Configurational entropy of charged AdS black holes

Directory of Open Access Journals (Sweden)

Chong Oh Lee

2017-09-01

Full Text Available When we consider charged AdS black holes in higher dimensional spacetime and a molecule number density along coexistence curves is numerically extended to higher dimensional cases. It is found that a number density difference of a small and large black holes decrease as a total dimension grows up. In particular, we find that a configurational entropy is a concave function of a reduced temperature and reaches a maximum value at a critical (second-order phase transition point. Furthermore, the bigger a total dimension becomes, the more concave function in a configurational entropy while the more convex function in a reduced pressure.

Benzofuranoid and bicyclooctanoid neolignans:absolute configuration

International Nuclear Information System (INIS)

Alvarenga, M.A. de; Giesbrecht, A.M.; Gottlieb, O.R.; Yoshida, M.

1977-01-01

The naturally occuring benzofuranoid and bicyclo (3,2,1) octanoid neolignans have their relative configurations established by 1 H and 13 C NMR, inclusively with aid of the solvent shift technique. Interconversion of the benzofuranoid type compounds, as well as for a benzofuranoid to a bicyclooctanoid derivate, make ORD correlations, ultimately with (2S, 3S) - and (2R,3R)-2,3- dihydrobenzofurans, possible, and led to the absolute configurations of both series of neolignans [pt

Total Synthesis and Absolute Configuration of the Marine Norditerpenoid Xestenone

Directory of Open Access Journals (Sweden)

Hiroaki Miyaoka

2009-11-01

Full Text Available Xestenone is a marine norditerpenoid found in the northeastern Pacific sponge Xestospongia vanilla. The relative configuration of C-3 and C-7 in xestenone was determined by NOESY spectral analysis. However the relative configuration of C-12 and the absolute configuration of this compound were not determined. The authors have now achieved the total synthesis of xestenone using their developed one-pot synthesis of cyclopentane derivatives employing allyl phenyl sulfone and an epoxy iodide as a key step. The relative and absolute configurations of xestenone were thus successfully determined by this synthesis.

Configurational entropy and effective temperature in systems of active Brownian particles

NARCIS (Netherlands)

Preisler, Zdeněk; Dijkstra, Marjolein

2016-01-01

We propose a method to determine the effective density of states and configurational entropy in systems of active Brownian particles by measuring the probability distribution function of potential energy at varying temperatures. Assuming that the entropy is a continuous and monotonically increasing

Breaking the glass ceiling: Configurational entropy measurements in extremely supercooled liquids

Science.gov (United States)

Berthier, Ludovic

Liquids relax extremely slowly on approaching the glass state. One explanation is that an entropy crisis, due to the rarefaction of available states, makes it increasingly arduous to reach equilibrium in that regime. Validating this scenario is challenging, because experiments offer limited resolution, while numerical studies lag more than eight orders of magnitude behind experimentally-relevant timescales. In this work we not only close the colossal gap between experiments and simulations but manage to create in-silico configurations that have no experimental analog yet. Deploying a range of computational tools, we obtain four independent estimates of their configurational entropy. These measurements consistently indicate that the steep entropy decrease observed in experiments is found in simulations even beyond the experimental glass transition. Our numerical results thus open a new observational window into the physics of glasses and reinforce the relevance of an entropy crisis for understanding their formation.

Ergodicity, configurational entropy and free energy in pigment solutions and plant photosystems: influence of excited state lifetime.

Science.gov (United States)

Jennings, Robert C; Zucchelli, Giuseppe

2014-01-01

We examine ergodicity and configurational entropy for a dilute pigment solution and for a suspension of plant photosystem particles in which both ground and excited state pigments are present. It is concluded that the pigment solution, due to the extreme brevity of the excited state lifetime, is non-ergodic and the configurational entropy approaches zero. Conversely, due to the rapid energy transfer among pigments, each photosystem is ergodic and the configurational entropy is positive. This decreases the free energy of the single photosystem pigment array by a small amount. On the other hand, the suspension of photosystems is non-ergodic and the configurational entropy approaches zero. The overall configurational entropy which, in principle, includes contributions from both the single excited photosystems and the suspension which contains excited photosystems, also approaches zero. Thus the configurational entropy upon photon absorption by either a pigment solution or a suspension of photosystem particles is approximately zero. Copyright © 2014 Elsevier B.V. All rights reserved.

Configurational entropy and ρ and ϕ mesons production in QCD

Science.gov (United States)

Karapetyan, G.

2018-06-01

In the present work the electroproduction for diffractive ρ and ϕ mesons by considering AdS/QCD correspondence and Color Glass Condensate (CGC) approximation are studied with respect to the associated dipole cross section, whose parameters are studied and analysed in the framework of the configurational entropy. Our results suggest different quantum states of the nuclear matter, showing that the extremal points of the nuclear configurational entropy is able to reflect a true description of the ρ and ϕ mesons production, using current data concerning light quark masses. During the computations parameters, obtained in fitting procedure, coincide to the experimental within ∼ 0.1%.

Configurational entropy measurements in extremely supercooled liquids that break the glass ceiling

Science.gov (United States)

Berthier, Ludovic; Charbonneau, Patrick; Coslovich, Daniele; Ninarello, Andrea; Ozawa, Misaki; Yaida, Sho

2017-10-01

Liquids relax extremely slowly on approaching the glass state. One explanation is that an entropy crisis, because of the rarefaction of available states, makes it increasingly arduous to reach equilibrium in that regime. Validating this scenario is challenging, because experiments offer limited resolution, while numerical studies lag more than eight orders of magnitude behind experimentally relevant timescales. In this work, we not only close the colossal gap between experiments and simulations but manage to create in silico configurations that have no experimental analog yet. Deploying a range of computational tools, we obtain four estimates of their configurational entropy. These measurements consistently confirm that the steep entropy decrease observed in experiments is also found in simulations, even beyond the experimental glass transition. Our numerical results thus extend the observational window into the physics of glasses and reinforce the relevance of an entropy crisis for understanding their formation.

Utilization of 1H NMR in the determination of absolute configuration of alcohols

International Nuclear Information System (INIS)

Barreiros, Marizeth L.; David, Jorge M.; David, Juceni P. . E-juceni@ufba.br

2005-01-01

This review reports the determination of absolute configuration of primary and secondary alcohols by 1 H NMR spectroscopy, using the Mosher method. This method consists in the derivatization of an alcohol possessing unknown absolute configuration with one or both enantiomers of an auxiliary reagent. The resulting diastereoisomer spectra are registered and compared, and the chemical shift differences (Δδ R,S = δ R - δ S ) are measured. The determination of the absolute configuration of the alcohol molecule is based on the correlation between its chiral center and the auxiliary reagent's chiral center. Therefore, the determination of the absolute configuration depends on aromatic ring shielding effects on the substituents of the alcohol as evidenced by the 1 H NMR spectrum. (author)

Confirmation of the absolute configuration of (−)-aurantioclavine

KAUST Repository

Behenna, Douglas C.; Krishnan, Shyam; Stoltz, Brian M.

2011-01-01

We confirm our previous assignment of the absolute configuration of (-)-aurantioclavine as 7R by crystallographically characterizing an advanced 3-bromoindole intermediate reported in our previous synthesis. This analysis also provides additional

Configurational entropy of polar glass formers and the effect of electric field on glass transition

Energy Technology Data Exchange (ETDEWEB)

Matyushov, Dmitry V., E-mail: dmitrym@asu.edu [Department of Physics and School of Molecular Sciences, Arizona State University, P.O. Box 871504, Tempe, Arizona 85287 (United States)

2016-07-21

A model of low-temperature polar liquids is constructed that accounts for the configurational heat capacity, entropy, and the effect of a strong electric field on the glass transition. The model is based on the Padé-truncated perturbation expansions of the liquid state theory. Depending on parameters, it accommodates an ideal glass transition of vanishing configurational entropy and its avoidance, with a square-root divergent enumeration function at the point of its termination. A composite density-temperature parameter ρ{sup γ}/T, often used to represent combined pressure and temperature data, follows from the model. The theory is in good agreement with the experimental data for excess (over the crystal state) thermodynamics of molecular glass formers. We suggest that the Kauzmann entropy crisis might be a signature of vanishing configurational entropy of a subset of degrees of freedom, multipolar rotations in our model. This scenario has observable consequences: (i) a dynamical crossover of the relaxation time and (ii) the fragility index defined by the ratio of the excess heat capacity and excess entropy at the glass transition. The Kauzmann temperature of vanishing configurational entropy and the corresponding glass transition temperature shift upward when the electric field is applied. The temperature shift scales quadratically with the field strength.

Configurational entropy of polar glass formers and the effect of electric field on glass transition.

Science.gov (United States)

Matyushov, Dmitry V

2016-07-21

A model of low-temperature polar liquids is constructed that accounts for the configurational heat capacity, entropy, and the effect of a strong electric field on the glass transition. The model is based on the Padé-truncated perturbation expansions of the liquid state theory. Depending on parameters, it accommodates an ideal glass transition of vanishing configurational entropy and its avoidance, with a square-root divergent enumeration function at the point of its termination. A composite density-temperature parameter ρ(γ)/T, often used to represent combined pressure and temperature data, follows from the model. The theory is in good agreement with the experimental data for excess (over the crystal state) thermodynamics of molecular glass formers. We suggest that the Kauzmann entropy crisis might be a signature of vanishing configurational entropy of a subset of degrees of freedom, multipolar rotations in our model. This scenario has observable consequences: (i) a dynamical crossover of the relaxation time and (ii) the fragility index defined by the ratio of the excess heat capacity and excess entropy at the glass transition. The Kauzmann temperature of vanishing configurational entropy and the corresponding glass transition temperature shift upward when the electric field is applied. The temperature shift scales quadratically with the field strength.

Calculating the configurational entropy of a landscape mosaic

Science.gov (United States)

Samuel A. Cushman

2016-01-01

Applications of entropy and the second law of thermodynamics in landscape ecology are rare and poorly developed. This is a fundamental limitation given the centrally important role the second law plays in all physical and biological processes. A critical first step to exploring the utility of thermodynamics in landscape ecology is to define the configurational...

Antiausterity activity of arctigenin enantiomers: importance of (2R,3R)-absolute configuration.

Science.gov (United States)

Awale, Suresh; Kato, Mamoru; Dibwe, Dya Fita; Li, Feng; Miyoshi, Chika; Esumi, Hiroyasu; Kadota, Shigetoshi; Tezuka, Yasuhiro

2014-01-01

From a MeOH extract of powdered roots of Wikstroemia indica, six dibenzyl-gamma-butyrolactone-type lignans with (2S,3S)-absolute configuration [(+)-arctigenin (1), (+)-matairesinol (2), (+)-trachelogenin (3), (+)-nortrachelogenin (4), (+)-hinokinin (5), and (+)-kusunokinin (6)] were isolated, whereas three dibenzyl-gamma-butyrolactone-type lignans with (2R,3R)-absolute configuration [(-)-arctigenin (1*), (-)-matairesinol (2*), (-)-trachelogenin (3*)] were isolated from Trachelospermum asiaticum. The in vitro preferential cytotoxic activity of the nine compounds was evaluated against human pancreatic PANC-1 cancer cells in nutrient-deprived medium (NDM), but none of the six lignans (1-6) with (2S,3S)-absolute configuration showed preferential cytotoxicity. On the other hand, three lignans (1*-3*) with (2R,3R)-absolute configuration exhibited preferential cytotoxicity in a concentration-dependent manner with PC50 values of 0.54, 6.82, and 5.85 microM, respectively. Furthermore, the effect of (-)- and (+)-arctigenin was evaluated against the activation of Akt, which is a key process in the tolerance to nutrition starvation. Interestingly, only (-)-arctigenin (1*) strongly suppressed the activation of Akt. These results indicate that the (2R,3R)-absolute configuration of (-)-enantiomers should be required for the preferential cytotoxicity through the inhibition of Akt activation.

Prediction of absolute entropy of ideal gas at 298 K of pure chemicals through GAMLR and FFNN

International Nuclear Information System (INIS)

Fazeli, Ali; Bagheri, Mehdi; Ghaniyari-Benis, Saeid; Aslebagh, Roshanak; Kamaloo, Elaheh

2011-01-01

Thermodynamical optimization for energy conversion system can be performed by decreasing entropy generation. For calculation of entropy, we need to know entropy of ideal gases at 298 K as a reference point. Entropy is a thermodynamic quantity which is not easily measured and prediction of entropy by molecular structures for new designed molecules may be a challenge. An easy and accurate equation for prediction of absolute entropy of pure ideal gas at 298 K was introduced for the first time based on the quantitative structure property relationship (QSPR) approach. Thousand seven hundred pure chemical compounds and 3224 molecular descriptors were used for finding this easy equation by genetic algorithm multi-linear regression (GAMLR) subset variable selection. Our work are based on 1700 chemicals in 81 chemical families that is the most comprehensive available data sets for absolute entropy of ideal gases. The final model is linear and has three molecular descriptors with the squared correlation coefficient of 0.9885 (R 2 = 0.9885). Also, feed forward neural network (FFNN) was used for considering non linearity effect of the model. It has the squared correlation coefficient of 0.9909 (R 2 = 0.9909). The model passes all validity check methods. The novel proposed model has the predictability for new designed molecules by having the molecular structures of them.

Absolute configuration and antiprotozoal activity of minquartynoic acid

DEFF Research Database (Denmark)

Rasmussen, H B; Christensen, Søren Brøgger; Kvist, L P

2000-01-01

Minquartynoic acid (1) was isolated as an antimalarial and antileishmanial constituent of the Peruvian tree Minquartia guianensis and its absolute configuration at C-17 established to be (+)-S through conversion to the known (+)-(S)-17-hydroxystearic acid (2) and confirmed using Mosher's method....

Distance-Based Configurational Entropy of Proteins from Molecular Dynamics Simulations.

Science.gov (United States)

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.

Structure and Absolute Configuration of Nyasol and Hinokiresinol via Synthesis and Vibrational Circular Dichroism Spectroscopy

DEFF Research Database (Denmark)

Lassen, Peter Rygaard

2005-01-01

The absolute configuration of the norlignan (+)-nyasol was determined to be S by comparison of the experimental vibrational circular dichroism data with first-principle calculations taking into account the eight lowest energy conformations. The established absolute configuration of (+)-nyasol...... enables establishment of the absolute configuration of (-)-hinokiresinol, which is concluded to be S. A total synthesis and resolution of hinokiresinol has been performed to resolve the conflicting reports of the coupling constant of the vinylic protons of the disubstituted double bond in this molecule...

Confirmation of the absolute configuration of (−)-aurantioclavine

KAUST Repository

Behenna, Douglas C.

2011-04-01

We confirm our previous assignment of the absolute configuration of (-)-aurantioclavine as 7R by crystallographically characterizing an advanced 3-bromoindole intermediate reported in our previous synthesis. This analysis also provides additional support for our model of enantioinduction in the palladium(II)-catalyzed oxidative kinetic resolution of secondary alcohols. © 2010 Elsevier Ltd. All rights reserved.

Maximum entropy reconstruction of the configurational density of states from microcanonical simulations

International Nuclear Information System (INIS)

Davis, Sergio

2013-01-01

In this work we develop a method for inferring the underlying configurational density of states of a molecular system by combining information from several microcanonical molecular dynamics or Monte Carlo simulations at different energies. This method is based on Jaynes' Maximum Entropy formalism (MaxEnt) for Bayesian statistical inference under known expectation values. We present results of its application to measure thermodynamic entropy and free energy differences in embedded-atom models of metals.

Configurational Information as Potentially Negative Entropy: The Triple Helix Model

Directory of Open Access Journals (Sweden)

Loet Leydesdorff

2008-10-01

Full Text Available Configurational information is generated when three or more sources of variance interact. The variations not only disturb each other relationally, but by selecting upon each other, they are also positioned in a configuration. A configuration can be stabilized and/or globalized. Different stabilizations can be considered as second-order variation, and globalization as a second-order selection. The positive manifestations and the negative selections operate upon one another by adding and reducing uncertainty, respectively. Reduction of uncertainty in a configuration can be measured in bits of information. The variables can also be considered as dimensions of the probabilistic entropy in the system(s under study. The configurational information then provides us with a measure of synergy within a complex system. For example, the knowledge base of an economy can be considered as such a synergy in the otherwise virtual (that is, fourth dimension of a regime

The iso-structural viscosity, configurational entropy and fragility of oxide liquids

DEFF Research Database (Denmark)

Yue, Yuanzheng

2009-01-01

the variation of the configurational entropy (Sc) with temperature (T) are obtained from the Avramov-Milchev (AM) and the Vogel-Fulcher- Tammann (VFT) viscosity equations, respectively. The two Sc(T) functions exhibit different relations to the liquid fragility. The AM Sc(T) function is a power function...

Communication: Probing the absolute configuration of chiral molecules at aqueous interfaces

Energy Technology Data Exchange (ETDEWEB)

Lotze, Stephan, E-mail: lotze@amolf.nl; Versluis, Jan [FOM Institute for Atomic and Molecular Physics, Science Park 104, 1098 XG Amsterdam (Netherlands); Olijve, Luuk L. C.; Schijndel, Luuk van; Milroy, Lech G.; Voets, Ilja K. [Laboratory of Macromolecular and Organic Chemistry, Department of Chemical Engineering and Chemistry, and Institute for Complex Molecular Systems, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven (Netherlands); Bakker, Huib J., E-mail: bakker@amolf.nl [FOM Institute AMOLF, Science Park 104, 1098 XG Amsterdam (Netherlands)

2015-11-28

We demonstrate that the enantiomers of chiral macromolecules at an aqueous interface can be distinguished with monolayer sensitivity using heterodyne-detected vibrational sum-frequency generation (VSFG). We perform VSFG spectroscopy with a polarization combination that selectively probes chiral molecular structures. By using frequencies far detuned from electronic resonances, we probe the chiral macromolecular structures with high surface specificity. The phase of the sum-frequency light generated by the chiral molecules is determined using heterodyne detection. With this approach, we can distinguish right-handed and left-handed helical peptides at a water-air interface. We thus show that heterodyne-detected VSFG is sensitive to the absolute configuration of complex, interfacial macromolecules and has the potential to determine the absolute configuration of enantiomers at interfaces.

Absolute configurations of zingiberenols isolated from ginger (Zingiber officinale) rhizomes

Science.gov (United States)

The sesquiterpene alcohol zingiberenol, or 1,10-bisaboladien-3-ol, was isolated some time ago from ginger, Zingiber officinale, rhizomes, but its absolute configuration had not been determined. With three chiral centers present in the molecule, zingiberenol can exist in eight stereoisomeric forms. ...

Absolute configuration of some dinorlabdanes from the copaiba oil

Energy Technology Data Exchange (ETDEWEB)

Romero, Adriano L.; Baptistela, Lucia H.B.; Imamura, Paulo M. [Universidade Estadual de Campinas (UNICAMP), SP (Brazil). Inst. de Quimica], e-mail: imam@iqm.unicamp.br

2009-07-01

A novel ent-dinorlabdane ({iota})-13(R)-14,15-dinorlabd-8(17)-ene-3,13-diol was isolated from commercial copaiba oil along with two known dinorlabdanes. The absolute configuration of these dinorditerpenes was established for the first time through synthesis starting from known ({iota})-3-hydroxycopalic acid, which was also isolated from the same oleoresin. (author)

Synthesis and absolute configurations of the cytotoxic polyacetylenes isolated from the callus of Panax ginseng.

Science.gov (United States)

Fujimoto, Y; Satoh, M; Takeuchi, N; Kirisawa, M

1990-06-01

Panaxacol (1) and dihydropanaxacol (2), cytotoxic polyacetylenes isolated from the callus of Panax ginseng, were synthesized starting from D-(-)-diethyl tartrate. The absolute configuration of 1 was determined to be 9R, 10R and the absolute configuration at C-3 of 2 was tentatively assigned as 3S by the application of the R(+)-alpha-methoxy-alpha-(trifluoro methyl)phenylacetyl (MTPA) method.

Explaining the entropy concept and entropy components

Directory of Open Access Journals (Sweden)

Marko Popovic

2018-04-01

Full Text Available Total entropy of a thermodynamic system consists of two components: thermal entropy due to energy, and residual entropy due to molecular orientation. In this article, a three-step method for explaining entropy is suggested. Step one is to use a classical method to introduce thermal entropy STM as a function of temperature T and heat capacity at constant pressure Cp: STM = ∫(Cp/T dT. Thermal entropy is the entropy due to uncertainty in motion of molecules and vanishes at absolute zero (zero-point energy state. It is also the measure of useless thermal energy that cannot be converted into useful work. The next step is to introduce residual entropy S0 as a function of the number of molecules N and the number of distinct orientations available to them in a crystal m: S0 = N kB ln m, where kB is the Boltzmann constant. Residual entropy quantifies the uncertainty in molecular orientation. Residual entropy, unlike thermal entropy, is independent of temperature and remains present at absolute zero. The third step is to show that thermal entropy and residual entropy add up to the total entropy of a thermodynamic system S: S = S0 + STM. This method of explanation should result in a better comprehension of residual entropy and thermal entropy, as well as of their similarities and differences. The new method was tested in teaching at Faculty of Chemistry University of Belgrade, Serbia. The results of the test show that the new method has a potential to improve the quality of teaching.

