected to be a general feature of black hole horizons in string theory.
Horizon as Critical Phenomenon
Lee, Sung-Sik
2016-01-01
We show that renormalization group(RG) flow can be viewed as a gradual wave function collapse, where a quantum state associated with the action of field theory evolves toward a final state that describes an IR fixed point. The process of collapse is described by the radial evolution in the dual holographic theory. If the theory is in the same phase as the assumed IR fixed point, the initial state is smoothly projected to the final state. If in a different phase, the initial state undergoes a phase transition which in turn gives rise to a horizon in the bulk geometry. We demonstrate the connection between critical behavior and horizon in an example, by deriving the bulk metrics that emerge in various phases of the U(N) vector model in the large N limit based on the holographic dual constructed from quantum RG. The gapped phase exhibits a geometry that smoothly ends at a finite proper distance in the radial direction. The geometric distance in the radial direction measures a complexity : the depth of RG transfo...
Giveon, Amit; Itzhaki, Nissan; Kutasov, David
2016-10-01
We show that the spectrum of normalizable states on a Euclidean SL(2, R)/U(1) black hole exhibits a duality between oscillator states and wound strings. This duality generalizes the identification between a normalizable mode of dilaton gravity on the cigar and a mode of the tachyon with winding number one around the Euclidean time circle, which plays an important role in the FZZ correspondence. It implies that normalizable states on a large Euclidean black hole have support at widely separated scales. In particular, localized states that are extended over the cap of the cigar (the Euclidian analog of the black hole atmosphere) have a component that is localized near the tip of the cigar (the analog of the stretched horizon). As a consequence of this duality, the states exhibit a transition as a function of radial excitation level. From the perspective of a low energy probe, low lying states are naturally thought of as oscillator states in the black hole atmosphere, while at large excitation level they are naturally described as wound strings. As the excitation level increases, the size of the states first decreases and then increases. This behavior is expected to be a general feature of black hole horizons in string theory.
Projective Power Entropy and Maximum Tsallis Entropy Distributions
Shinto Eguchi; Shogo Kato; Osamu Komori
2011-01-01
We discuss a one-parameter family of generalized cross entropy between two distributions with the power index, called the projective power entropy. The cross entropy is essentially reduced to the Tsallis entropy if two distributions are taken to be equal. Statistical and probabilistic properties associated with the projective power entropy are extensively investigated including a characterization problem of which conditions uniquely determine the projective power entropy up to the power index...
Mathur, Samir D
2013-01-01
The Schwarzschild metric has an apparent singularity at the horizon r=2M. What really happens there? If physics at the horizon is 'normal' laboratory physics, then we run into Hawking's information paradox. If we want nontrivial structure at the horizon, then we need a mechanism to generate this structure that evades the 'no hair' conjectures of the past. Further, if we have such structure, then what would the role of the traditional black hole metric which continues smoothly past the horizon? Recent work has provided an answer to these questions, and in the process revealed a beautiful tie-up between gravity, string theory and thermodynamics.
Mathur, Samir D.
2013-07-01
The Schwarzschild metric has an apparent singularity at the horizon r = 2M. What really happens there? If physics at the horizon is "normal" laboratory physics, then we run into Hawking's information paradox. If we want nontrivial structure at the horizon, then we need a mechanism to generate this structure that evades the "no hair" conjectures of the past. Further, if we have such structure, then what would be the role of the traditional black hole metric which continues smoothly past the horizon? Recent work has provided an answer to these questions, and in the process revealed a beautiful tie-up between gravity, string theory and thermodynamics.