Synthesis and Absolute Configuration of Enantiomerically Pure Vitamin K3 2,3-Epoxide

NARCIS (Netherlands)

Snatzke, Günther; Wijnberg, Hans; Feringa, Bernard; Marsman, Bea G.; Greydanus, Ben; Pluim, Henk

1980-01-01

The 2,3-epoxide of vitamin K3 (menadione, 1) has been prepared in enantiomerically pure form, and the absolute configuration has been deduced from the CD spectrum. The compound with the negative Cotton effect between 340 and 400 nm has the 2R,3S configuration.

Maximum entropy tokamak configurations

International Nuclear Information System (INIS)

Minardi, E.

1989-01-01

The new entropy concept for the collective magnetic equilibria is applied to the description of the states of a tokamak subject to ohmic and auxiliary heating. The condition for the existence of steady state plasma states with vanishing entropy production implies, on one hand, the resilience of specific current density profiles and, on the other, severe restrictions on the scaling of the confinement time with power and current. These restrictions are consistent with Goldston scaling and with the existence of a heat pinch. (author)

Partition Function and Configurational Entropy in Non-Equilibrium States: A New Theoretical Model

Directory of Open Access Journals (Sweden)

Akira Takada

2018-03-01

Full Text Available A new model of non-equilibrium thermodynamic states has been investigated on the basis of the fact that all thermodynamic variables can be derived from partition functions. We have thus attempted to define partition functions for non-equilibrium conditions by introducing the concept of pseudo-temperature distributions. These pseudo-temperatures are configurational in origin and distinct from kinetic (phonon temperatures because they refer to the particular fragments of the system with specific energies. This definition allows thermodynamic states to be described either for equilibrium or non-equilibrium conditions. In addition; a new formulation of an extended canonical partition function; internal energy and entropy are derived from this new temperature definition. With this new model; computational experiments are performed on simple non-interacting systems to investigate cooling and two distinct relaxational effects in terms of the time profiles of the partition function; internal energy and configurational entropy.

Enantiomeric Mixtures in Natural Product Chemistry: Separation and Absolute Configuration Assignment.

Science.gov (United States)

N L Batista, Andrea; M Dos Santos, Fernando; Batista, João M; Cass, Quezia B

2018-02-23

Chiral natural product molecules are generally assumed to be biosynthesized in an enantiomerically pure or enriched fashion. Nevertheless, a significant amount of racemates or enantiomerically enriched mixtures has been reported from natural sources. This number is estimated to be even larger since the enantiomeric purity of secondary metabolites is rarely checked in the natural product isolation pipeline. This latter fact may have drastic effects on the evaluation of the biological activity of chiral natural products. A second bottleneck is the determination of their absolute configurations. Despite the widespread use of optical rotation and electronic circular dichroism, most of the stereochemical assignments are based on empirical correlations with similar compounds reported in the literature. As an alternative, the combination of vibrational circular dichroism and quantum chemical calculations has emerged as a powerful and reliable tool for both conformational and configurational analysis of natural products, even for those lacking UV-Vis chromophores. In this review, we aim to provide the reader with a critical overview of the occurrence of enantiomeric mixtures of secondary metabolites in nature as well the best practices for their detection, enantioselective separation using liquid chromatography, and determination of absolute configuration by means of vibrational circular dichroism and density functional theory calculations.

Enantiomeric high-performance liquid chromatography resolution and absolute configuration of 6β-benzoyloxy-3α-tropanol.

Science.gov (United States)

Muñoz, Marcelo A; González, Natalia; Joseph-Nathan, Pedro

2016-07-01

The absolute configuration of the naturally occurring isomers of 6β-benzoyloxy-3α-tropanol (1) has been established by the combined use of chiral high-performance liquid chromatography with electronic circular dichroism detection and optical rotation detection. For this purpose (±)-1, prepared in two steps from racemic 6-hydroxytropinone (4), was subjected to chiral high-performance liquid chromatography with electronic circular dichroism and optical rotation detection allowing the online measurement of both chiroptical properties for each enantiomer, which in turn were compared with the corresponding values obtained from density functional theory calculations. In an independent approach, preparative high-performance liquid chromatography separation using an automatic fraction collector, yielded an enantiopure sample of OR (+)-1 whose vibrational circular dichroism spectrum allowed its absolute configuration assignment when the bands in the 1100-950 cm(-1) region were compared with those of the enantiomers of esters derived from 3α,6β-tropanediol. In addition, an enantiomerically enriched sample of 4, instead of OR (±)-4, was used for the same transformation sequence, whose high-performance liquid chromatography follow-up allowed their spectroscopic correlation. All evidences lead to the OR (+)-(1S,3R,5S,6R) and OR (-)-(1R,3S,5R,6S) absolute configurations, from where it follows that samples of 1 isolated from Knightia strobilina and Erythroxylum zambesiacum have the OR (+)-(1S,3R,5S,6R) absolute configuration, while the sample obtained from E. rotundifolium has the OR (-)-(1R,3S,5R,6S) absolute configuration. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Absolute Configuration from Different Multifragmentation Pathways in Light-Induced Coulomb Explosion Imaging.

Science.gov (United States)

Pitzer, Martin; Kastirke, Gregor; Kunitski, Maksim; Jahnke, Till; Bauer, Tobias; Goihl, Christoph; Trinter, Florian; Schober, Carl; Henrichs, Kevin; Becht, Jasper; Zeller, Stefan; Gassert, Helena; Waitz, Markus; Kuhlins, Andreas; Sann, Hendrik; Sturm, Felix; Wiegandt, Florian; Wallauer, Robert; Schmidt, Lothar Ph H; Johnson, Allan S; Mazenauer, Manuel; Spenger, Benjamin; Marquardt, Sabrina; Marquardt, Sebastian; Schmidt-Böcking, Horst; Stohner, Jürgen; Dörner, Reinhard; Schöffler, Markus; Berger, Robert

2016-08-18

The absolute configuration of individual small molecules in the gas phase can be determined directly by light-induced Coulomb explosion imaging (CEI). Herein, this approach is demonstrated for ionization with a single X-ray photon from a synchrotron light source, leading to enhanced efficiency and faster fragmentation as compared to previous experiments with a femtosecond laser. In addition, it is shown that even incomplete fragmentation pathways of individual molecules from a racemic CHBrClF sample can give access to the absolute configuration in CEI. This leads to a significant increase of the applicability of the method as compared to the previously reported complete break-up into atomic ions and can pave the way for routine stereochemical analysis of larger chiral molecules by light-induced CEI. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Entropy of self-gravitating radiation

International Nuclear Information System (INIS)

Sorkin, R.D.; Wald, R.M.; Jiu, Z.Z.

1981-01-01

The entropy of self-gravitating radiation confined to a spherical box of radius R is examined in the context of general relativity. It is expected that configurations (i.e., initial data) which extremize total entropy will be spherically symmetric, time symmetric distributions of radiation in local thermodynamic equilibrium. Assuming this is the case, it is proved that extrema of S coincide precisely with static equilibrium configurations of the radiation fluid. Furthermore, dynamically stable equilibrium configurations are shown to coincide with local maxima of S. The equilibrium configurations and their entropies are calculated and their properties are discussed. However, it is shown that entropies higher than these local extrema can be achieved and, indeed, arbitrarily high entropies can be attained by configurations inside of or outside but arbitrarily near their own Schwarzschild radius. However, consideration is limited to configurations which are outside their own Schwarzschild radius by at least one radiation wavelength, then the entropy is bounded and it is found Ssub(max) < is approximately equal to MR, where M is the total mass. This supports the validity for self-gravitating systems of the Bekenstein upper limit on the entropy to energy ratio of material bodies. (author)

Determining the Absolute Configuration of Two Marine Compounds Using Vibrational Chiroptical Spectroscopy

Czech Academy of Sciences Publication Activity Database

Hopmann, K. H.; Šebestík, Jaroslav; Novotná, J.; Stensen, W.; Urbanová, M.; Svenson, J.; Svendsen, J. S.; Bouř, Petr; Ruud, K.

2012-01-01

Roč. 77, č. 2 (2012), s. 858-869 ISSN 0022-3263 R&D Projects: GA ČR GAP208/11/0105; GA MŠk(CZ) LH11033 Institutional research plan: CEZ:AV0Z40550506 Keywords : vibrational circular dichroism * Raman optical activity * absolute configuration * bioprospecting Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 4.564, year: 2012

Parametric scaling from species relative abundances to absolute abundances in the computation of biological diversity: a first proposal using Shannon's entropy.

Science.gov (United States)

Ricotta, Carlo

2003-01-01

Traditional diversity measures such as the Shannon entropy are generally computed from the species' relative abundance vector of a given community to the exclusion of species' absolute abundances. In this paper, I first mention some examples where the total information content associated with a given community may be more adequate than Shannon's average information content for a better understanding of ecosystem functioning. Next, I propose a parametric measure of statistical information that contains both Shannon's entropy and total information content as special cases of this more general function.

New Compounds from Euphorbia helioscopia and Absolute Configuration Determination by Computational Methods

International Nuclear Information System (INIS)

He, Jiangbo; Zhu, Hua Jie; Luo, Gui Fen; Li, Yan; Cheng, Yong Xian; Chen, Hao; Chen, Shaopeng; Lu, Xin; Zhou, Guochun; Liu, Guang Ming

2010-01-01

The whole plant of Euphorbia helioscopia is an important traditional Chinese medicine. Fom its BuOH soluble extract, one new lactam, three new terpenoids including a new naturally occurring compound, and three known compounds were isolated. Their structures were identified by spectroscopic evidences. In particular, the absolute configurations of side chain of compounds 1 and 2 were determined using computational methods

Exciton Coupling in Circular Dichroic Spectroscopy as a Tool for Establishing the Absolute Configuration of alpha,beta-Unsaturated Esters of Allylic Alcohols

DEFF Research Database (Denmark)

Lauridsen, A.; Cornett, Claus; Christensen, S. B.

1991-01-01

alpha-beta-Unsaturated esters of allylic alcohols have been shown to exhibit exciton coupling by circular dichroic spectroscopy. This coupling permits the establishment of the absolute configuration. The method was used to prove the absolute configuration at C-2 of archangelolide. Detailed NMR sp...

Determination of the absolute configuration of (+)-neopentyl-1-d alcohol by neutron and x-ray diffraction analysis.

Science.gov (United States)

Yuan, H S; Stevens, R C; Bau, R; Mosher, H S; Koetzle, T F

1994-12-20

The absolute configuration of (+)-neopentyl-1-d alcohol, prepared by the reduction of 2,2-dimethylpropanal-1-d by actively fermenting yeast, has been determined to be S by neutron diffraction. The neutron study was carried out on the phthalate half ester of neopentyl-1-d alcohol, crystallized as its strychnine salt. The absolute configuration of the (-)-strychninium cation was first determined by an x-ray anomalous dispersion study of its iodide salt. The chiral skeleton of strychnine then served as a reference from which the absolute configuration of the -O-CHD-C(CH3)3 group of neopentyl phthalate was determined. Difference Fourier maps calculated from the neutron data showed unambiguously that the -O-CHD-C(CH3)3 groups of both independent molecules in the unit cell had the S configuration. This work proves conclusively that the yeast system reduces aldehydes by delivering hydrogen to the re face of the carbonyl group. Crystallographic details: (-)-strychninium (+)-neopentyl-1-d phthalate, space group P2(1) (monoclinic), a = 18.564(6) A, b = 7.713(2) A, c = 23.361(8) A, beta = 94.18(4) degrees, V = 3336.0(5) A3, Z = 2 (T = 100 K). Final agreement factors are R(F) = 0.073 for 2768 reflections collected at room temperature (x-ray analysis) and R(F) = 0.144 for 960 reflections collected at 100 K (neutron analysis).

Absolute Configuration of Andrographolide and Its Proliferation of Osteoblast Cell Lines

Science.gov (United States)

Chantrapromma, S.; Boonnak, N.; Pitakpornpreecha, T.; Yordthong, T.; Chidan Kumar, C. S.; Fun, H. K.

2018-05-01

Andrographolide, C20H30O5, is a labdane diterpenoid which was isolated from the leave of Andrographis paniculata. Its crystal structure is determined by single crystal X-ray diffraction: monoclinic, sp. gr. P21, Z = 2. Absolute configuration is determined by the refinement of the Flack parameter to 0.21(19). In the crystal, molecules are linked by O-H···O hydrogen bonds and C-H···O interactions into two dimensional network parallel to the (001) plane. Its proliferation of osteoblast cell lines is reported.

Determination of the absolute configuration of (+)-neopentyl-1-d alcohol by neutron and x-ray diffraction analysis

Energy Technology Data Exchange (ETDEWEB)

Yuan, H.S.H.; Stevens, R.C.; Bau, R. (Univ. of Southern California, Los Angeles, CA (United States)); Mosher, H.S. (Stanford Univ., CA (United States)); Koetzle, T.F. (Brookhaven National Lab., Upton, NY (United States))

1994-12-20

The absolute configuration of (+)-neopentyl-1-d alcohol, prepared by the reduction of 2,2-dimethylpropanol-1-d by actively fermenting yeast, has been determined to be S by neutron diffraction. The neutron study was carried out on the phthalate half ester of neopentyl-1-d alcohol, crystallized as its strychnine salt. The absolute configuration of the (-)-strychninium cation was first determined by an x-ray anomalous dispersion study of its iodide salt. The chiral skeleton of strychnine then served as a reference from which the absolute configuration of the -O-CHD-C(CH[sub 3])[sub 3] group of neopentyl phthalate was determined. Difference Fourier maps calculated from the neutron data showed unambiguously that the -O-CHD-C(CH[sub 3])[sub 3] groups of both independent molecules in the unit cell had the S configuration. This work proves conclusively that the yeast system reduces aldehydes by delivering hydrogen to the re face of the carbonyl group. Crystallographic details: (-)-strychninium (+)-neopentyl-1-d phthalate, space group P2[sub 1] (monoclinic), a = 18.564(6) [angstrom], b = 7.713(2) [angstrom], c = 23.361(8) [angstrom], [beta] = 94.18(4)[degrees], V = 3336.0(5) [angstrom][sup 3], Z = 2 (T = 100 K). Final agreement factors are R(F) = 0.073 for 2768 reflections collected at room temperature (x-ray analysis) and R(F) = 0.144 for 960 reflections collected at 100 K (neutron analysis). 49 refs., 7 figs., 2 tabs.

Configurational entropy as a tool to select a physical thick brane model

Science.gov (United States)

Chinaglia, M.; Cruz, W. T.; Correa, R. A. C.; de Paula, W.; Moraes, P. H. R. S.

2018-04-01

We analize braneworld scenarios via a configurational entropy (CE) formalism. Braneworld scenarios have drawn attention mainly due to the fact that they can explain the hierarchy problem and unify the fundamental forces through a symmetry breaking procedure. Those scenarios localize matter in a (3 + 1) hypersurface, the brane, which is inserted in a higher dimensional space, the bulk. Novel analytical braneworld models, in which the warp factor depends on a free parameter n, were recently released in the literature. In this article we will provide a way to constrain this parameter through the relation between information and dynamics of a system described by the CE. We demonstrate that in some cases the CE is an important tool in order to provide the most probable physical system among all the possibilities. In addition, we show that the highest CE is correlated to a tachyonic sector of the configuration, where the solutions for the corresponding model are dynamically unstable.

Determination of the absolute configuration of monosaccharides in complex carbohydrates by capillary G.L.C.

NARCIS (Netherlands)

Vliegenthart, J.F.G.; Gerwig, G.J.; Kamerling, J.P.

1979-01-01

The absolute configuration of neutral monosaccharides, 2-acetamido-2-deoxy sugars, and uronic acids can be determined by capillary g.l.c. on SE-30 after glycosidation with (-)-2-butanol and protection of the remaining polar groups. The method is illustrated by application to mixtures of the

Direct Determination of Absolute Configuration of Methyl-Substituted Phenyloxiranes: A Combined Experimental and Theoretical Approach

DEFF Research Database (Denmark)

Fristrup, Peter; Lassen, Peter Rygaard; Johannessen, Christian

2006-01-01

obtained from quantum mechanical calculations (density functional theory with the B3LYP hybrid exchange correlation functional with 6-31++G**, aug-cc-pVDZ, or aug-cc-pVTZ basis set) and related to the physical structure of the compounds. The absolute configuration could be established directly in each case...

Cooperative use of VCD and XRD for the determination of tetrahydrobenzoisoquinolines absolute configuration: a reliable proof of memory of chirality and retention of configuration in enediyne rearrangements.

Science.gov (United States)

Mondal, Shovan; Naubron, Jean-Valère; Campolo, Damien; Giorgi, Michel; Bertrand, Michéle P; Nechab, Malek

2013-12-01

The absolute configurations (AC) of azaheterocylic compounds resulting from the cascade rearrangement of enediynes involving only light atoms were unambiguously assigned by the joint use of vibrational circular dichroism (VCD) and copper radiation single crystal X-ray diffraction (XRD). These AC determinations proved that the rearrangements of enediynes proceeded with memory of chirality and retention of configuration. © 2013 Wiley Periodicals, Inc.

Structure and absolute configuration of Jurassic polyketide-derived spiroborate pigments obtained from microgram quantities.

OpenAIRE

Wolkenstein, K.; Sun , H.; Falk, H.; Griesinger, C.

2015-01-01

Complete structural elucidation of natural products is often challenging due to structural complexity and limited availability. This is true for present-day secondary metabolites, but even more for exceptionally preserved secondary metabolites of ancient organisms that potentially provide insights into the evolutionary history of natural products. Here, we report the full structure and absolute configuration of the borolithochromes, enigmatic boron-containing pigments from a Jurassic putative...

a Chiral Tagging Strategy for Determining Absolute Configuration and Enantiomeric Excess by Molecular Rotational Spectroscopy

Science.gov (United States)

Evangelisti, Luca; Caminati, Walther; Patterson, David; Thomas, Javix; Xu, Yunjie; West, Channing; Pate, Brooks

2017-06-01

The introduction of three wave mixing rotational spectroscopy by Patterson, Schnell, and Doyle [1,2] has expanded applications of molecular rotational spectroscopy into the field of chiral analysis. Chiral analysis of a molecule is the quantitative measurement of the relative abundances of all stereoisomers of the molecule and these include both diastereomers (with distinct molecular rotational spectra) and enantiomers (with equivalent molecular rotational spectra). This work adapts a common strategy in chiral analysis of enantiomers to molecular rotational spectroscopy. A "chiral tag" is attached to the molecule of interest by making a weakly bound complex in a pulsed jet expansion. When this tag molecule is enantiopure, it will create diastereomeric complexes with the two enantiomers of the molecule being analyzed and these can be differentiated by molecule rotational spectroscopy. Identifying the structure of this complex, with knowledge of the absolute configuration of the tag, establishes the absolute configuration of the molecule of interest. Furthermore, the diastereomer complex spectra can be used to determine the enantiomeric excess of the sample. The ability to perform chiral analysis will be illustrated by a study of solketal using propylene oxide as the tag. The possibility of using current methods of quantum chemistry to assign a specific structure to the chiral tag complex will be discussed. Finally, chiral tag rotational spectroscopy offers a "gold standard" method for determining the absolute configuration of the molecule through determination of the substitution structure of the complex. When this measurement is possible, rotational spectroscopy can deliver a quantitative three dimensional structure of the molecule with correct stereochemistry as the analysis output. [1] David Patterson, Melanie Schnell, John M. Doyle, Nature 497, 475 (2013). [2] David Patterson, John M. Doyle, Phys. Rev. Lett. 111, 023008 (2013).

Absolute Configuration of 3-METHYLCYCLOHEXANONE by Chiral Tag Rotational Spectroscopy and Vibrational Circular Dichroism

Science.gov (United States)

Evangelisti, Luca; Holdren, Martin S.; Mayer, Kevin J.; Smart, Taylor; West, Channing; Pate, Brooks

2017-06-01

The absolute configuration of 3-methylcyclohexanone was established by chiral tag rotational spectroscopy measurements using 3-butyn-2-ol as the tag partner. This molecule was chosen because it is a benchmark measurement for vibrational circular dichroism (VCD). A comparison of the analysis approaches of chiral tag rotational spectroscopy and VCD will be presented. One important issue in chiral analysis by both methods is the conformational flexibility of the molecule being analyzed. The analysis of conformational composition of samples will be illustrated. In this case, the high spectral resolution of molecular rotational spectroscopy and potential for spectral simplification by conformational cooling in the pulsed jet expansion are advantages for chiral tag spectroscopy. The computational chemistry requirements for the two methods will also be discussed. In this case, the need to perform conformer searches for weakly bound complexes and to perform reasonably high level quantum chemistry geometry optimizations on these complexes makes the computational time requirements less favorable for chiral tag rotational spectroscopy. Finally, the issue of reliability of the determination of the absolute configuration will be considered. In this case, rotational spectroscopy offers a "gold standard" analysis method through the determination of the ^{13}C-subsitution structure of the complex between 3-methylcyclohexanone and an enantiopure sample of the 3-butyn-2-ol tag.

Absolute configuration of a tetrahydrophenanthrene from Heliotropium ovalifolium by LC-NMR of its Mosher esters.

Science.gov (United States)

Guilet, David; Guntern, Alain; Ioset, Jean-Robert; Queiroz, Emerson F; Ndjoko, Karine; Foggin, Chris M; Hostettmann, Kurt

2003-01-01

A new tetrahydrophenanthrene (1, (1R,2R)-1-hydroxy-2-methoxy-6,9-dimethyl-2,3-dihydrophenanthren-4(1H)-one (heliophenanthrone)) has been isolated from the aerial parts of Heliotropium ovalifolium. Its structure was elucidated on the basis of spectroscopic data, and the absolute configuration of the asymmetric centers was determined from LC-NMR data of the Mosher ester derivatives.

Entropy Bounds for Constrained Two-Dimensional Fields

DEFF Research Database (Denmark)

Forchhammer, Søren Otto; Justesen, Jørn

1999-01-01

The maximum entropy and thereby the capacity of 2-D fields given by certain constraints on configurations are considered. Upper and lower bounds are derived.......The maximum entropy and thereby the capacity of 2-D fields given by certain constraints on configurations are considered. Upper and lower bounds are derived....

Configuration Entropy Calculations for Complex Compounds Technetium

International Nuclear Information System (INIS)

Muhayatun; Susanto Imam Rahayu; Surdia, N.M.; Abdul Mutalib

2002-01-01

Recently, the study of technetium complexes is rapidly increasing, due to the benefit of 99m Tc complexes (one of Tc nuclear isomers), which are widely used for diagnostics. Study of the structure-stability relationship of Tc complexes based on solid angle has been done by Kung using a Solid Angle Factor Sum (SAS). The SAS is hypothesized to be related to stability. SAS has been used by several researchers either for synthesis or designing the reaction route of the Tc complex formation and predicting the geometry of complex structures. Although the advantages of the SAS were very gratifying, but the model does not have the theoretical basis which is able to explain the correlation of steric parameters to physicochemical properties of complexes especially to those connected to a complex's stability. To improve the SAS model, in this research the model was modified by providing a theoretical basis for SAS. The results obtained from the correlation of the SAS value to the thermodynamic stability parameters of simple complexes show the values to have a similar trend as the standard entropy (S 0 ). The entropy approximation model was created by involving some factors which are not used in Kung's model. Entropy optimization to the bond length (ML) has also been done to several complexes. The calculations of SAS value using the calculated R for more than 100 Tc complexes provide a normalized mean value of 0.8545 ± 0.0851 and have similar curve profiles as those of Kung's model. The entropy value can be obtained by multiplying the natural logarithm of the a priori degeneracy of a certain distribution (Ω) and the Boltzmann constant. The results of Ω and In Ω of the Tc complexes have a narrow range. The results of this research are able to provide a basic concept for the SAS to explain the structure-stability relationship and to improve Kung's model. (author)

Entropy in the Tangled Nature Model of Evolution

Directory of Open Access Journals (Sweden)

Ty N. F. Roach

2017-04-01

Full Text Available Applications of entropy principles to evolution and ecology are of tantamount importance given the central role spatiotemporal structuring plays in both evolution and ecological succession. We obtain here a qualitative interpretation of the role of entropy in evolving ecological systems. Our interpretation is supported by mathematical arguments using simulation data generated by the Tangled Nature Model (TNM, a stochastic model of evolving ecologies. We define two types of configurational entropy and study their empirical time dependence obtained from the data. Both entropy measures increase logarithmically with time, while the entropy per individual decreases in time, in parallel with the growth of emergent structures visible from other aspects of the simulation. We discuss the biological relevance of these entropies to describe niche space and functional space of ecosystems, as well as their use in characterizing the number of taxonomic configurations compatible with different niche partitioning and functionality. The TNM serves as an illustrative example of how to calculate and interpret these entropies, which are, however, also relevant to real ecosystems, where they can be used to calculate the number of functional and taxonomic configurations that an ecosystem can realize.

Incommensurately modulated structure of morpholinium tetrafluoroborate and configurational versus chemical entropies at the incommensurate and lock-in phase transitions

Czech Academy of Sciences Publication Activity Database

Noohinejad, L.; van Smaalen, S.; Petříček, Václav; Schönleber, A.

2017-01-01

Roč. 73, Jun (2017), s. 836-843 ISSN 2052-5206 R&D Projects: GA ČR(CZ) GA15-12653S Institutional support: RVO:68378271 Keywords : incommensurately modulated structure * morpholinium tetrafluoroborate * configurational entropy Subject RIV: BM - Solid Matter Physics ; Magnetism OBOR OECD: Condensed matter physics (including formerly solid state physics, supercond.) Impact factor: 2.032, year: 2016

Direct determination of absolute configuration: a vibrational circular dichroism study on dimethyl-substituted phenyloxiranes synthesized by Shi epoxidation

DEFF Research Database (Denmark)

Fristrup, Peter; Lassen, Peter Rygaard; Tanner, David Ackland

2008-01-01

obtained using DFT/B3LYP calculations, and the differences between experiment and theory are discussed. The absolute configuration at the benzylic position was established as being (R), (S) and (R) for the cis, trans and geminal dimethylsubstituted phenyloxiranes, respectively. In all three cases...

Giant onsite electronic entropy enhances the performance of ceria for water splitting.

Science.gov (United States)

Naghavi, S Shahab; Emery, Antoine A; Hansen, Heine A; Zhou, Fei; Ozolins, Vidvuds; Wolverton, Chris

2017-08-18

Previous studies have shown that a large solid-state entropy of reduction increases the thermodynamic efficiency of metal oxides, such as ceria, for two-step thermochemical water splitting cycles. In this context, the configurational entropy arising from oxygen off-stoichiometry in the oxide, has been the focus of most previous work. Here we report a different source of entropy, the onsite electronic configurational entropy, arising from coupling between orbital and spin angular momenta in lanthanide f orbitals. We find that onsite electronic configurational entropy is sizable in all lanthanides, and reaches a maximum value of ≈4.7 k B per oxygen vacancy for Ce 4+ /Ce 3+ reduction. This unique and large positive entropy source in ceria explains its excellent performance for high-temperature catalytic redox reactions such as water splitting. Our calculations also show that terbium dioxide has a high electronic entropy and thus could also be a potential candidate for solar thermochemical reactions.Solid-state entropy of reduction increases the thermodynamic efficiency of ceria for two-step thermochemical water splitting. Here, the authors report a large and different source of entropy, the onsite electronic configurational entropy arising from coupling between orbital and spin angular momenta in f orbitals.

Infinite Shannon entropy

International Nuclear Information System (INIS)

Baccetti, Valentina; Visser, Matt

2013-01-01

Even if a probability distribution is properly normalizable, its associated Shannon (or von Neumann) entropy can easily be infinite. We carefully analyze conditions under which this phenomenon can occur. Roughly speaking, this happens when arbitrarily small amounts of probability are dispersed into an infinite number of states; we shall quantify this observation and make it precise. We develop several particularly simple, elementary, and useful bounds, and also provide some asymptotic estimates, leading to necessary and sufficient conditions for the occurrence of infinite Shannon entropy. We go to some effort to keep technical computations as simple and conceptually clear as possible. In particular, we shall see that large entropies cannot be localized in state space; large entropies can only be supported on an exponentially large number of states. We are for the time being interested in single-channel Shannon entropy in the information theoretic sense, not entropy in a stochastic field theory or quantum field theory defined over some configuration space, on the grounds that this simple problem is a necessary precursor to understanding infinite entropy in a field theoretic context. (paper)

Black hole entropy, curved space and monsters

International Nuclear Information System (INIS)

Hsu, Stephen D.H.; Reeb, David

2008-01-01

We investigate the microscopic origin of black hole entropy, in particular the gap between the maximum entropy of ordinary matter and that of black holes. Using curved space, we construct configurations with entropy greater than the area A of a black hole of equal mass. These configurations have pathological properties and we refer to them as monsters. When monsters are excluded we recover the entropy bound on ordinary matter S 3/4 . This bound implies that essentially all of the microstates of a semiclassical black hole are associated with the growth of a slightly smaller black hole which absorbs some additional energy. Our results suggest that the area entropy of black holes is the logarithm of the number of distinct ways in which one can form the black hole from ordinary matter and smaller black holes, but only after the exclusion of monster states

Structure and Absolute Configuration of Ginkgolide B Characterized by IR- and VCD Spectroscopy

DEFF Research Database (Denmark)

Andersen, Niels Højmark; Christensen, N.J.; Lassen, Peter Rygaard

2010-01-01

Experimental and calculated (B3LYP/6-31G(d)) vibrational Circular dichroism (VCD) and IR spectra are compared, illustrating that the structure and absolute configuration of ginkgolide B (GB) may be characterized directly in solution. A conformational search for GB using MacroModel and subsequent...... DFT optimizations (B3LYP/6-31G(d)) provides a structure for the lowest energy conformer which agrees well with the structure determined by X-ray diffraction. In addition, a conformer at all energy of 7 kJ mol(-1) (B3LYP/6-311+G(2d,2p)) with respect to the lowest energy conformer is predicted...

A Single Chiroptical Spectroscopic Method May Not Be Able To Establish the Absolute Configurations of Diastereomers: Dimethylesters of Hibiscus and Garcinia Acids

Science.gov (United States)

Polavarapu, Prasad L.; Donahue, Emily A.; Shanmugam, Ganesh; Scalmani, Giovanni; Hawkins, Edward K.; Rizzo, Carmelo; Ibnusaud, Ibrahim; Thomas, Grace; Habel, Deenamma; Sebastian, Dellamol

2013-01-01

Electronic circular dichroism (ECD), optical rotatory dispersion (ORD), and vibrational circular dichroism (VCD) spectra of hibiscus acid dimethyl ester have been measured and analyzed in combination with quantum chemical calculations of corresponding spectra. These results, along with those reported previously for garcinia acid dimethyl ester, reveal that none of these three (ECD, ORD, or VCD) spectroscopic methods, in isolation, can unequivocally establish the absolute configurations of diastereomers. This deficiency is eliminated when a combined spectral analysis of either ECD and VCD or ORD and VCD methods is used. It is also found that the ambiguities in the assignment of absolute configurations of diastereomers may also be overcome when unpolarized vibrational absorption is included in the spectral analysis. PMID:21568330

Quantum information entropies of ultracold atomic gases in a ...

Indian Academy of Sciences (India)

The position and momentum space information entropies of weakly interacting trapped atomic Bose–Einstein condensates and spin-polarized trapped atomic Fermi gases at absolute zero temperature are evaluated. We find that sum of the position and momentum space information entropies of these quantum systems ...

Editorial: Entropy in Landscape Ecology

Directory of Open Access Journals (Sweden)

Samuel A. Cushman

2018-04-01

Full Text Available Entropy and the second law of thermodynamics are the central organizing principles of nature, but the ideas and implications of the second law are poorly developed in landscape ecology. The purpose of this Special Issue “Entropy in Landscape Ecology” in Entropy is to bring together current research on applications of thermodynamics in landscape ecology, to consolidate current knowledge and identify key areas for future research. The special issue contains six articles, which cover a broad range of topics including relationships between entropy and evolution, connections between fractal geometry and entropy, new approaches to calculate configurational entropy of landscapes, example analyses of computing entropy of landscapes, and using entropy in the context of optimal landscape planning. Collectively these papers provide a broad range of contributions to the nascent field of ecological thermodynamics. Formalizing the connections between entropy and ecology are in a very early stage, and that this special issue contains papers that address several centrally important ideas, and provides seminal work that will be a foundation for the future development of ecological and evolutionary thermodynamics.

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.

Third law of thermodynamics as a key test of generalized entropies.

Science.gov (United States)

Bento, E P; Viswanathan, G M; da Luz, M G E; Silva, R

2015-02-01

The laws of thermodynamics constrain the formulation of statistical mechanics at the microscopic level. The third law of thermodynamics states that the entropy must vanish at absolute zero temperature for systems with nondegenerate ground states in equilibrium. Conversely, the entropy can vanish only at absolute zero temperature. Here we ask whether or not generalized entropies satisfy this fundamental property. We propose a direct analytical procedure to test if a generalized entropy satisfies the third law, assuming only very general assumptions for the entropy S and energy U of an arbitrary N-level classical system. Mathematically, the method relies on exact calculation of β=dS/dU in terms of the microstate probabilities p(i). To illustrate this approach, we present exact results for the two best known generalizations of statistical mechanics. Specifically, we study the Kaniadakis entropy S(κ), which is additive, and the Tsallis entropy S(q), which is nonadditive. We show that the Kaniadakis entropy correctly satisfies the third law only for -1law for q<1. Finally, we give a concrete example of the power of our proposed method by applying it to a paradigmatic system: the one-dimensional ferromagnetic Ising model with nearest-neighbor interactions.

The Elusive Nature of Entropy and Its Physical Meaning

Directory of Open Access Journals (Sweden)

Milivoje M. Kostic

2014-02-01

Full Text Available Entropy is the most used and often abused concept in science, but also in philosophy and society. Further confusions are produced by some attempts to generalize entropy with similar but not the same concepts in other disciplines. The physical meaning of phenomenological, thermodynamic entropy is reasoned and elaborated by generalizing Clausius definition with inclusion of generated heat, since it is irrelevant if entropy is changed due to reversible heat transfer or irreversible heat generation. Irreversible, caloric heat transfer is introduced as complementing reversible heat transfer. It is also reasoned and thus proven why entropy cannot be destroyed but is always generated (and thus over-all increased locally and globally, at every space and time scales, without any exception. It is concluded that entropy is a thermal displacement (dynamic thermal-volume of thermal energy due to absolute temperature as a thermal potential (dQ = TdS, and thus associated with thermal heat and absolute temperature, i.e., distribution of thermal energy within thermal micro-particles in space. Entropy is an integral measure of (random thermal energy redistribution (due to heat transfer and/or irreversible heat generation within a material system structure in space, per absolute temperature level: dS = dQSys/T = mCSysdT/T, thus logarithmic integral function, with J/K unit. It may be also expressed as a measure of “thermal disorder”, being related to logarithm of number of all thermal, dynamic microstates W (their position and momenta, S = kBlnW, or to the sum of their logarithmic probabilities S = −kB∑pilnpi, that correspond to, or are consistent with the given thermodynamic macro-state. The number of thermal microstates W, is correlated with macro-properties temperature T and volume V for ideal gases. A system form and/or functional order or disorder are not (thermal energy order/disorder and the former is not related to Thermodynamic entropy. Expanding

Structural contributions to the third-law entropy of uranyl phases

International Nuclear Information System (INIS)

Chen, F.; Ewing, R.C.

1999-01-01

Entropies that are used in geochemical calculations are usually based on calorimetric measurements. However, because of the contributions of neglected residual entropies which cannot be determined by calorimetric measurements, the true third-law entropies for many phases may be quite different from those derived from thermal data. The residual entropies are caused by site-mixing, structural disorder and magnetic spin disorder and may result in a considerable contribution to the third-law entropy of solid phases. Magnetic spin-configurational entropy is not expected to be significant in uranyl phases. However, because most uranyl phases are based on sheet or chain structures and usually contain several molecular water groups, site-mixing, vacancies, as well as disorder in the orientation of hydrogen bonds and the polar H 2 O molecules may occur. Calculations of the ideal site-mixing configurational entropy for some uranyl phases indicate that the residual contributions that arise from substitution and vacancies to the third-law entropies of uranyl phases may be large. A brief examination of the crystal chemistry of water molecules in uranyl phases suggests that considerable residual entropy may be caused by the disorder of hydrogen bonds associated with interstitial H 2 O groups

Entropy for theories with indefinite causal structure

International Nuclear Information System (INIS)

Markes, Sonia; Hardy, Lucien

2011-01-01

Any theory with definite causal structure has a defined past and future, be it defined by light cones or an absolute time scale. Entropy is a concept that has traditionally been reliant on a definite notion of causality. However, without a definite notion of causality, the concept of entropy is not all lost. Indefinite causal structure results from combining probabilistic predictions and dynamical space-time. The causaloid framework lays the mathematical groundwork to be able to treat indefinite causal structure. In this paper, we build on the causaloid mathematics and define a causally-unbiased entropy for an indefinite causal structure. In defining a causally-unbiased entropy, there comes about an emergent idea of causality in the form of a measure of causal connectedness, termed the Q factor.

The "Case of Two Compounds with Similar Configuration but Nearly Mirror Image CD Spectra" Refuted. Reassignment of the Absolute Configuration of N-Formyl-3',4'-dihydrospiro[indan-1,2'(1'H)-pyridine].

Science.gov (United States)

Padula, Daniele; Di Bari, Lorenzo; Pescitelli, Gennaro

2016-09-02

In 1997, Sandström and co-workers reported the case of two chiral spiro compounds with very similar skeletons but showing almost mirror-image electronic circular dichroism (ECD) spectra for the corresponding absolute configuration. The paper has been often cited as a proof and good educational example of the pronounced sensitivity of ECD toward molecular conformation, and a clear warning against the use of ECD spectral correlations to assign absolute configurations. Although both concepts remain valid, they are not exemplified by the quoted paper. We demonstrate that the original configurational assignment of one compound was wrong and revise it by using TDDFT calculations. The main reason for the observed failure is the use of the matrix method, a popular approach to predict ECD spectra of compounds which can be treated with an independent system approximation (ISA), including proteins. Using a modern version of the matrix method, we demonstrate that the ISA is not valid for the title compound. Even in the absence of apparent conjugation between the component chromophores, the validity of the ISA should never be taken for granted and the effective extent of orbital overlap should always be verified.

Entanglement Entropy of AdS Black Holes

Directory of Open Access Journals (Sweden)

Maurizio Melis

2010-11-01

Full Text Available We review recent progress in understanding the entanglement entropy of gravitational configurations for anti-de Sitter gravity in two and three spacetime dimensions using the AdS/CFT correspondence. We derive simple expressions for the entanglement entropy of two- and three-dimensional black holes. In both cases, the leading term of the entanglement entropy in the large black hole mass expansion reproduces exactly the Bekenstein-Hawking entropy, whereas the subleading term behaves logarithmically. In particular, for the BTZ black hole the leading term of the entanglement entropy can be obtained from the large temperature expansion of the partition function of a broad class of 2D CFTs on the torus.

Resolution and Determination of the Absolute Configuration of a Twisted Bis-Lactam Analogue of Troger's Base: A Comparative Spectroscopic and Computational Study

DEFF Research Database (Denmark)

Rúnarsson, Ögmundur Vidar; Benkhäuser, Christian; Christensen, Niels Johan

2015-01-01

) and electronic circular dichroism (ECD) spectra. The absolute configuration of (-)-2 was determined by comparing experimental and calculated electronic circular dichroism (ECD) spectra. The corresponding theoretical spectra were calculated using the lowest energy conformation of (R,R)-2 and (S,S)-2 at the B3LYP...

Absolute Configurations and NO Inhibitory Activities of Terpenoids from Curcuma longa.

Science.gov (United States)

Xu, Jing; Ji, Feifei; Kang, Jing; Wang, Hao; Li, Shen; Jin, Da-Qing; Zhang, Qiang; Sun, Hongwei; Guo, Yuanqiang

2015-06-24

Curcuma longa L., belonging to the Zingiberaceae family, is a perennial herb and has been used as a spice and a pigment in the food industry. In the ongoing search for inhibitory reagents of NO production and survey of the chemical composition of natural vegetable foods, the chemical constituents of C. longa used as spice were investigated. This investigation resulted in the isolation of 2 new terpenoids and 14 known analogues. Their structures were established on the basis of the extensive analyses of 1D and 2D NMR spectroscopic data, and the absolute configurations of 1-4 were elucidated by comparison of the calculated and experimental ECD spectra. Among them, compound 1 is a rare norditerpene with an ent-labdane skeleton, and 2 is a skeletally novel sesquiterpene having an eight-membered ring. All of the compounds were found to possess NO inhibitory activities in murine microglial BV-2 cells. The discovery of two new compounds in this chemical investigation further disclosed the chemical composition of C. longa used a food spice, and the bioassay implied that the natural food spice C. longa, containing terpenoids with NO inhibitory activities, may be potentially promotive to human health.

Phase equilibrium of PuO2-x - Pu2O3 based on first-principles calculations and configurational entropy change

International Nuclear Information System (INIS)

Minamoto, Satoshi; Kato, Masato; Konashi, Kenji

2011-01-01

Combination of an oxygen vacancy formation energy calculated using first-principles approach and the configurational entropy change treated within the framework of statistical mechanics gives an expression of the Gibbs free energy at large deviation from stoichiometry of plutonium oxide PuO 2 . An oxygen vacancy formation energy 4.20 eV derived from our previously first-principles calculation was used to evaluate the Gibbs free energy change due to oxygen vacancies in the crystal. The oxygen partial pressures then can be evaluated from the change of the free energy with two fitting parameters (a vacancy-vacancy interaction energy and vibration entropy change due to induced vacancies). Derived thermodynamic expression for the free energy based on the SGTE thermodynamic data for the stoichiometric PuO 2 and the Pu 2 O 3 compounds was further incorporated into the CALPHAD modeling, then phase equilibrium between the stoichiometric Pu 2 O 3 and non-stoichiometric PuO 2-x were reproduced.

Application of the entropy generation minimization method to a solar heat exchanger: A pseudo-optimization design process based on the analysis of the local entropy generation maps

International Nuclear Information System (INIS)

Giangaspero, Giorgio; Sciubba, Enrico

2013-01-01

This paper presents an application of the entropy generation minimization method to the pseudo-optimization of the configuration of the heat exchange surfaces in a Solar Rooftile. An initial “standard” commercial configuration is gradually improved by introducing design changes aimed at the reduction of the thermodynamic losses due to heat transfer and fluid friction. Different geometries (pins, fins and others) are analysed with a commercial CFD (Computational Fluid Dynamics) code that also computes the local entropy generation rate. The design improvement process is carried out on the basis of a careful analysis of the local entropy generation maps and the rationale behind each step of the process is discussed in this perspective. The results are compared with other entropy generation minimization techniques available in the recent technical literature. It is found that the geometry with pin-fins has the best performance among the tested ones, and that the optimal pin array shape parameters (pitch and span) can be determined by a critical analysis of the integrated and local entropy maps and of the temperature contours. - Highlights: ► An entropy generation minimization method is applied to a solar heat exchanger. ► The approach is heuristic and leads to a pseudo-optimization process with CFD as main tool. ► The process is based on the evaluation of the local entropy generation maps. ► The geometry with pin-fins in general outperforms all other configurations. ► The entropy maps and temperature contours can be used to determine the optimal pin array design parameters

Testing the mutual information expansion of entropy with multivariate Gaussian distributions.

Science.gov (United States)

Goethe, Martin; Fita, Ignacio; Rubi, J Miguel

2017-12-14

The mutual information expansion (MIE) represents an approximation of the configurational entropy in terms of low-dimensional integrals. It is frequently employed to compute entropies from simulation data of large systems, such as macromolecules, for which brute-force evaluation of the full configurational integral is intractable. Here, we test the validity of MIE for systems consisting of more than m = 100 degrees of freedom (dofs). The dofs are distributed according to multivariate Gaussian distributions which were generated from protein structures using a variant of the anisotropic network model. For the Gaussian distributions, we have semi-analytical access to the configurational entropy as well as to all contributions of MIE. This allows us to accurately assess the validity of MIE for different situations. We find that MIE diverges for systems containing long-range correlations which means that the error of consecutive MIE approximations grows with the truncation order n for all tractable n ≪ m. This fact implies severe limitations on the applicability of MIE, which are discussed in the article. For systems with correlations that decay exponentially with distance, MIE represents an asymptotic expansion of entropy, where the first successive MIE approximations approach the exact entropy, while MIE also diverges for larger orders. In this case, MIE serves as a useful entropy expansion when truncated up to a specific truncation order which depends on the correlation length of the system.

Arithmetic of quantum entropy function

International Nuclear Information System (INIS)

Sen, Ashoke

2009-01-01

Quantum entropy function is a proposal for computing the entropy associated with the horizon of a black hole in the extremal limit, and is related via AdS/CFT correspondence to the dimension of the Hilbert space in a dual quantum mechanics. We show that in N = 4 supersymmetric string theories, quantum entropy function formalism naturally explains the origin of the subtle differences between the microscopic degeneracies of quarter BPS dyons carrying different torsion, i.e. different arithmetical properties. These arise from additional saddle points in the path integral - whose existence depends on the arithmetical properties of the black hole charges - constructed as freely acting orbifolds of the original AdS 2 x S 2 near horizon geometry. During this analysis we demonstrate that the quantum entropy function is insensitive to the details of the infrared cutoff used in the computation, and the details of the boundary terms added to the action. We also discuss the role of the asymptotic symmetries of AdS 2 in carrying out the path integral in the definition of quantum entropy function. Finally we show that even though quantum entropy function is expected to compute the absolute degeneracy in a given charge and angular momentum sector, it can also be used to compute the index. This can then be compared with the microscopic computation of the index.

Absolute Configuration Determination by Quantum Mechanical Calculation of Chiroptical Spectra: Basics and Applications to Fungal Metabolites.

Science.gov (United States)

Superchi, Stefano; Scafato, Patrizia; Gorecki, Marcin; Pescitelli, Gennaro

2018-01-01

Quantum mechanical simulations of chiroptical properties, such as electronic circular dichroism (ECD), optical rotation (OR), and vibrational circular dichroism (VCD), have rapidly become very popular to assign the absolute configuration of novel natural products. We review the application of the ECD/OR/VCD computational methodology to chiral metabolites of fungal origin. First, we summarize the fundamentals of the three spectroscopies; then, we focus on the specific experimental and computational issues allied to the application of their calculations. We surveyed the entire literature describing the use of ECD/OR/VCD computations for fungal metabolites, and catalogued all papers according to the method employed and to the structural family of compounds. Then, we chose several examples to illustrate the use of the techniques and highlight the practical application of the computational approach. Our literature survey demonstrates that the simulation of ECD/OR/VCD spectra is nowadays widespread and accessible also to non-experts, although a good computational practice is necessary to avoid wrong assignments. ECD is still the most common technique used in the context of fungal metabolites. OR and VCD may be profitably employed when the compound of interest lacks chromophoric groups. Our examples illustrate that the combination of two or more chiroptical methods is strongly advisable in some cases, especially in the presence of high conformational flexibility, where a single technique does not lead to a safe conclusion. The ECD/OR/VCD computational approach is a reliable and versatile method to assign the absolute configuration of fungal metabolites and related natural products. Copyright© Bentham Science Publishers; For any queries, please email at epub@benthamscience.org.

Effects of specific surface area and porosity on cube counting fractal dimension, lacunarity, configurational entropy, and permeability of model porous networks: Random packing simulations and NMR micro-imaging study

Science.gov (United States)

Lee, Bum Han; Lee, Sung Keun

2013-07-01

Despite the importance of understanding and quantifying the microstructure of porous networks in diverse geologic settings, the effects of the specific surface area and porosity on the key structural parameters of the networks have not been fully understood. We performed cube-counting fractal dimension (Dcc) and lacunarity analyses of 3D porous networks of model sands and configurational entropy analysis of 2D cross sections of model sands using random packing simulations and nuclear magnetic resonance (NMR) micro-imaging. We established relationships among porosity, specific surface area, structural parameters (Dcc and lacunarity), and the corresponding macroscopic properties (configurational entropy and permeability). The Dcc of the 3D porous networks increases with increasing specific surface area at a constant porosity and with increasing porosity at a constant specific surface area. Predictive relationships correlating Dcc, specific surface area, and porosity were also obtained. The lacunarity at the minimum box size decreases with increasing porosity, and that at the intermediate box size (∼0.469 mm in the current model sands) was reproduced well with specific surface area. The maximum configurational entropy increases with increasing porosity, and the entropy length of the pores decreases with increasing specific surface area and was used to calculate the average connectivity among the pores. The correlation among porosity, specific surface area, and permeability is consistent with the prediction from the Kozeny-Carman equation. From the relationship between the permeability and the Dcc of pores, the permeability can be expressed as a function of the Dcc of pores and porosity. The current methods and these newly identified correlations among structural parameters and properties provide improved insights into the nature of porous media and have useful geophysical and hydrological implications for elasticity and shear viscosity of complex composites of rock

Low Streamflow Forcasting using Minimum Relative Entropy

Science.gov (United States)

Cui, H.; Singh, V. P.

2013-12-01

Minimum relative entropy spectral analysis is derived in this study, and applied to forecast streamflow time series. Proposed method extends the autocorrelation in the manner that the relative entropy of underlying process is minimized so that time series data can be forecasted. Different prior estimation, such as uniform, exponential and Gaussian assumption, is taken to estimate the spectral density depending on the autocorrelation structure. Seasonal and nonseasonal low streamflow series obtained from Colorado River (Texas) under draught condition is successfully forecasted using proposed method. Minimum relative entropy determines spectral of low streamflow series with higher resolution than conventional method. Forecasted streamflow is compared to the prediction using Burg's maximum entropy spectral analysis (MESA) and Configurational entropy. The advantage and disadvantage of each method in forecasting low streamflow is discussed.

Entropy-driven metastable defects in silicon

International Nuclear Information System (INIS)

Hamilton, B.; Peaker, A.R.; Pantelides, S.T.

1989-01-01

The known metastable defects are usually describable by a configuration coordinate diagram in which two energy minima are separated by a barrier. This diagram does not change with temperature and each configuration is stable over some temperature range. Here we report the observation of a novel metastability: A configuration change occurs spontaneously and abruptly at a critical temperature, giving rise to a discontinuous DLTS (deep level transient spectroscopy) spectrum. We propose that this phenomenon is a manifestation of entropy variations in the configurational space. (author) 12 refs., 4 figs

Entropy in the Tangled Nature Model of evolution

DEFF Research Database (Denmark)

Roach, Ty N.F.; Nulton, James; Sibani, Paolo

2017-01-01

Applications of entropy principles to evolution and ecology are of tantamount importance given the central role spatiotemporal structuring plays in both evolution and ecological succession. We obtain here a qualitative interpretation of the role of entropy in evolving ecological systems. Our...... interpretation is supported by mathematical arguments using simulation data generated by the Tangled Nature Model (TNM), a stochastic model of evolving ecologies. We define two types of configurational entropy and study their empirical time dependence obtained from the data. Both entropy measures increase...... logarithmically with time, while the entropy per individual decreases in time, in parallel with the growth of emergent structures visible from other aspects of the simulation. We discuss the biological relevance of these entropies to describe niche space and functional space of ecosystems, as well as their use...

The Nernst theorem and statistical entropy in a (1+1)-dimensional charged black hole

International Nuclear Information System (INIS)

Ren, Z.; Junfang, Z.; Lichun, Z.

2001-01-01

It was derived that the bosonic and fermionic entropies in (1+1)-dimensional charged black hole directly by using the quantum statistical method. The result is the same as the integral expression obtained by solving the wave equation approximately. Then it is obtained the statistical entropy of the black hole by integration via the improved brick-wall method, membrane model. The derived entropy satisfies the thermodynamic relation. When the radiation temperature of the black hole tends to zero, so does the entropy. It obeys Nernst theorem. So it can be taken as Planck absolute entropy

Picrotoxane sesquiterpenoids from the stems of Dendrobium nobile and their absolute configurations and angiogenesis effect.

Science.gov (United States)

Meng, Chun-Wang; He, Yu-Lin; Peng, Cheng; Ding, Xing-Jie; Guo, Li; Xiong, Liang

2017-09-01

Five picrotoxane sesquiterpenoids belonging to the unusual dendrobine-type (1 and 4) and the picrotoxinin-type (2, 3, and 5) were isolated from the stems of Dendrobium nobile Lindl. Their structures were established by spectroscopic analyses and physical properties. Compound 1 was a new dendrobine analogue. Although the planar structure of 2 and 3 had been reported, their absolute configurations were first determined by single-crystal X-ray diffraction and circular dichroism. Compound 2 exhibited angiogenesis effect against sunitinib-induced damage on intersegmental blood vessels in Tg (flk1: EGFP) and Tg (fli1: nEGFP) transgenic zebrafish at concentrations of 3.13, 6.25, 12.50, and 25.00μM. Copyright © 2017. Published by Elsevier B.V.

The sesquiterpenoid nootkatone and the absolute configuration of a dibromo derivative.

Science.gov (United States)

Sauer, Anne M; Fronczek, Frank R; Zhu, Betty C R; Crowe, William E; Henderson, Gregg; Laine, Roger A

2003-05-01

Nootkatone, or (4R,4aS,6R)-4,4a,5,6,7,8-hexahydro-4,4a-dimethyl-6-(1-methylethenyl)naphthalen-2(3H)-one, C(15)H(22)O, a sesquiterpene with strong repellent properties against Formosan subterranean termites and other insects, has the valencene skeleton. The dibromo derivative (1S,3R,4S,4aS,6R,8aR)-1,3-dibromo-6-isopropyl-4,4a-dimethyl-1,2,3,4,5,6,7,8-octahydronaphthalen-2-one, C(15)H(24)Br(2)O, has two independent molecules in the asymmetric unit, which differ in the rotation of the isopropyl group with respect to the main skeleton. The C-Br distances are in the range 1.950 (4)-1.960 (4) A. Both independent molecules form zigzag chains, with very short intermolecular carbonyl-carbonyl interactions, having the perpendicular motif and O...C distances of 2.886 (6) and 2.898 (6) A. These chains are flanked by intermolecular Br...Br interactions of distances in the range 4.067 (1)-4.218 (1) A. The absolute configuration of the dibromo derivative was determined, from which that of nootkatone was inferred.

Nonthreshold D-brane bound states and black holes with nonzero entropy

International Nuclear Information System (INIS)

Costa, M.S.; Cvetic, M.

1997-01-01

We start with Bogomol close-quote nyi-Prasad-Sommerfield- (BPS) saturated configurations of two (orthogonally) intersecting M-branes and use the electromagnetic duality or dimensional reduction along a boost, in order to obtain new p-brane bound states. In the first case the resulting configurations are interpreted as BPS-saturated nonthreshold bound states of intersecting p-branes, and in the second case as p-branes intersecting at angles and their duals. As a by-product we deduce the enhancement of supersymmetry as the angle approaches zero. We also comment on the D-brane theory describing these new bound states, and a connection between the angle and the world-volume gauge fields of the D-brane system. We use these configurations to find new embeddings of the four- and five-dimensional black holes with nonzero entropy, whose entropy now also depends on the angle and world-volume gauge fields. The corresponding D-brane configuration sheds light on the microscopic entropy of such black holes. copyright 1997 The American Physical Society

Entropy estimates for simple random fields

DEFF Research Database (Denmark)

Forchhammer, Søren; Justesen, Jørn

1995-01-01

We consider the problem of determining the maximum entropy of a discrete random field on a lattice subject to certain local constraints on symbol configurations. The results are expected to be of interest in the analysis of digitized images and two dimensional codes. We shall present some examples...... of binary and ternary fields with simple constraints. Exact results on the entropies are known only in a few cases, but we shall present close bounds and estimates that are computationally efficient...

Brain entropy and human intelligence: A resting-state fMRI study

Science.gov (United States)

Calderone, Daniel; Morales, Leah J.

2018-01-01

Human intelligence comprises comprehension of and reasoning about an infinitely variable external environment. A brain capable of large variability in neural configurations, or states, will more easily understand and predict variable external events. Entropy measures the variety of configurations possible within a system, and recently the concept of brain entropy has been defined as the number of neural states a given brain can access. This study investigates the relationship between human intelligence and brain entropy, to determine whether neural variability as reflected in neuroimaging signals carries information about intellectual ability. We hypothesize that intelligence will be positively associated with entropy in a sample of 892 healthy adults, using resting-state fMRI. Intelligence is measured with the Shipley Vocabulary and WASI Matrix Reasoning tests. Brain entropy was positively associated with intelligence. This relation was most strongly observed in the prefrontal cortex, inferior temporal lobes, and cerebellum. This relationship between high brain entropy and high intelligence indicates an essential role for entropy in brain functioning. It demonstrates that access to variable neural states predicts complex behavioral performance, and specifically shows that entropy derived from neuroimaging signals at rest carries information about intellectual capacity. Future work in this area may elucidate the links between brain entropy in both resting and active states and various forms of intelligence. This insight has the potential to provide predictive information about adaptive behavior and to delineate the subdivisions and nature of intelligence based on entropic patterns. PMID:29432427

Brain entropy and human intelligence: A resting-state fMRI study.

Science.gov (United States)

Saxe, Glenn N; Calderone, Daniel; Morales, Leah J

2018-01-01

Human intelligence comprises comprehension of and reasoning about an infinitely variable external environment. A brain capable of large variability in neural configurations, or states, will more easily understand and predict variable external events. Entropy measures the variety of configurations possible within a system, and recently the concept of brain entropy has been defined as the number of neural states a given brain can access. This study investigates the relationship between human intelligence and brain entropy, to determine whether neural variability as reflected in neuroimaging signals carries information about intellectual ability. We hypothesize that intelligence will be positively associated with entropy in a sample of 892 healthy adults, using resting-state fMRI. Intelligence is measured with the Shipley Vocabulary and WASI Matrix Reasoning tests. Brain entropy was positively associated with intelligence. This relation was most strongly observed in the prefrontal cortex, inferior temporal lobes, and cerebellum. This relationship between high brain entropy and high intelligence indicates an essential role for entropy in brain functioning. It demonstrates that access to variable neural states predicts complex behavioral performance, and specifically shows that entropy derived from neuroimaging signals at rest carries information about intellectual capacity. Future work in this area may elucidate the links between brain entropy in both resting and active states and various forms of intelligence. This insight has the potential to provide predictive information about adaptive behavior and to delineate the subdivisions and nature of intelligence based on entropic patterns.

Carnot to Clausius: Caloric to Entropy

Science.gov (United States)

Newburgh, Ronald

2009-01-01

This paper discusses how the Carnot engine led to the formulation of the second law of thermodynamics and entropy. The operation of the engine is analysed both in terms of heat as the caloric fluid and heat as a form of energy. A keystone of Carnot's thinking was the absolute conservation of caloric. Although the Carnot analysis was partly…

Structure and Absolute Configuration of Jurassic Polyketide-Derived Spiroborate Pigments Obtained from Microgram Quantities.

Science.gov (United States)

Wolkenstein, Klaus; Sun, Han; Falk, Heinz; Griesinger, Christian

2015-10-28

Complete structural elucidation of natural products is often challenging due to structural complexity and limited availability. This is true for present-day secondary metabolites, but even more for exceptionally preserved secondary metabolites of ancient organisms that potentially provide insights into the evolutionary history of natural products. Here, we report the full structure and absolute configuration of the borolithochromes, enigmatic boron-containing pigments from a Jurassic putative red alga, from samples of less than 50 μg using microcryoprobe NMR, circular dichroism spectroscopy, and density functional theory calculations and reveal their polyketide origin. The pigments are identified as spiroborates with two pentacyclic sec-butyl-trihydroxy-methyl-benzo[gh]tetraphen-one ligands and less-substituted derivatives. The configuration of the sec-butyl group is found to be (S). Because the exceptional benzo[gh]tetraphene scaffold is otherwise only observed in the recently discovered polyketide clostrubin from a present-day Clostridium bacterium, the Jurassic borolithochromes now can be unambiguously linked to the modern polyketide, providing evidence that the fossil pigments are almost originally preserved secondary metabolites and suggesting that the pigments in fact may have been produced by an ancient bacterium. The borolithochromes differ fundamentally from previously described boronated polyketides and represent the first boronated aromatic polyketides found so far. Our results demonstrate the potential of microcryoprobe NMR in the analysis of previously little-explored secondary metabolites from ancient organisms and reveal the evolutionary significance of clostrubin-type polyketides.

Combined use of three forms of chiroptical spectroscopies in the study of the absolute configuration and conformational properties of 3-phenylcyclopentanone, 3-phenylcyclohexanone, and 3-phenylcycloheptanone

Czech Academy of Sciences Publication Activity Database

Scafato, P.; Caprioli, F.; Pisani, L.; Padula, Daniele; Santoro, F.; Mazzeo, G.; Abbate, S.; Lebon, F.; Longhi, G.

2013-01-01

Roč. 69, č. 50 (2013), s. 10752-10762 ISSN 0040-4020 Institutional support: RVO:61388963 Keywords : ORD * ECD * VCD * vibronic features * absolute configuration * conformations * phenyl hindered rotation Subject RIV: CC - Organic Chemistry Impact factor: 2.817, year: 2013

Connecting diffusion and entropy of bulk water at the single particle ...

Indian Academy of Sciences (India)

The relation between the dynamic (e.g., diffusion) and thermodynamic (e.g., entropy) properties of water and water-like liquids has been an active area of research for a long time. Although several studies have investigated the diffusivity and entropy for different systems, these studies have probed either the configurational ...

Phase equilibrium of PuO{sub 2-x} - Pu{sub 2}O{sub 3} based on first-principles calculations and configurational entropy change

Energy Technology Data Exchange (ETDEWEB)

Minamoto, Satoshi, E-mail: satoshi.minamoto@ctc-g.co.jp [ITOCHU Techno-Solutions Corporation, Kasumigaseki, 2-5, Kasumigaseki 3-chome, Chiyoda-ku, Tokyo 100-6080 (Japan); Kato, Masato [Japan Atomic Energy Agency, Tokai-mura, Naka-gun, Ibaraki (Japan); Konashi, Kenji [Institute for Materials Research, Tohoku University, Oarai-chou, Ibaraki (Japan)

2011-05-31

Combination of an oxygen vacancy formation energy calculated using first-principles approach and the configurational entropy change treated within the framework of statistical mechanics gives an expression of the Gibbs free energy at large deviation from stoichiometry of plutonium oxide PuO{sub 2}. An oxygen vacancy formation energy 4.20 eV derived from our previously first-principles calculation was used to evaluate the Gibbs free energy change due to oxygen vacancies in the crystal. The oxygen partial pressures then can be evaluated from the change of the free energy with two fitting parameters (a vacancy-vacancy interaction energy and vibration entropy change due to induced vacancies). Derived thermodynamic expression for the free energy based on the SGTE thermodynamic data for the stoichiometric PuO{sub 2} and the Pu{sub 2}O{sub 3} compounds was further incorporated into the CALPHAD modeling, then phase equilibrium between the stoichiometric Pu{sub 2}O{sub 3} and non-stoichiometric PuO{sub 2-x} were reproduced.

MoNbTaV Medium-Entropy Alloy

Directory of Open Access Journals (Sweden)

Hongwei Yao

2016-05-01

Full Text Available Guided by CALPHAD (Calculation of Phase Diagrams modeling, the refractory medium-entropy alloy MoNbTaV was synthesized by vacuum arc melting under a high-purity argon atmosphere. A body-centered cubic solid solution phase was experimentally confirmed in the as-cast ingot using X-ray diffraction and scanning electron microscopy. The measured lattice parameter of the alloy (3.208 Å obeys the rule of mixtures (ROM, but the Vickers microhardness (4.95 GPa and the yield strength (1.5 GPa are about 4.5 and 4.6 times those estimated from the ROM, respectively. Using a simple model on solid solution strengthening predicts a yield strength of approximately 1.5 GPa. Thermodynamic analysis shows that the total entropy of the alloy is more than three times the configurational entropy at room temperature, and the entropy of mixing exhibits a small negative departure from ideal mixing.

Parameters Tuning of Model Free Adaptive Control Based on Minimum Entropy

Institute of Scientific and Technical Information of China (English)

Chao Ji; Jing Wang; Liulin Cao; Qibing Jin

2014-01-01

Dynamic linearization based model free adaptive control(MFAC) algorithm has been widely used in practical systems, in which some parameters should be tuned before it is successfully applied to process industries. Considering the random noise existing in real processes, a parameter tuning method based on minimum entropy optimization is proposed,and the feature of entropy is used to accurately describe the system uncertainty. For cases of Gaussian stochastic noise and non-Gaussian stochastic noise, an entropy recursive optimization algorithm is derived based on approximate model or identified model. The extensive simulation results show the effectiveness of the minimum entropy optimization for the partial form dynamic linearization based MFAC. The parameters tuned by the minimum entropy optimization index shows stronger stability and more robustness than these tuned by other traditional index,such as integral of the squared error(ISE) or integral of timeweighted absolute error(ITAE), when the system stochastic noise exists.

Cryogenic, Absolute, High Pressure Sensor

Science.gov (United States)

Chapman, John J. (Inventor); Shams. Qamar A. (Inventor); Powers, William T. (Inventor)

2001-01-01

A pressure sensor is provided for cryogenic, high pressure applications. A highly doped silicon piezoresistive pressure sensor is bonded to a silicon substrate in an absolute pressure sensing configuration. The absolute pressure sensor is bonded to an aluminum nitride substrate. Aluminum nitride has appropriate coefficient of thermal expansion for use with highly doped silicon at cryogenic temperatures. A group of sensors, either two sensors on two substrates or four sensors on a single substrate are packaged in a pressure vessel.

Numerical viscosity of entropy stable schemes for systems of conservation laws. Final Report

International Nuclear Information System (INIS)

Tadmor, E.

1985-11-01

Discrete approximations to hyperbolic systems of conservation laws are studied. The amount of numerical viscosity present in such schemes is quantified and related to their entropy stability by means of comparison. To this end conservative schemes which are also entropy conservative are constructed. These entropy conservative schemes enjoy second-order accuracy; moreover, they admit a particular interpretation within the finite-element frameworks, and hence can be formulated on various mesh configurations. It is then shown that conservative schemes are entropy stable if and only if they contain more viscosity than the mentioned above entropy conservative ones

Glass Transition, Crystallization of Glass-Forming Melts, and Entropy

Directory of Open Access Journals (Sweden)

Jürn W. P. Schmelzer

2018-02-01

Full Text Available A critical analysis of possible (including some newly proposed definitions of the vitreous state and the glass transition is performed and an overview of kinetic criteria of vitrification is presented. On the basis of these results, recent controversial discussions on the possible values of the residual entropy of glasses are reviewed. Our conclusion is that the treatment of vitrification as a process of continuously breaking ergodicity with entropy loss and a residual entropy tending to zero in the limit of zero absolute temperature is in disagreement with the absolute majority of experimental and theoretical investigations of this process and the nature of the vitreous state. This conclusion is illustrated by model computations. In addition to the main conclusion derived from these computations, they are employed as a test for several suggestions concerning the behavior of thermodynamic coefficients in the glass transition range. Further, a brief review is given on possible ways of resolving the Kauzmann paradox and its implications with respect to the validity of the third law of thermodynamics. It is shown that neither in its primary formulations nor in its consequences does the Kauzmann paradox result in contradictions with any basic laws of nature. Such contradictions are excluded by either crystallization (not associated with a pseudospinodal as suggested by Kauzmann or a conventional (and not an ideal glass transition. Some further so far widely unexplored directions of research on the interplay between crystallization and glass transition are anticipated, in which entropy may play—beyond the topics widely discussed and reviewed here—a major role.

The existence of negative absolute temperatures in Axelrod’s social influence model

Science.gov (United States)

Villegas-Febres, J. C.; Olivares-Rivas, W.

2008-06-01

We introduce the concept of temperature as an order parameter in the standard Axelrod’s social influence model. It is defined as the relation between suitably defined entropy and energy functions, T=(. We show that at the critical point, where the order/disorder transition occurs, this absolute temperature changes in sign. At this point, which corresponds to the transition homogeneous/heterogeneous culture, the entropy of the system shows a maximum. We discuss the relationship between the temperature and other properties of the model in terms of cultural traits.

Mathematical and information-geometrical entropy for phenomenological Fourier and non-Fourier heat conduction

Science.gov (United States)

Li, Shu-Nan; Cao, Bing-Yang

2017-09-01

The second law of thermodynamics governs the direction of heat transport, which provides the foundational definition of thermodynamic Clausius entropy. The definitions of entropy are further generalized for the phenomenological heat transport models in the frameworks of classical irreversible thermodynamics and extended irreversible thermodynamics (EIT). In this work, entropic functions from mathematics are combined with phenomenological heat conduction models and connected to several information-geometrical conceptions. The long-time behaviors of these mathematical entropies exhibit a wide diversity and physical pictures in phenomenological heat conductions, including the tendency to thermal equilibrium, and exponential decay of nonequilibrium and asymptotics, which build a bridge between the macroscopic and microscopic modelings. In contrast with the EIT entropies, the mathematical entropies expressed in terms of the internal energy function can avoid singularity paired with nonpositive local absolute temperature caused by non-Fourier heat conduction models.

Residual Entropy, the Third Law and Latent Heat

Directory of Open Access Journals (Sweden)

Frank L. Lambert

2008-09-01

Full Text Available A novel thermodynamic treatment of residual entropy in crystals, involving the configurational partition function, is suggested, which is consistent with both classical and statistical thermodynamics. It relates residual entropy to the inherent latent heat which would be released upon cooling if the reversible path were available. The nature of this heat is that if the crystal possessing residual entropy freezes above its Boltzmann’s characteristic temperature of molecular alignment, the difference in energy between different molecular arrangements is overcome by the kT heat bath to form a nearly-ideal solution. However, upon cooling below this characteristic temperature, they would separate with a concomitant release of the corresponding energy, provided the reversible path were available.

SpatEntropy: Spatial Entropy Measures in R

OpenAIRE

Altieri, Linda; Cocchi, Daniela; Roli, Giulia

2018-01-01

This article illustrates how to measure the heterogeneity of spatial data presenting a finite number of categories via computation of spatial entropy. The R package SpatEntropy contains functions for the computation of entropy and spatial entropy measures. The extension to spatial entropy measures is a unique feature of SpatEntropy. In addition to the traditional version of Shannon's entropy, the package includes Batty's spatial entropy, O'Neill's entropy, Li and Reynolds' contagion index, Ka...

Adjoint entropy vs topological entropy

OpenAIRE

Giordano Bruno, Anna

2012-01-01

Recently the adjoint algebraic entropy of endomorphisms of abelian groups was introduced and studied. We generalize the notion of adjoint entropy to continuous endomorphisms of topological abelian groups. Indeed, the adjoint algebraic entropy is defined using the family of all finite-index subgroups, while we take only the subfamily of all open finite-index subgroups to define the topological adjoint entropy. This allows us to compare the (topological) adjoint entropy with the known topologic...

Upper entropy axioms and lower entropy axioms

International Nuclear Information System (INIS)

Guo, Jin-Li; Suo, Qi

2015-01-01

The paper suggests the concepts of an upper entropy and a lower entropy. We propose a new axiomatic definition, namely, upper entropy axioms, inspired by axioms of metric spaces, and also formulate lower entropy axioms. We also develop weak upper entropy axioms and weak lower entropy axioms. Their conditions are weaker than those of Shannon–Khinchin axioms and Tsallis axioms, while these conditions are stronger than those of the axiomatics based on the first three Shannon–Khinchin axioms. The subadditivity and strong subadditivity of entropy are obtained in the new axiomatics. Tsallis statistics is a special case of satisfying our axioms. Moreover, different forms of information measures, such as Shannon entropy, Daroczy entropy, Tsallis entropy and other entropies, can be unified under the same axiomatics

Studies on the Diels-Alder adduct from cyclopentadiene and p-benzoquinone: Biotransformation, enantiomeric excess and absolute configuration

Directory of Open Access Journals (Sweden)

Felipe Camargo Braga

2012-06-01

Full Text Available The use of microorganisms or isolated enzymes in synthetic routes has been extensively used by industry and academic research. A great advantage of biotransformation in a synthetic route is highly regio- and enatiosselective control, which can be achieved through microbial catalyzed reaction. Biotransformation is one of the most efficient methods in a production of high purity optical compounds and development of efficient routes for target molecules. Biotransformation by Mucor ramosissimus of enedione 1 gave the keto-alcohol (--2 with enantiomeric excess (ee>99,9% (determined by 1H NMR with [(+-Eu(hfc]3 and their epimer (--3. Determination of the absolute configuration of epimer (--3 was accomplished by controlled reaction and measuring of optical rotation (scheme 1. The fungus M. ramosissimus is a promising species to perform desymmetrization of diketones with high enantioselectivity.

Plasma radiation dynamics with the upgraded Absolute Extreme Ultraviolet tomographical system in the Tokamak à Configuration Variable

Energy Technology Data Exchange (ETDEWEB)

Tal, B.; Nagy, D.; Veres, G. [Institute for Particle and Nuclear Physics, Wigner Research Centre for Physics, Hungarian Academy of Sciences, Association EURATOM, P. O. Box 49, H-1525 Budapest (Hungary); Labit, B.; Chavan, R.; Duval, B. [Ecole Polytechnique Fédérale de Lausanne (EPFL), Centre de Recherches en Physique des Plasmas, Association EURATOM-Confédération Suisse, EPFL SB CRPP, Station 13, CH-1015 Lausanne (Switzerland)

2013-12-15

We introduce an upgraded version of a tomographical system which is built up from Absolute Extreme Ultraviolet-type (AXUV) detectors and has been installed on the Tokamak à Configuration Variable (TCV). The system is suitable for the investigation of fast radiative processes usually observed in magnetically confined high-temperature plasmas. The upgrade consists in the detector protection by movable shutters, some modifications to correct original design errors and the improvement in the data evaluation techniques. The short-term sensitivity degradation of the detectors, which is caused by the plasma radiation itself, has been monitored and found to be severe. The results provided by the system are consistent with the measurements obtained with the usual plasma radiation diagnostics installed on TCV. Additionally, the coupling between core plasma radiation and plasma-wall interaction is revealed. This was impossible with other available diagnostics on TCV.

Soft hairy warped black hole entropy

Science.gov (United States)

Grumiller, Daniel; Hacker, Philip; Merbis, Wout

2018-02-01

We reconsider warped black hole solutions in topologically massive gravity and find novel boundary conditions that allow for soft hairy excitations on the horizon. To compute the associated symmetry algebra we develop a general framework to compute asymptotic symmetries in any Chern-Simons-like theory of gravity. We use this to show that the near horizon symmetry algebra consists of two u (1) current algebras and recover the surprisingly simple entropy formula S = 2 π( J 0 + + J 0 - ), where J 0 ± are zero mode charges of the current algebras. This provides the first example of a locally non-maximally symmetric configuration exhibiting this entropy law and thus non-trivial evidence for its universality.

Nonsymmetric entropy and maximum nonsymmetric entropy principle

International Nuclear Information System (INIS)

Liu Chengshi

2009-01-01

Under the frame of a statistical model, the concept of nonsymmetric entropy which generalizes the concepts of Boltzmann's entropy and Shannon's entropy, is defined. Maximum nonsymmetric entropy principle is proved. Some important distribution laws such as power law, can be derived from this principle naturally. Especially, nonsymmetric entropy is more convenient than other entropy such as Tsallis's entropy in deriving power laws.

Phonon broadening in high entropy alloys

Science.gov (United States)

Körmann, Fritz; Ikeda, Yuji; Grabowski, Blazej; Sluiter, Marcel H. F.

2017-09-01

Refractory high entropy alloys feature outstanding properties making them a promising materials class for next-generation high-temperature applications. At high temperatures, materials properties are strongly affected by lattice vibrations (phonons). Phonons critically influence thermal stability, thermodynamic and elastic properties, as well as thermal conductivity. In contrast to perfect crystals and ordered alloys, the inherently present mass and force constant fluctuations in multi-component random alloys (high entropy alloys) can induce significant phonon scattering and broadening. Despite their importance, phonon scattering and broadening have so far only scarcely been investigated for high entropy alloys. We tackle this challenge from a theoretical perspective and employ ab initio calculations to systematically study the impact of force constant and mass fluctuations on the phonon spectral functions of 12 body-centered cubic random alloys, from binaries up to 5-component high entropy alloys, addressing the key question of how chemical complexity impacts phonons. We find that it is crucial to include both mass and force constant fluctuations. If one or the other is neglected, qualitatively wrong results can be obtained such as artificial phonon band gaps. We analyze how the results obtained for the phonons translate into thermodynamically integrated quantities, specifically the vibrational entropy. Changes in the vibrational entropy with increasing the number of elements can be as large as changes in the configurational entropy and are thus important for phase stability considerations. The set of studied alloys includes MoTa, MoTaNb, MoTaNbW, MoTaNbWV, VW, VWNb, VWTa, VWNbTa, VTaNbTi, VWNbTaTi, HfZrNb, HfMoTaTiZr.

Critical study on conventional concept of entropy

International Nuclear Information System (INIS)

Afridi, M.K.; Nizami, S.

2006-01-01

The concept of increase in entropy or disorder as a result of all natural processes has been critically reviewed on the basis of experimental facts and ongoing phenomena on our Globe. Similarly, order-disorder statements have also been judged under new and fresh look. In fact, these are not absolute but depend upon defining specific purpose and considering that whether that purpose is being served or not. The new concept has been elaborated by considering natural biological processes, spontaneous mixing of four different gases, distribution of four points in space and assembling of a packaged electronic gadget. Actually, this order-disorder dilemma is the result of not defining the specific purpose of a process which leads to so-called concept that disorder is increasing day by day in our universe. The traditional concept of entropy has been finally tested under heat exchange and probability considerations, which also yield no information to discern it as a measure of disorder. Consequently, increase of entropy translating into increase of disorder could not be applied to all natural processes especially the natural biological systems. (author)

Experimental heat capacities, excess entropies, and magnetic properties of bulk and nano Fe3O4-Co3O4 and Fe3O4-Mn3O4 spinel solid solutions

Science.gov (United States)

Schliesser, Jacob M.; Huang, Baiyu; Sahu, Sulata K.; Asplund, Megan; Navrotsky, Alexandra; Woodfield, Brian F.

2018-03-01

We have measured the heat capacities of several well-characterized bulk and nanophase Fe3O4-Co3O4 and Fe3O4-Mn3O4 spinel solid solution samples from which magnetic properties of transitions and third-law entropies have been determined. The magnetic transitions show several features common to effects of particle and magnetic domain sizes. From the standard molar entropies, excess entropies of mixing have been generated for these solid solutions and compared with configurational entropies determined previously by assuming appropriate cation and valence distributions. The vibrational and magnetic excess entropies for bulk materials are comparable in magnitude to the respective configurational entropies indicating that excess entropies of mixing must be included when analyzing entropies of mixing. The excess entropies for nanophase materials are even larger than the configurational entropies. Changes in valence, cation distribution, bonding and microstructure between the mixing ions are the likely sources of the positive excess entropies of mixing.

Definition of Turbulent Boundary-Layer with Entropy Concept

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Zhao Rui

2016-01-01

Full Text Available The relationship between the entropy increment and the viscosity dissipation in turbulent boundary-layer is systematically investigated. Through theoretical analysis and direct numerical simulation (DNS, an entropy function fs is proposed to distinguish the turbulent boundary-layer from the external flow. This approach is proved to be reliable after comparing its performance in the following complex flows, namely, low-speed airfoil flows with different wall temperature, supersonic cavity-ramp flow dominated by the combination of free-shear layer, larger recirculation and shocks, and the hypersonic flow past an aeroplane configuration. Moreover, fs is deduced from the point of energy, independent of any particular turbulent quantities. That is, this entropy concept could be utilized by other engineering applications related with turbulent boundary-layer, such as turbulence modelling transition prediction and engineering thermal protection.

Entropy, neutro-entropy and anti-entropy for neutrosophic information

OpenAIRE

Vasile Patrascu

2017-01-01

This approach presents a multi-valued representation of the neutrosophic information. It highlights the link between the bifuzzy information and neutrosophic one. The constructed deca-valued structure shows the neutrosophic information complexity. This deca-valued structure led to construction of two new concepts for the neutrosophic information: neutro-entropy and anti-entropy. These two concepts are added to the two existing: entropy and non-entropy. Thus, we obtained the following triad: e...

Remarks on entanglement entropy in string theory

Science.gov (United States)

Balasubramanian, Vijay; Parrikar, Onkar

2018-03-01

Entanglement entropy for spatial subregions is difficult to define in string theory because of the extended nature of strings. Here we propose a definition for bosonic open strings using the framework of string field theory. The key difference (compared to ordinary quantum field theory) is that the subregion is chosen inside a Cauchy surface in the "space of open string configurations." We first present a simple calculation of this entanglement entropy in free light-cone string field theory, ignoring subtleties related to the factorization of the Hilbert space. We reproduce the answer expected from an effective field theory point of view, namely a sum over the one-loop entanglement entropies corresponding to all the particle-excitations of the string, and further show that the full string theory regulates ultraviolet divergences in the entanglement entropy. We then revisit the question of factorization of the Hilbert space by analyzing the covariant phase-space associated with a subregion in Witten's covariant string field theory. We show that the pure gauge (i.e., BRST exact) modes in the string field become dynamical at the entanglement cut. Thus, a proper definition of the entropy must involve an extended Hilbert space, with new stringy edge modes localized at the entanglement cut.

An exploration for the macroscopic physical meaning of entropy

Institute of Scientific and Technical Information of China (English)

无

2010-01-01

The macroscopic physical meaning of entropy is analyzed based on the exergy (availability) of a combined system (a closed system and its environment), which is the maximum amount of useful work obtainable from the system and the environment as the system is brought into equilibrium with the environment. The process the system experiences can be divided in two sequent sub-processes, the process at constant volume, which represents the heat interaction of the system with the environment, and the adiabatic process, which represents the work interaction of the system with the environment. It is shown that the macroscopic physical meaning of entropy is a measure of the unavailable energy of a closed system for doing useful work through heat interaction. This statement is more precise than those reported in prior literature. The unavailability function of a closed system can be defined as T0S and p0V in volume constant process and adiabatic process, respectively. Their changes, that is, AiTgS) and A (p0V) represent the unusable parts of the internal energy of a closed system for doing useful work in corresponding processes. Finally, the relation between Clausius entropy and Boltzmann entropy is discussed based on the comparison of their expressions for absolute entropy.

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.

Investigating the Configurations in Cross-Shareholding: A Joint Copula-Entropy Approach

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Roy Cerqueti

2018-02-01

Full Text Available The complex nature of the interlacement of economic actors is quite evident at the level of the Stock market, where any company may actually interact with the other companies buying and selling their shares. In this respect, the companies populating a Stock market, along with their connections, can be effectively modeled through a directed network, where the nodes represent the companies, and the links indicate the ownership. This paper deals with this theme and discusses the concentration of a market. A cross-shareholding matrix is considered, along with two key factors: the node out-degree distribution which represents the diversification of investments in terms of the number of involved companies, and the node in-degree distribution which reports the integration of a company due to the sales of its own shares to other companies. While diversification is widely explored in the literature, integration is most present in literature on contagions. This paper captures such quantities of interest in the two frameworks and studies the stochastic dependence of diversification and integration through a copula approach. We adopt entropies as measures for assessing the concentration in the market. The main question is to assess the dependence structure leading to a better description of the data or to market polarization (minimal entropy or market fairness (maximal entropy. In so doing, we derive information on the way in which the in- and out-degrees should be connected in order to shape the market. The question is of interest to regulators bodies, as witnessed by specific alert threshold published on the US mergers guidelines for limiting the possibility of acquisitions and the prevalence of a single company on the market. Indeed, all countries and the EU have also rules or guidelines in order to limit concentrations, in a country or across borders, respectively. The calibration of copulas and model parameters on the basis of real data serves as an

Evanescent magnetic field effects on entropy generation at the onset ...

Indian Academy of Sciences (India)

application of evanescent magnetic field not only suppresses the fluctuation of the ..... the Prigogine's theorem of minimum entropy production is unproven. ... consists in a double spiral configuration and viscous boundary layers in close ...

Marine natural products. XXXII. Absolute configurations of C-4 of the manoalide family, biologically active sesterterpenes from the marine sponge Hyrtios erecta.

Science.gov (United States)

Kobayashi, M; Okamoto, T; Hayashi, K; Yokoyama, N; Sasaki, T; Kitagawa, I

1994-02-01

Cytotoxic sesterterpenes, manoalide 25-acetals (1a, 1b), seco-manoalide (2), (E)-neomanoalide (3), (Z)-neomanoalide (4), and heteronemin (6), were isolated from the marine sponge Hyrtios erecta (collected at Amami Island, Kagoshima Prefecture, Japan) by bioassay-guided separation and the absolute configurations of these manoalide family members have been determined. Manoalide 25-acetals (1a, 1b) were shown to exhibit in vivo antitumor activity and to inhibit the DNA-relaxing activity of mouse DNA topoisomerase I and the DNA-unknotting activity of calf thymus DNA topoisomerase II.

Entropy, neutro-entropy and anti-entropy for neutrosophic information

OpenAIRE

Vasile Patrascu

2017-01-01

This article shows a deca-valued representation of neutrosophic information in which are defined the following features: truth, falsity, weak truth, weak falsity, ignorance, contradiction, saturation, neutrality, ambiguity and hesitation. Using these features, there are constructed computing formulas for entropy, neutro-entropy and anti-entropy.

Central-to-axial chirality transfer revealed by liquid crystals: a combined experimental and computational approach for the determination of absolute configuration of carboxylic acids with an α chirality centre.

Science.gov (United States)

Ferrarini, Alberta; Ferroni, Fiammetta; Pieraccini, Silvia; Rosini, Carlo; Superchi, Stefano; Spada, Gian Piero

2011-10-01

The conversion into 6,7-dihydro-5H-dibenz[c,e]azepine (DAZ) N-protected amides is a viable route for the determination of the absolute configuration of chiral 2-substituted carboxylic acids. The biphenyl moiety of DAZ, besides being a probe of chirality for the electronic circular dichroism (ECD) spectroscopy, makes these systems suitable for configuration assignment by exploiting the chirality amplification which occurs in nematic liquid crystals. To assess the reliability of the liquid crystal method in detecting the absolute stereochemistry of chiral amides bound to a biphenyl group, we measured the helical twisting power of a series of DAZ-N-protected amides and compared these data with the results obtained from ECD measurements. We will show that the liquid crystal method, corroborated by HTP predictions, is trustworthy with our biphenyl derivatives, even when ECD spectra are ambiguous for the presence of aryl moieties displaying strong UV absorptions in the same range of the biphenyl chromophore. © 2011 Wiley-Liss, Inc.

Equipartition of entropy production

International Nuclear Information System (INIS)

Tondeur, D.

1990-01-01

This paper deals with the optimal design or operation of heat and mass transfer processes and develops the following conjecture: for a given duty, the best configuration of the process is that in which the entropy production rate is most uniformly distributed. This principle is first analyzed in detail on the simple example of tubular heat exchangers, and within the framework of linear irreversible thermodynamics. A main result is established, which states that the total entropy production is minimal when the local production is uniformly distributed (equipartition). Corollaries then result, which relate the entropy production and the variance of its distribution to economic factors such as the duty, the exchange area, the fluid flow-rates, and the temperature changes. The equipartition principle is then extended to multiple independent variables (time and space), multicomponent transfer, and non-linear but concave flux vs force relationship. Chemical Engineering examples are discussed, where the equipartition property has been applied implicitly or explicitly: design of distillation plates, cyclic distillation, optimal state of feed, and flow-sheets in chromatographic separations. Finally, a generalization of the equipartition principle is proposed, for systems with a distributed design variable (such as the size of the various elements of a system). The optimal distribution of investment is such that the investment in each element (properly amortized) is equal to the cost of irreversible energy degradation in this element. This is equivalent to saying that the ratio of these two quantities is uniformly distributed over the system, and reduces to equipartition of entropy production when the cost factors are constant over the whole system

Manufacturing of High Entropy Alloys

Science.gov (United States)

Jablonski, Paul D.; Licavoli, Joseph J.; Gao, Michael C.; Hawk, Jeffrey A.

2015-07-01

High entropy alloys (HEAs) have generated interest in recent years due to their unique positioning within the alloy world. By incorporating a number of elements in high proportion they have high configurational entropy, and thus they hold the promise of interesting and useful properties such as enhanced strength and phase stability. The present study investigates the microstructure of two single-phase face-centered cubic (FCC) HEAs, CoCrFeNi and CoCrFeNiMn, with special attention given to melting, homogenization and thermo-mechanical processing. Large-scale ingots were made by vacuum induction melting to avoid the extrinsic factors inherent in small-scale laboratory button samples. A computationally based homogenization heat treatment was applied to both alloys in order to eliminate segregation due to normal ingot solidification. The alloys fabricated well, with typical thermo-mechanical processing parameters being employed.

Design of high entropy alloys based on the experience from commercial superalloys

Science.gov (United States)

Wang, Z.; Huang, Y.; Wang, J.; Liu, C. T.

2015-01-01

High entropy alloys (HEAs) have been drawing increasing attention recently and gratifying results have been obtained. However, the existing metallurgic rules of HEAs could not provide specific information of selecting candidate alloys for structural applications. Our brief survey reveals that many commercial superalloys have medium and even to high configurational entropies. The experience of commercial superalloys provides a clue for helping us in the development of HEAs for structural applications.

Thermal Expansion Anomaly Regulated by Entropy

Science.gov (United States)

Liu, Zi-Kui; Wang, Yi; Shang, Shunli

2014-11-01

Thermal expansion, defined as the temperature dependence of volume under constant pressure, is a common phenomenon in nature and originates from anharmonic lattice dynamics. However, it has been poorly understood how thermal expansion can show anomalies such as colossal positive, zero, or negative thermal expansion (CPTE, ZTE, or NTE), especially in quantitative terms. Here we show that changes in configurational entropy due to metastable micro(scopic)states can lead to quantitative prediction of these anomalies. We integrate the Maxwell relation, statistic mechanics, and first-principles calculations to demonstrate that when the entropy is increased by pressure, NTE occurs such as in Invar alloy (Fe3Pt, for example), silicon, ice, and water, and when the entropy is decreased dramatically by pressure, CPTE is expected such as in anti-Invar cerium, ice and water. Our findings provide a theoretic framework to understand and predict a broad range of anomalies in nature in addition to thermal expansion, which may include gigantic electrocaloric and electromechanical responses, anomalously reduced thermal conductivity, and spin distributions.

Multivariate multiscale entropy of financial markets

Science.gov (United States)

Lu, Yunfan; Wang, Jun

2017-11-01

In current process of quantifying the dynamical properties of the complex phenomena in financial market system, the multivariate financial time series are widely concerned. In this work, considering the shortcomings and limitations of univariate multiscale entropy in analyzing the multivariate time series, the multivariate multiscale sample entropy (MMSE), which can evaluate the complexity in multiple data channels over different timescales, is applied to quantify the complexity of financial markets. Its effectiveness and advantages have been detected with numerical simulations with two well-known synthetic noise signals. For the first time, the complexity of four generated trivariate return series for each stock trading hour in China stock markets is quantified thanks to the interdisciplinary application of this method. We find that the complexity of trivariate return series in each hour show a significant decreasing trend with the stock trading time progressing. Further, the shuffled multivariate return series and the absolute multivariate return series are also analyzed. As another new attempt, quantifying the complexity of global stock markets (Asia, Europe and America) is carried out by analyzing the multivariate returns from them. Finally we utilize the multivariate multiscale entropy to assess the relative complexity of normalized multivariate return volatility series with different degrees.

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.

Applied thermodynamics of the real gas with respect to the thermodynamic zeros of the entropy and internal energy

International Nuclear Information System (INIS)

Elsner, Albrecht

2012-01-01

Gibbs's work on the thermodynamic properties of substances presented a complete thermodynamic theory. The formulations of the entropy S and internal energy U as extensive quantities allow the zeros of the real gas to be given: S=0 at absolute zero (Nernst, Planck) and U=0 at the critical point. Consequently, every thermodynamic function is unique and absolutely specified. Interdependences among quantities such as temperature, vapor pressure, chemical potential, volume, entropy, internal energy, and heat capacity are likewise unique and numerically well defined. This is shown for the saturated fluid, water, in the region between absolute zero and the critical point. As a consequence of the calculation of the chemical potential, it follows that the free particle flow in an inhomogeneous system is essentially governed by the difference in chemical potential, and not through the difference in pressure, this effect being of importance for meteorology and oceanography.

Entropy in Collisionless Self-gravitating Systems

Science.gov (United States)

Barnes, Eric; Williams, L.

2010-01-01

Collisionless systems, like simulated dark matter halos or gas-less elliptical galaxies, often times have properties suggesting that a common physical principle controls their evolution. For example, N-body simulations of dark matter halos present nearly scale-free density/velocity-cubed profiles. In an attempt to understand the origins of such relationships, we adopt a thermodynamics approach. While it is well-known that self-gravitating systems do not have physically realizable thermal equilibrium configurations, we are interested in the behavior of entropy as mechanical equilibrium is acheived. We will discuss entropy production in these systems from a kinetic theory point of view. This material is based upon work supported by the National Aeronautics and Space Administration under grant NNX07AG86G issued through the Science Mission Directorate.

Competition between intermolecular interaction and configuration entropy as the structure-determining factor for inclusion compounds

Energy Technology Data Exchange (ETDEWEB)

Subbotin, O.; Belosludov, V.; Adamova, T. [Russian Academy of Science, Novosibirsk (Russian Federation). Nikolaev Inst. of Inorganic Chemistry; Belosludov, R.; Kawazoe, Y. [Tohoku Univ., Aoba-ku, Sendai (Japan). Inst. for Materials Research; Kudoh, J.I. [Tohoku Univ., Aoba-ku, Sendai (Japan). Center for Northeast Asia Studies

2008-07-01

This paper presented a newly developed method to accurately predict the thermodynamic properties of clathrate hydrates, particularly their structural phase transitions under pressure. The method is based on the theory of Van-der-Waals and Platteeuw with some modifications that include the influence of guest molecules on the host lattice. The model was used to explain the exception from the established rule that small guest molecules form structure s1 and large molecules form structure s2 hydrates. In this study, the thermodynamic properties of argon (Ar) hydrate and methane hydrate, each in both cubic structure s1 and s2 were modelled. The model showed that two competing factors play a role in the formation of inclusions, notably the intermolecular interaction of guest molecules with water molecules, and the configuration entropy. Competition of these 2 factors determines the structure of hydrate formed at different pressures. The model provides an accurate description of the thermodynamic properties of gas hydrates and how they behave under pressure. For the argon hydrates, the structural phase transition from structure s2 to s1 at high pressure was predicted, while methane hydrates were predicted to be metastable in the s2 structure. The model can be used for other inclusion compounds with the same type of composition such as clathrate silicon, zeolites, and inclusion compounds of semiconductor elements. 17 refs., 5 figs.

Holographic entanglement entropy and the extended phase structure of STU black holes

International Nuclear Information System (INIS)

Caceres, Elena; Nguyen, Phuc H.; Pedraza, Juan F.

2015-01-01

We study the extended thermodynamics, obtained by considering the cosmological constant as a thermodynamic variable, of STU black holes in 4-dimensions in the fixed charge ensemble. The associated phase structure is conjectured to be dual to an RG-flow on the space of field theories. We find that for some charge configurations the phase structure resembles that of a Van der Waals gas: the system exhibits a family of first order phase transitions ending in a second order phase transition at a critical temperature. We calculate the holographic entanglement entropy for several charge configurations and show that for the cases where the gravity background exhibits Van der Waals behavior, the entanglement entropy presents a transition at the same critical temperature. To further characterize the phase transition we calculate appropriate critical exponents and show that they coincide. Thus, the entanglement entropy successfully captures the information of the extended phase structure. Finally, we discuss the physical interpretation of the extended space in terms of the boundary QFT and construct various holographic heat engines dual to STU black holes.

On the Possibility of Calculating Entropy, Free Energy, and Enthalpy of Vitreous Substances

Directory of Open Access Journals (Sweden)

Sergei V. Nemilov

2018-03-01

Full Text Available A critical analysis for the arguments in support of, and against, the traditional approach to thermodynamics of vitreous state is provided. In this approach one presumes that there is a continuous variation of the entropy in the glass-liquid transition temperature range, or a “continuous entropy approach” towards 0 K which produces a positive value of the entropy at T → 0 K. I find that arguments given against this traditional approach use a different understanding of the thermodynamics of glass transition on cooling a liquid, because it suggests a discontinuity or “entropy loss approach” in the variation of entropy in the glass-liquid transition range. That is based on: (1 an unjustifiable use of the classical Boltzmann statistics for interpreting the value of entropy at absolute zero; (2 the rejection of thermodynamic analysis of systems with broken ergodicity, even though the possibility of analogous analysis was proposed already by Gibbs; (3 the possibility of a finite change in entropy of a system without absorption or release of heat; and, (4 describing the thermodynamic properties of glasses in the framework of functions, instead of functionals. The last one is necessary because for glasses the entropy and enthalpy are not functions of the state, but functionals, as defined by Gibbs’ in his classification.

Determination of the absolute configurations at stereogenic centers in the presence of axial chirality.

Science.gov (United States)

Polavarapu, Prasad L; Jeirath, Neha; Kurtán, Tibor; Pescitelli, Gennaro; Krohn, Karsten

2009-01-01

Cephalochromin, a homodimeric naphthpyranone natural product, contains both axial chirality due to the hindered rotation along the biaryl axis and central chirality due to the C-2, C-2' stereogenic centers of the fused pyranone ring. For determining the absolute configurations (ACs) of central chirality elements, different chiroptical spectroscopic methods, namely vibrational circular dichroism (VCD), electronic circular dichroism (ECD), and optical rotation (OR), have been used. From these experimental data, in conjunction with corresponding quantum chemical predictions at B3LYP/6-311G* level, it is found that the ECD spectra of cephalochromin are dominated by its axial chirality and are not suitable to distinguish the (aS,2S,2'S) and (aS,2R,2'R) diastereomers and hence to determine the ACs of the central chirality elements. OR signs also did not distinguish the (aS,2S,2'S) and (aS,2R,2'R) diastereomers. On other hand, VCD spectrum of cephalochromin exhibited separate spectral features attributable to axial chirality and stereogenic centers, thereby allowing the determination of both types of chirality elements. This is the first investigation demonstrating that, because of vibrations specific to the studied stereogenic centers, VCD spectroscopy can be used to simultaneously determine the ACs of axial and central chirality elements whenever other chiroptical methods (ECD and OR) fail to report on them. (c) 2009 Wiley-Liss, Inc.

Structure and Absolute Configuration of 20β-Hydroxyprednisolone, a Biotransformed Product of Predinisolone by the Marine Endophytic Fungus Penicilium lapidosum

Directory of Open Access Journals (Sweden)

Sadia Sultan

2014-09-01

Full Text Available The anti-inflammatory drug predinisolone (1 was reduced to 20β-hydroxyprednisolone (2 by the marine endophytic fungus Penicilium lapidosum isolated from an alga. The structural elucidation of 2 was achieved by 1D- and 2D-NMR, MS, IR data. Although, 2 is a known compound previously obtained through microbial transformation, the data provided failed to prove the C20 stereochemistry. To solve this issue, DFT and TD-DFT calculations have been carried out at the B3LYP/6–31+G (d,p level of theory in gas and solvent phase. The absolute configuration of C20 was eventually assigned by combining experimental and calculated electronic circular dichroism spectra and 3JHH chemical coupling constants.

Nonadditive entropy: The concept and its use

International Nuclear Information System (INIS)

Tsallis, C.

2009-01-01

The thermodynamical concept of entropy was introduced by Clausius in 1865 in order to construct the exact differential dS=δQ/T, where δQ is the heat transfer and the absolute temperature T its integrating factor. A few years later, in the period 1872-1877, it was shown by Boltzmann that this quantity can be expressed in terms of the probabilities associated with the microscopic configurations of the system. We refer to this fundamental connection as the Boltzmann-Gibbs (BG) entropy, namely (in its discrete form) S BG =-k sum i=1 W p i lnp i , where k is the Boltzmann constant, and {p i } the probabilities corresponding to the W microscopic configurations hence sum W i=1 p i =1. This entropic form, further discussed by Gibbs, von Neumann and Shannon, and constituting the basis of the celebrated BG statistical mechanics, is additive. Indeed, if we consider a system composed by any two probabilistically independent subsystems A and B (i.e., p ij A+B =p i A p j B , for each (i,j)), we verify that S BG (A+B)=S BG (A)+S BG (B). If a system is constituted by N equal elements which are either independent or quasi-independent (i.e., not too strongly correlated, in some specific nonlocal sense), this additivity guarantees S BG to be extensive in the thermodynamical sense, i.e., that S BG (N)∝N in the N>>1 limit. If, on the contrary, the correlations between the N elements are strong enough, then the extensivity of S BG is lost, being therefore incompatible with classical thermodynamics. In such a case, the many and precious relations described in textbooks of thermodynamics become invalid. Along a line which will be shown to overcome this difficulty, and which consistently enables the generalization of BG statistical mechanics, it was proposed in 1988 the entropy S q =k[- sum i=1 W p i q ]/(q-1) (q element of R; S 1 =S BG ). In the context of cybernetics and information theory, this and similar forms have in fact been repeatedly introduced before 1988. The entropic form

Nonadditive entropy: The concept and its use

Science.gov (United States)

Tsallis, C.

2009-06-01

The thermodynamical concept of entropy was introduced by Clausius in 1865 in order to construct the exact differential dS = δ Q/ T , where δ Q is the heat transfer and the absolute temperature T its integrating factor. A few years later, in the period 1872-1877, it was shown by Boltzmann that this quantity can be expressed in terms of the probabilities associated with the microscopic configurations of the system. We refer to this fundamental connection as the Boltzmann-Gibbs (BG) entropy, namely (in its discrete form) ensuremath S_{BG}=-ksum_{i=1}^W p_i ln p_i , where k is the Boltzmann constant, and { p i} the probabilities corresponding to the W microscopic configurations (hence ∑W i=1 p i = 1 . This entropic form, further discussed by Gibbs, von Neumann and Shannon, and constituting the basis of the celebrated BG statistical mechanics, is additive. Indeed, if we consider a system composed by any two probabilistically independent subsystems A and B ( i.e., ensuremath p_{ij}^{A+B}=p_i^A p_j^B, forall(i,j) , we verify that ensuremath S_{BG}(A+B)=S_{BG}(A)+S_{BG}(B) . If a system is constituted by N equal elements which are either independent or quasi-independent ( i.e., not too strongly correlated, in some specific nonlocal sense), this additivity guarantees SBG to be extensive in the thermodynamical sense, i.e., that ensuremath S_{BG}(N) ∝ N in the N ≫ 1 limit. If, on the contrary, the correlations between the N elements are strong enough, then the extensivity of SBG is lost, being therefore incompatible with classical thermodynamics. In such a case, the many and precious relations described in textbooks of thermodynamics become invalid. Along a line which will be shown to overcome this difficulty, and which consistently enables the generalization of BG statistical mechanics, it was proposed in 1988 the entropy ensuremath S_q=k [1-sum_{i=1}^W p_i^q]/(q-1) (qin{R}; S_1=S_{BG}) . In the context of cybernetics and information theory, this and similar forms

Absolute configurations of phytotoxins seiricardine A and inuloxin A obtained by chiroptical studies.

Science.gov (United States)

Santoro, Ernesto; Mazzeo, Giuseppe; Petrovic, Ana G; Cimmino, Alessio; Koshoubu, Jun; Evidente, Antonio; Berova, Nina; Superchi, Stefano

2015-08-01

The absolute configuration (AC) of the plant phytotoxin inuloxin A, produced by Inula viscosa, and of the fungal phytotoxin seiricardine A, obtained from Seiridium fungi, pathogen for cypress, has been determined by experimental measurements and theoretical simulations of chiroptical properties of three related methods, namely, Optical Rotatory Dispersion (ORD), Electronic Circular Dichroism (ECD), and Vibrational Circular Dichroism (VCD). Computational prediction by Density Functional Theory (DFT) of VCD spectra and by Time-dependent DFT (TDDFT) of ORD and ECD spectra allowed to assign (7R,8R,10S) AC to naturally occurring (+)-inuloxin A. In the case of compound (-)-seiricardine A, which lacks useful for the analysis UV-Vis absorption, and thus provides a hardly detectable ECD spectrum and quite low ORD values, an introduction of a suitable chromophore by chemical derivatization was performed. The corresponding derivative, 2-O-p-bromobenzoate ester, gave rise to an intense ECD spectrum and higher ORD and VCD values. The comparison of computed spectra with the experimental ones allowed to assign (1S,2R,3aS,4S,5R,7aS) AC to (-)-2-O-p-bromobenzoate ester of seiricardine A and then to (-)-seiricardine A. This study further supports a recent trend of concerted application of more than a single chiroptical technique toward an unambiguous assignment of AC of flexible and complex natural products. Moreover, the use of chemical derivatization, with insertion of suitable chromophoric moieties has allowed to treat also UV-Vis transparent molecules by ECD and ORD spectroscopies. Copyright © 2015 Elsevier Ltd. All rights reserved.

The absolute configurations of hydroxy fatty acids from the royal jelly of honeybees (Apis mellifera).

Science.gov (United States)

Kodai, Tetsuya; Nakatani, Takafumi; Noda, Naoki

2011-03-01

9-Hydroxy-2E-decenoic acid (9-HDA) is a precursor of the queen-produced substance, 9-oxo-2E-decenoic acid (9-ODA), which has various important functions and roles for caste maintenance in honeybee colonies (Apis mellifera). 9-HDA in royal jelly is considered to be a metabolite of 9-ODA produced by worker bees, and it is fed back to the queen who then transforms it into 9-ODA. Recently we found that 9-HDA is present in royal jelly as a mixture of optical isomers (R:S, 2:1). The finding leads us to suspect that chiral fatty acids in royal jelly are precursors of semiochemicals. Rather than looking for semiochemicals in the mandibular glands of the queen bee, this study involves the search for precursors of pheromones from large quantities of royal jelly. Seven chiral hydroxy fatty acids, 9,10-dihydroxy-2E-decenoic, 4,10-dihydroxy-2E-decenoic, 4,9-dihydroxy-2E-decenoic, 3-hydroxydecanoic, 3,9-dihydroxydecanoic, 3,11-dihydroxydodecanoic, and 3,10-dihydroxydecanoic acids were isolated. The absolute configurations of these acids were determined using the modified Mosher's method, and it was revealed that, similar to 9-HDA, five acids are present in royal jelly as mixtures of optical isomers.

Connectivity in the human brain dissociates entropy and complexity of auditory inputs.

Science.gov (United States)

Nastase, Samuel A; Iacovella, Vittorio; Davis, Ben; Hasson, Uri

2015-03-01

Complex systems are described according to two central dimensions: (a) the randomness of their output, quantified via entropy; and (b) their complexity, which reflects the organization of a system's generators. Whereas some approaches hold that complexity can be reduced to uncertainty or entropy, an axiom of complexity science is that signals with very high or very low entropy are generated by relatively non-complex systems, while complex systems typically generate outputs with entropy peaking between these two extremes. In understanding their environment, individuals would benefit from coding for both input entropy and complexity; entropy indexes uncertainty and can inform probabilistic coding strategies, whereas complexity reflects a concise and abstract representation of the underlying environmental configuration, which can serve independent purposes, e.g., as a template for generalization and rapid comparisons between environments. Using functional neuroimaging, we demonstrate that, in response to passively processed auditory inputs, functional integration patterns in the human brain track both the entropy and complexity of the auditory signal. Connectivity between several brain regions scaled monotonically with input entropy, suggesting sensitivity to uncertainty, whereas connectivity between other regions tracked entropy in a convex manner consistent with sensitivity to input complexity. These findings suggest that the human brain simultaneously tracks the uncertainty of sensory data and effectively models their environmental generators. Copyright © 2014. Published by Elsevier Inc.

Entropy Coherent and Entropy Convex Measures of Risk

NARCIS (Netherlands)

Laeven, R.J.A.; Stadje, M.A.

2011-01-01

We introduce two subclasses of convex measures of risk, referred to as entropy coherent and entropy convex measures of risk. We prove that convex, entropy convex and entropy coherent measures of risk emerge as certainty equivalents under variational, homothetic and multiple priors preferences,

Entropy, exergy, and cost analyses of solar driven cogeneration systems using supercritical CO_2 Brayton cycles and MEE-TVC desalination system

International Nuclear Information System (INIS)

Kouta, Amine; Al-Sulaiman, Fahad; Atif, Maimoon; Marshad, Saud Bin

2016-01-01

Highlights: • The entropy, exergy, and cost analyses for two solar cogeneration configurations are conducted. • The recompression cogeneration cycle achieves lower LCOE as compared to the regeneration cogeneration cycle. • The solar tower is the largest contributor to entropy generation in both configurations reaching almost 80%. • The specific entropy generation in the MEE-TVC decreases with decreasing the fraction. - Abstract: In this study, performance and cost analyses are conducted for a solar power tower integrated with supercritical CO_2 (sCO_2) Brayton cycles for power production and a multiple effect evaporation with a thermal vapor compression (MEE-TVC) desalination system for water production. The study is performed for two configurations based on two different supercritical cycles: the regeneration and recompression sCO_2 Brayton cycles. A two-tank molten salt storage is utilized to ensure a uniform operation throughout the day. From the entropy analysis, it was shown that the solar tower is the largest contributor to entropy generation in both configurations, reaching almost 80% from the total entropy generation, followed by the MEE-TVC desalination system, and the sCO_2 power cycle. The entropy generation in the two-tank thermal storage is negligible, around 0.3% from the total generation. In the MEE-TVC system the highest contributing component is the steam jet ejector, which is varying between 50% and 60% for different number of effects. The specific entropy generation in the MEE-TVC decreases as the fraction of the input heat to the desalination system decreases; while the specific entropy generation of the sCO_2 cycle remains constant. The cost analysis performed for different regions in Saudi Arabia and the findings reveal that the regions characterized by the highest average solar irradiation throughout the year have the lowest LCOE and LCOW values. The region achieving the lowest cost is Yanbu, followed by Khabt Al-Ghusn in the second

Parametrized overview of CO_2 power cycles for different operation conditions and configurations – An absolute and relative performance analysis

International Nuclear Information System (INIS)

Cardemil, José M.; Silva, Alexandre K. da

2016-01-01

Highlights: • Thermodynamic modeling of CO_2-based power cycles. • A multi-parameter analysis for different cycle configurations. • Performance comparison between CO_2 and four other fluids. • Detailed discussion considering optimized operational parameters (i.e., pressure, HX size). • Overview of the technical applicability of the CO_2. - Abstract: This thermodynamically based study focuses on the thermal performance of power cycles using CO_2 as the working fluid. The work considers numerous aspects that can influence the cycle's performance, such as the type of cycle (i.e., Rankine or Brayton), its configuration (i.e., with and without a recuperator), and different operational conditions (i.e., heat source temperature and the upper and lower operating pressures of the CO_2). To account for all possible scenarios, a thermodynamic routine was especially implemented and linked to a library that contained all the thermodynamics properties of CO_2. The results are mostly presented in terms of the absolute and relative 1st and 2nd Law efficiencies of CO_2 as well as the cycle's scale, here represented by the global conductance (UA) of the heat exchangers used within the cycle. For the relative performance assessment, four other working fluids, commonly used in energy conversion cycles, were considered (i.e., ethane, toluene, D4 siloxane and water). As expected, the absolute performance results indicate a strong dependence of the cycle's efficiencies on the operational conditions. As for the relative performance, the results suggest that while the CO_2's 1st Law efficiency might be lower than other fluids, its exergetic efficiency can be significantly higher. Furthermore, the calculations also indicate that the CO_2's needed global conductance is potentially lower than competing fluids (e.g., toluene) for certain operational conditions, which suggests that CO_2-based power plants can be more compact, since they might require smaller heat exchangers to produce

Entropy coherent and entropy convex measures of risk

NARCIS (Netherlands)

Laeven, Roger; Stadje, M.A.

2010-01-01

We introduce entropy coherent and entropy convex measures of risk and prove a collection of axiomatic characterization and duality results. We show in particular that entropy coherent and entropy convex measures of risk emerge as negative certainty equivalents in (the regular and a generalized

Determination of the absolute configuration of (+) - surinamensin's via diastereomeric O-methylmandelic esters

International Nuclear Information System (INIS)

Santos, L. da S.; Barata, L.E.S.

1990-01-01

The absolute configurarion of (+) surinamensin, a 8.0.4' neolignan, has been determined based on its O-methymandalates esters. Nuclear magnetic resonance and infrared and mass spectroscopy analysis are presented. (C.G.C.) [pt

Entropy coherent and entropy convex measures of risk

NARCIS (Netherlands)

Laeven, R.J.A.; Stadje, M.

2013-01-01

We introduce two subclasses of convex measures of risk, referred to as entropy coherent and entropy convex measures of risk. Entropy coherent and entropy convex measures of risk are special cases of φ-coherent and φ-convex measures of risk. Contrary to the classical use of coherent and convex

Antenna entropy in plant photosystems does not reduce the free energy for primary charge separation.

Science.gov (United States)

Jennings, Robert C; Zucchelli, Giuseppe

2014-12-01

We have investigated the concept of the so-called "antenna entropy" of higher plant photosystems. Several interesting points emerge: 1. In the case of a photosystemwhich harbours an excited state, the “antenna entropy” is equivalent to the configurational (mixing) entropy of a thermodynamic canonical ensemble. The energy associated with this parameter has been calculated for a hypothetical isoenergetic photosystem, photosystem I and photosystem II, and comes out in the range of 3.5 - 8% of the photon energy considering 680 nm. 2. The “antenna entropy” seems to be a rather unique thermodynamic phenomenon, in as much as it does not modify the free energy available for primary photochemistry, as has been previously suggested. 3. It is underlined that this configurational (mixing) entropy, unlike heat dispersal in a thermal system, does not involve energy dilution. This points out an important difference between thermal and electronic energy dispersal. Copyright © 2014 Elsevier B.V. All rights reserved.

Logarithmic black hole entropy corrections and holographic Renyi entropy

Energy Technology Data Exchange (ETDEWEB)

Mahapatra, Subhash [The Institute of Mathematical Sciences, Chennai (India); KU Leuven - KULAK, Department of Physics, Kortrijk (Belgium)

2018-01-15

The entanglement and Renyi entropies for spherical entangling surfaces in CFTs with gravity duals can be explicitly calculated by mapping these entropies first to the thermal entropy on hyperbolic space and then, using the AdS/CFT correspondence, to the Wald entropy of topological black holes. Here we extend this idea by taking into account corrections to the Wald entropy. Using the method based on horizon symmetries and the asymptotic Cardy formula, we calculate corrections to the Wald entropy and find that these corrections are proportional to the logarithm of the area of the horizon. With the corrected expression for the entropy of the black hole, we then find corrections to the Renyi entropies. We calculate these corrections for both Einstein and Gauss-Bonnet gravity duals. Corrections with logarithmic dependence on the area of the entangling surface naturally occur at the order G{sub D}{sup 0}. The entropic c-function and the inequalities of the Renyi entropy are also satisfied even with the correction terms. (orig.)

Logarithmic black hole entropy corrections and holographic Renyi entropy

International Nuclear Information System (INIS)

Mahapatra, Subhash

2018-01-01

The entanglement and Renyi entropies for spherical entangling surfaces in CFTs with gravity duals can be explicitly calculated by mapping these entropies first to the thermal entropy on hyperbolic space and then, using the AdS/CFT correspondence, to the Wald entropy of topological black holes. Here we extend this idea by taking into account corrections to the Wald entropy. Using the method based on horizon symmetries and the asymptotic Cardy formula, we calculate corrections to the Wald entropy and find that these corrections are proportional to the logarithm of the area of the horizon. With the corrected expression for the entropy of the black hole, we then find corrections to the Renyi entropies. We calculate these corrections for both Einstein and Gauss-Bonnet gravity duals. Corrections with logarithmic dependence on the area of the entangling surface naturally occur at the order G D 0 . The entropic c-function and the inequalities of the Renyi entropy are also satisfied even with the correction terms. (orig.)

Landau degeneracy and black hole entropy

International Nuclear Information System (INIS)

Costa, M.S.; Perry, M.J.

1998-01-01

We consider the supergravity solution describing a configuration of intersecting D4-branes with non-vanishing world-volume gauge fields. The entropy of such a black hole is calculated in terms of the D-branes quantised charges. The non-extreme solution is also considered and the corresponding thermodynamical quantities are calculated in terms of a D-brane/anti-D-brane system. To perform the quantum mechanical D-brane analysis we study open strings with their ends on branes with a magnetic condensate. Applying the results to our D-brane system we manage to have a perfect agreement between the D-brane entropy counting and the corresponding semi-classical result. The Landau degeneracy of the open string states describing the excitations of the D-brane system enters in a crucial way. We also derive the near-extreme results which agree with the semi-classical calculations. (orig.)

Absolute configuration and enantiomeric composition of partially resolved mandelic, atrolactic and lactic acids by {sup 1}H NMR of their (S)-2-methylbutyl esters

Energy Technology Data Exchange (ETDEWEB)

Andrade, Francisco A. da C.; Mendes, Maricleide P. de L.; Fonseca, Neuracy C. da, E-mail: fandrade@ufba.br [Universidade Federal da Bahia (UFBA), Salvador, BA (Brazil). Instituto de Quimica. Departamento de Quimica Organica

2013-06-15

The mandelic, atrolactic and lactic acid esters of the (S)-2-methyl-1-butanol were examined as diastereomeric derivatives for the stereochemical analysis of the mentioned acids by {sup 1}H nuclear magnetic resonance (NMR) at 300 MHz. The diastereomeric esters showed distinctive signals in the methylenic absorption range (O-CH{sub 2}-CH) of the alcoholic moieties. By spectral analysis at this region, absolute configurations were attributed, chemical shifts of the correspondent pro-(R) and pro-(S) hydrogens from the methylene group of the alcohol moiety were assigned and enantiomeric compositions were determined for the original partially resolved acids. (author)

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.

Entropy of the Mixture of Sources and Entropy Dimension

OpenAIRE

Smieja, Marek; Tabor, Jacek

2011-01-01

We investigate the problem of the entropy of the mixture of sources. There is given an estimation of the entropy and entropy dimension of convex combination of measures. The proof is based on our alternative definition of the entropy based on measures instead of partitions.

Maximum-Entropy Inference with a Programmable Annealer

Science.gov (United States)

Chancellor, Nicholas; Szoke, Szilard; Vinci, Walter; Aeppli, Gabriel; Warburton, Paul A.

2016-03-01

Optimisation problems typically involve finding the ground state (i.e. the minimum energy configuration) of a cost function with respect to many variables. If the variables are corrupted by noise then this maximises the likelihood that the solution is correct. The maximum entropy solution on the other hand takes the form of a Boltzmann distribution over the ground and excited states of the cost function to correct for noise. Here we use a programmable annealer for the information decoding problem which we simulate as a random Ising model in a field. We show experimentally that finite temperature maximum entropy decoding can give slightly better bit-error-rates than the maximum likelihood approach, confirming that useful information can be extracted from the excited states of the annealer. Furthermore we introduce a bit-by-bit analytical method which is agnostic to the specific application and use it to show that the annealer samples from a highly Boltzmann-like distribution. Machines of this kind are therefore candidates for use in a variety of machine learning applications which exploit maximum entropy inference, including language processing and image recognition.

Determination of the Absolute Configurations Using Exciton Chirality Method for Vibrational Circular Dichroism: Right Answers for the Wrong Reasons?

Science.gov (United States)

Covington, Cody L; Nicu, Valentin P; Polavarapu, Prasad L

2015-10-22

Quantum chemical (QC) predictions of vibrational circular dichroism (VCD) spectra for the keto form of 3-benzoylcamphor and conformationally flexible diacetates of spiroindicumide A and B are presented. The exciton chirality (EC) model has been briefly reviewed, and a procedure to evaluate the relevance of the EC model has been presented. The QC results are compared with literature experimental VCD spectra as well as with those obtained using the EC model for VCD. These comparisons reveal that the EC contributions to bisignate VCD couplets associated with the C═O stretching vibrations of benzoylcamphor, spiroindicumide A diacetate, and spiroindicumide B diacetate are only ∼30%, ∼3%, and ∼15%, respectively. With such meager EC contributions, the correct absolute configurations (ACs) suggested in the literature for spiroindicumide A diacetate and spiroindicumide B diacetate molecules using the EC concepts can be considered fortuitous. The possibilities for obtaining wrong AC predictions using the EC concepts for VCD are identified, and guidelines for the future use of this model are presented.

Entanglement entropy and differential entropy for massive flavors

International Nuclear Information System (INIS)

Jones, Peter A.R.; Taylor, Marika

2015-01-01

In this paper we compute the holographic entanglement entropy for massive flavors in the D3-D7 system, for arbitrary mass and various entangling region geometries. We show that the universal terms in the entanglement entropy exactly match those computed in the dual theory using conformal perturbation theory. We derive holographically the universal terms in the entanglement entropy for a CFT perturbed by a relevant operator, up to second order in the coupling; our results are valid for any entangling region geometry. We present a new method for computing the entanglement entropy of any top-down brane probe system using Kaluza-Klein holography and illustrate our results with massive flavors at finite density. Finally we discuss the differential entropy for brane probe systems, emphasising that the differential entropy captures only the effective lower-dimensional Einstein metric rather than the ten-dimensional geometry.

Bubble Entropy: An Entropy Almost Free of Parameters.

Science.gov (United States)

Manis, George; Aktaruzzaman, Md; Sassi, Roberto

2017-11-01

Objective : A critical point in any definition of entropy is the selection of the parameters employed to obtain an estimate in practice. We propose a new definition of entropy aiming to reduce the significance of this selection. Methods: We call the new definition Bubble Entropy . Bubble Entropy is based on permutation entropy, where the vectors in the embedding space are ranked. We use the bubble sort algorithm for the ordering procedure and count instead the number of swaps performed for each vector. Doing so, we create a more coarse-grained distribution and then compute the entropy of this distribution. Results: Experimental results with both real and synthetic HRV signals showed that bubble entropy presents remarkable stability and exhibits increased descriptive and discriminating power compared to all other definitions, including the most popular ones. Conclusion: The definition proposed is almost free of parameters. The most common ones are the scale factor r and the embedding dimension m . In our definition, the scale factor is totally eliminated and the importance of m is significantly reduced. The proposed method presents increased stability and discriminating power. Significance: After the extensive use of some entropy measures in physiological signals, typical values for their parameters have been suggested, or at least, widely used. However, the parameters are still there, application and dataset dependent, influencing the computed value and affecting the descriptive power. Reducing their significance or eliminating them alleviates the problem, decoupling the method from the data and the application, and eliminating subjective factors. Objective : A critical point in any definition of entropy is the selection of the parameters employed to obtain an estimate in practice. We propose a new definition of entropy aiming to reduce the significance of this selection. Methods: We call the new definition Bubble Entropy . Bubble Entropy is based on permutation

Logarithmic black hole entropy corrections and holographic Rényi entropy

Science.gov (United States)

Mahapatra, Subhash

2018-01-01

The entanglement and Rényi entropies for spherical entangling surfaces in CFTs with gravity duals can be explicitly calculated by mapping these entropies first to the thermal entropy on hyperbolic space and then, using the AdS/CFT correspondence, to the Wald entropy of topological black holes. Here we extend this idea by taking into account corrections to the Wald entropy. Using the method based on horizon symmetries and the asymptotic Cardy formula, we calculate corrections to the Wald entropy and find that these corrections are proportional to the logarithm of the area of the horizon. With the corrected expression for the entropy of the black hole, we then find corrections to the Rényi entropies. We calculate these corrections for both Einstein and Gauss-Bonnet gravity duals. Corrections with logarithmic dependence on the area of the entangling surface naturally occur at the order GD^0. The entropic c-function and the inequalities of the Rényi entropy are also satisfied even with the correction terms.

Numerical investigation of heat transfer and entropy generation of laminar flow in helical tubes with various cross sections

International Nuclear Information System (INIS)

Kurnia, Jundika C.; Sasmito, Agus P.; Shamim, Tariq; Mujumdar, Arun S.

2016-01-01

Highlights: • Heat transfers of helical coiled tube with several cross section profiles are evaluated. • Helical tubes offer higher heat transfer and lower entropy generation. • Square cross-section generates the highest entropy, followed by ellipse and circular. • Study could serve as a guideline in designing an efficient helical tube heat exchanger. - Abstract: This study evaluates heat transfer performance and entropy generation of laminar flow in coiled tubes with various cross-sections geometries i.e. circular, ellipse and square, relatives to the straight tubes of similar cross-sections. A computational fluid dynamics model is developed and validated against empirical correlations. Good agreement is obtained within range of Reynolds and Dean numbers considered. Effect of geometry, wall temperature, Reynolds number and heating/cooling mode were examined. To evaluate the heat transfer performance of the coiled tube configurations, a parameter referred as Figure of Merit (FoM) is defined as the ratio heat transfer rate to the required pumping power. In addition, exergy analysis is carried out to examine the inefficiency of the coiled tube configurations. The results indicate that coiled tubes provide higher heat transfer rate. In addition, it was found to be more efficient as reflected by lower entropy generation as compared to straight tubes. Among the studied cross-section, square cross-section generates the highest entropy, followed by ellipse and circular counterpart. Entropy production from heat transfer contribution is two order-of-magnitude higher than that of entropy contribution from viscous dissipation. Cooling case produces slightly higher entropy than heating counterpart. Finally, this study can provide practical guideline to design more efficient coiled heat exchanger.

Symplectic entropy

International Nuclear Information System (INIS)

De Nicola, Sergio; Fedele, Renato; Man'ko, Margarita A; Man'ko, Vladimir I

2007-01-01

The tomographic-probability description of quantum states is reviewed. The symplectic tomography of quantum states with continuous variables is studied. The symplectic entropy of the states with continuous variables is discussed and its relation to Shannon entropy and information is elucidated. The known entropic uncertainty relations of the probability distribution in position and momentum of a particle are extended and new uncertainty relations for symplectic entropy are obtained. The partial case of symplectic entropy, which is optical entropy of quantum states, is considered. The entropy associated to optical tomogram is shown to satisfy the new entropic uncertainty relation. The example of Gaussian states of harmonic oscillator is studied and the entropic uncertainty relations for optical tomograms of the Gaussian state are shown to minimize the uncertainty relation

Two aspects of black hole entropy in Lanczos-Lovelock models of gravity

Science.gov (United States)

Kolekar, Sanved; Kothawala, Dawood; Padmanabhan, T.

2012-03-01

We consider two specific approaches to evaluate the black hole entropy which are known to produce correct results in the case of Einstein’s theory and generalize them to Lanczos-Lovelock models. In the first approach (which could be called extrinsic), we use a procedure motivated by earlier work by Pretorius, Vollick, and Israel, and by Oppenheim, and evaluate the entropy of a configuration of densely packed gravitating shells on the verge of forming a black hole in Lanczos-Lovelock theories of gravity. We find that this matter entropy is not equal to (it is less than) Wald entropy, except in the case of Einstein theory, where they are equal. The matter entropy is proportional to the Wald entropy if we consider a specific mth-order Lanczos-Lovelock model, with the proportionality constant depending on the spacetime dimensions D and the order m of the Lanczos-Lovelock theory as (D-2m)/(D-2). Since the proportionality constant depends on m, the proportionality between matter entropy and Wald entropy breaks down when we consider a sum of Lanczos-Lovelock actions involving different m. In the second approach (which could be called intrinsic), we generalize a procedure, previously introduced by Padmanabhan in the context of general relativity, to study off-shell entropy of a class of metrics with horizon using a path integral method. We consider the Euclidean action of Lanczos-Lovelock models for a class of metrics off shell and interpret it as a partition function. We show that in the case of spherically symmetric metrics, one can interpret the Euclidean action as the free energy and read off both the entropy and energy of a black hole spacetime. Surprisingly enough, this leads to exactly the Wald entropy and the energy of the spacetime in Lanczos-Lovelock models obtained by other methods. We comment on possible implications of the result.

Absolute continuity of the distribution of some Markov geometric series

Institute of Scientific and Technical Information of China (English)

Ai-hua; FAN; Ji-hong; ZHANG

2007-01-01

Let (∈n)≥0 be the Markov chain of two states with respect to the probability measure of the maximal entropy on the subshift space ∑A defined by Fibonacci incident matrix A.We consider the measure μλ of the probability distribution of the random series ∑∞n=0 εnλn (0 ＜λ＜ 1).It is proved that μλ is singular if λ∈ (0,√5-1/2) and that μλ is absolutely continuous for almost all λ∈ (√5-1/2,0.739).

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.

The improvement of Clausius entropy and its application in entropy analysis

Institute of Scientific and Technical Information of China (English)

WU Jing; GUO ZengYuan

2008-01-01

The defects of Cleusius entropy which Include s premise of reversible process and a process quantlty of heat in Its definition are discussed in this paper. Moreover, the heat temperature quotient under reversible conditions, i.e. (δQ/T)rev, is essentially a process quantity although it is numerically equal to the entropy change. The sum of internal energy temperature quotient and work temperature quotient is defined as the improved form of Clausius entropy and it can be further proved to be a state funcllon. Unlike Clausius entropy, the improved deflnltion consists of system properties wlthout premise just like other state functions, for example, pressure p and enthalpy h, etc. it is unnecessary to invent reversible paths when calculating entropy change for irreversible processes based on the improved form of entropy since it is independent of process. Furthermore, entropy balance equations for internally and externally irreversible processes are deduced respectively based on the concepts of thermal reservoir entropy transfer and system entropy transfer. Finally, some examples are presented to show that the improved deflnitlon of Clausius entropy provides a clear concept as well as a convenient method for en-tropy change calculation.

Nonadditive entropy: The concept and its use

Energy Technology Data Exchange (ETDEWEB)

Tsallis, C. [Centro Brasileiro de Pesquisas Fisicas and National Institute of Science and Technology for Complex Systems, Rio de Janeiro-RJ (Brazil); Santa Fe Institute, Santa Fe (United States)

2009-06-15

The thermodynamical concept of entropy was introduced by Clausius in 1865 in order to construct the exact differential dS={delta}Q/T, where {delta}Q is the heat transfer and the absolute temperature T its integrating factor. A few years later, in the period 1872-1877, it was shown by Boltzmann that this quantity can be expressed in terms of the probabilities associated with the microscopic configurations of the system. We refer to this fundamental connection as the Boltzmann-Gibbs (BG) entropy, namely (in its discrete form) S{sub BG}=-k sum {sub i=1}{sup W}p{sub i}lnp{sub i}, where k is the Boltzmann constant, and {l_brace}p{sub i}{r_brace} the probabilities corresponding to the W microscopic configurations hence sum {sup W}{sub i=1}p{sub i}=1. This entropic form, further discussed by Gibbs, von Neumann and Shannon, and constituting the basis of the celebrated BG statistical mechanics, is additive. Indeed, if we consider a system composed by any two probabilistically independent subsystems A and B (i.e., p{sub ij}{sup A+B}=p{sub i}{sup A}p{sub j}{sup B}, for each (i,j)), we verify that S{sub BG}(A+B)=S{sub BG}(A)+S{sub BG}(B). If a system is constituted by N equal elements which are either independent or quasi-independent (i.e., not too strongly correlated, in some specific nonlocal sense), this additivity guarantees S{sub BG} to be extensive in the thermodynamical sense, i.e., that S{sub BG}(N){proportional_to}N in the N>>1 limit. If, on the contrary, the correlations between the N elements are strong enough, then the extensivity of S{sub BG} is lost, being therefore incompatible with classical thermodynamics. In such a case, the many and precious relations described in textbooks of thermodynamics become invalid. Along a line which will be shown to overcome this difficulty, and which consistently enables the generalization of BG statistical mechanics, it was proposed in 1988 the entropy S{sub q}=k[- sum {sub i=1}{sup W}p{sub i}{sup q}]/(q-1) (q element of R; S

Entropy and information

CERN Document Server

Volkenstein, Mikhail V

2009-01-01

The book "Entropy and Information" deals with the thermodynamical concept of entropy and its relationship to information theory. It is successful in explaining the universality of the term "Entropy" not only as a physical phenomenon, but reveals its existence also in other domains. E.g., Volkenstein discusses the "meaning" of entropy in a biological context and shows how entropy is related to artistic activities. Written by the renowned Russian bio-physicist Mikhail V. Volkenstein, this book on "Entropy and Information" surely serves as a timely introduction to understand entropy from a thermodynamic perspective and is definitely an inspiring and thought-provoking book that should be read by every physicist, information-theorist, biologist, and even artist.

Parametric Bayesian Estimation of Differential Entropy and Relative Entropy

OpenAIRE

Gupta; Srivastava

2010-01-01

Given iid samples drawn from a distribution with known parametric form, we propose the minimization of expected Bregman divergence to form Bayesian estimates of differential entropy and relative entropy, and derive such estimators for the uniform, Gaussian, Wishart, and inverse Wishart distributions. Additionally, formulas are given for a log gamma Bregman divergence and the differential entropy and relative entropy for the Wishart and inverse Wishart. The results, as always with Bayesian est...

The improvement of Clausius entropy and its application in entropy analysis

Institute of Scientific and Technical Information of China (English)

2008-01-01

The defects of Clausius entropy which include a premise of reversible process and a process quantity of heat in its definition are discussed in this paper. Moreover, the heat temperature quotient under reversible conditions, i.e. (δQ/T)rev, is essentially a process quantity although it is numerically equal to the entropy change. The sum of internal energy temperature quotient and work temperature quotient is defined as the improved form of Clausius entropy and it can be further proved to be a state function. Unlike Clausius entropy, the improved definition consists of system properties without premise just like other state functions, for example, pressure p and enthalpy h, etc. It is unnecessary to invent reversible paths when calculating entropy change for irreversible processes based on the improved form of entropy since it is independent of process. Furthermore, entropy balance equations for internally and externally irreversible processes are deduced respectively based on the concepts of thermal reservoir entropy transfer and system entropy transfer. Finally, some examples are presented to show that the improved definition of Clausius entropy provides a clear concept as well as a convenient method for en- tropy change calculation.

Quantum dynamical entropy revisited

International Nuclear Information System (INIS)

Hudetz, T.

1996-10-01

We define a new quantum dynamical entropy, which is a 'hybrid' of the closely related, physically oriented entropy introduced by Alicki and Fannes in 1994, and of the mathematically well-developed, single-argument entropy introduced by Connes, Narnhofer and Thirring in 1987. We show that this new quantum dynamical entropy has many properties similar to the ones of the Alicki-Fannes entropy, and also inherits some additional properties from the CNT entropy. In particular, the 'hybrid' entropy interpolates between the two different ways in which both the AF and the CNT entropy of the shift automorphism on the quantum spin chain agree with the usual quantum entropy density, resulting in even better agreement. Also, the new quantum dynamical entropy generalizes the classical dynamical entropy of Kolmogorov and Sinai in the same way as does the AF entropy. Finally, we estimate the 'hybrid' entropy both for the Powers-Price shift systems and for the noncommutative Arnold map on the irrational rotation C * -algebra, leaving some interesting open problems. (author)

Cyclic Diarylheptanoids from Corylus avellana Green Leafy Covers: Determination of Their Absolute Configurations and Evaluation of Their Antioxidant and Antimicrobial Activities.

Science.gov (United States)

Cerulli, Antonietta; Lauro, Gianluigi; Masullo, Milena; Cantone, Vincenza; Olas, Beata; Kontek, Bogdan; Nazzaro, Filomena; Bifulco, Giuseppe; Piacente, Sonia

2017-06-23

The methanol extract of the leafy covers of Corylus avellana, source of the Italian PGI (protected geographical indication) product "Nocciola di Giffoni", afforded two new cyclic diarylheptanoids, giffonins T and U (2 and 3), along with two known cyclic diarylheptanoids, a quinic acid, flavonoid-, and citric acid derivatives. The structures of giffonins T and U were determined as highly hydroxylated cyclic diarylheptanoids by 1D and 2D NMR experiments. Their relative configurations were assigned by a combined quantum mechanical/NMR approach, comparing the experimental 13 C/ 1 H NMR chemical shift data and the related predicted values. The absolute configurations of carpinontriol B (1) and giffonins T and U (2 and 3) were assigned by comparison of their experimental electronic circular dichroism curves with the TDDFT-predicted curves. The ability of the compounds to inhibit the lipid peroxidation induced by H 2 O 2 and H 2 O 2 /Fe 2+ was determined by measuring the concentration of thiobarbituric acid reactive substances. Furthermore, the antimicrobial activity of the methanol extract of leafy covers of C. avellana and of the isolated compounds against the Gram-positive strains Bacillus cereus and Staphylococcus aureus and the Gram-negative strains Escherichia coli and Pseudomonas aeruginosa was evaluated. Carpinontriol B (1) and giffonin U (3) at 40 μg/disk caused the formation of zones of inhibition.

Nonlinear symmetries of black hole entropy in gauged supergravity

Energy Technology Data Exchange (ETDEWEB)

Klemm, Dietmar [Dipartimento di Fisica, Università di Milano,and INFN, Sezione di Milano,Via Celoria 16, I-20133 Milano (Italy); Marrani, Alessio [Museo Storico della Fisica e Centro Studi e Ricerche ‘Enrico Fermi’,Via Panisperna 89A, I-00184 Roma (Italy); Dipartimento di Fisica e Astronomia ‘Galileo Galilei’, Università di Padova,and INFN, Sezione di Padova,Via Marzolo 8, I-35131 Padova (Italy); Petri, Nicolò; Rabbiosi, Marco [Dipartimento di Fisica, Università di Milano,and INFN, Sezione di Milano,Via Celoria 16, I-20133 Milano (Italy)

2017-04-04

Freudenthal duality in N=2, D=4 ungauged supergravity is generated by an anti-involutive operator that acts on the electromagnetic fluxes, and results to be a symmetry of the Bekenstein-Hawking entropy. We show that, with a suitable extension, this duality can be generalized to the abelian gauged case as well, even in presence of hypermultiplets. By defining Freudenthal duality along the scalar flow, one can prove that two configurations of charges and gaugings linked by the Freudenthal operator share the same set of values of the scalar fields at the black hole horizon. Consequently, Freudenthal duality is promoted to a nonlinear symmetry of the black hole entropy. We explicitly show this invariance for the model with prepotential F=−iX{sup 0}X{sup 1} and Fayet-Iliopoulos gauging.

Taxi trips distribution modeling based on Entropy-Maximizing theory: A case study in Harbin city-China

Science.gov (United States)

Tang, Jinjun; Zhang, Shen; Chen, Xinqiang; Liu, Fang; Zou, Yajie

2018-03-01

Understanding Origin-Destination distribution of taxi trips is very important for improving effects of transportation planning and enhancing quality of taxi services. This study proposes a new method based on Entropy-Maximizing theory to model OD distribution in Harbin city using large-scale taxi GPS trajectories. Firstly, a K-means clustering method is utilized to partition raw pick-up and drop-off location into different zones, and trips are assumed to start from and end at zone centers. A generalized cost function is further defined by considering travel distance, time and fee between each OD pair. GPS data collected from more than 1000 taxis at an interval of 30 s during one month are divided into two parts: data from first twenty days is treated as training dataset and last ten days is taken as testing dataset. The training dataset is used to calibrate model while testing dataset is used to validate model. Furthermore, three indicators, mean absolute error (MAE), root mean square error (RMSE) and mean percentage absolute error (MPAE), are applied to evaluate training and testing performance of Entropy-Maximizing model versus Gravity model. The results demonstrate Entropy-Maximizing model is superior to Gravity model. Findings of the study are used to validate the feasibility of OD distribution from taxi GPS data in urban system.

Information Entropy Measures for Stand Structural Diversity:Joint Entropy

Institute of Scientific and Technical Information of China (English)

Lei Xiangdong; Lu Yuanchang

2004-01-01

Structural diversity is the key attribute of a stand. A set of biodiversity measures in ecology was introduced in forest management for describing stand structure, of which Shannon information entropy (Shannon index) has been the most widely used measure of species diversity. It is generally thought that tree size diversity could serve as a good proxy for height diversity. However, tree size diversity and height diversity for stand structure is not completely consistent. Stand diameter cannot reflect height information completely. Either tree size diversity or height diversity is one-dimensional information entropy measure. This paper discussed the method of multiple-dimensional information entropy measure with the concept of joint entropy. It is suggested that joint entropy is a good measure for describing overall stand structural diversity.

Quantum chaos: entropy signatures

International Nuclear Information System (INIS)

Miller, P.A.; Sarkar, S.; Zarum, R.

1998-01-01

A definition of quantum chaos is given in terms of entropy production rates for a quantum system coupled weakly to a reservoir. This allows the treatment of classical and quantum chaos on the same footing. In the quantum theory the entropy considered is the von Neumann entropy and in classical systems it is the Gibbs entropy. The rate of change of the coarse-grained Gibbs entropy of the classical system with time is given by the Kolmogorov-Sinai (KS) entropy. The relation between KS entropy and the rate of change of von Neumann entropy is investigated for the kicked rotator. For a system which is classically chaotic there is a linear relationship between these two entropies. Moreover it is possible to construct contour plots for the local KS entropy and compare it with the corresponding plots for the rate of change of von Neumann entropy. The quantitative and qualitative similarities of these plots are discussed for the standard map (kicked rotor) and the generalised cat maps. (author)

Entropy Maximization as a Basis for Information Recovery in Dynamic Economic Behavioral Systems

Directory of Open Access Journals (Sweden)

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.

Volume-law scaling for the entanglement entropy in spin-1/2 chains

International Nuclear Information System (INIS)

Vitagliano, G; Riera, A; Latorre, J I

2010-01-01

Entanglement entropy obeys area law scaling for typical physical quantum systems. This may naively be argued to follow from the locality of interactions. We show that this is not the case by constructing an explicit simple spin chain Hamiltonian with nearest-neighbor interactions that presents an entanglement volume scaling law. This non-translational model is contrived to have couplings that force the accumulation of singlet bonds across the half-chain. This configuration of the couplings is suggested by real-space renormalization group arguments. Computation of the entanglement entropy is performed by mapping the system to free fermions and diagonalizing numerically its correlation matrix. An analytical relationship between the entanglement entropy and the Frobenius norm of the correlation matrix is also established. Our result is complementary to the known relationship between non-translational invariant, nearest-neighbor interacting Hamiltonians and quantum Merlin-Arthur (QMA)-complete problems.

Absolute configuration, stability, and interconversion of 6,7-dihydro-7-hydroxy-1-hydroxymethyl-5H-pyrrolizine valine adducts and their phenylthiohydantoin derivatives

Directory of Open Access Journals (Sweden)

Xiao Jiang

2015-06-01

Full Text Available Pyrrolizidine alkaloid-containing plants are widespread in the world and probably the most common poisonous plants affecting livestock, wildlife, and humans. Pyrrolizidine alkaloids require metabolic activation to form dehydropyrrolizidine alkaloids that bind to cellular proteins and DNA leading to hepatotoxicity, genotoxicity, and tumorigenicity. At present, it is not clear how dehydropyrrolizidine alkaloids bind to cellular amino acids and proteins to induced toxicity. We previously reported that reaction of dehydromonocrotaline with valine generated four highly unstable 6,7-dihydro-7-hydroxy-1-hydroxymethyl-5H-pyrrolizine (DHP-derived valine (DHP-valine adducts that upon reaction with phenyl isothiocyanate (PITC formed four DHP-valine-PITC adduct isomers. In this study, we report the absolute configuration and stability of DHP-valine and DHP-valine-PITC adducts, and the mechanism of interconversion between DHP-valine-PITC adducts.

Quantum key distribution with finite resources: Smooth Min entropy vs. Smooth Renyi entropy

Energy Technology Data Exchange (ETDEWEB)

Mertz, Markus; Abruzzo, Silvestre; Bratzik, Sylvia; Kampermann, Hermann; Bruss, Dagmar [Institut fuer Theoretische Physik III, Duesseldorf (Germany)

2010-07-01

We consider different entropy measures that play an important role in the analysis of the security of QKD with finite resources. The smooth min entropy leads to an optimal bound for the length of a secure key. Another bound on the secure key length was derived by using Renyi entropies. Unfortunately, it is very hard or even impossible to calculate these entropies for realistic QKD scenarios. To estimate the security rate it becomes important to find computable bounds on these entropies. Here, we compare a lower bound for the smooth min entropy with a bound using Renyi entropies. We compare these entropies for the six-state protocol with symmetric attacks.

Enantioselective synthesis of (+-polyzonimine, defensive monoterpene alkaloid produced by a milliped Polyzonium rosalbum, and determination of its S absolute configuration by Its conversion to (4S,5R,6S-(+-nitropolyzonamine

Directory of Open Access Journals (Sweden)

Takagi Yasuyo

2000-01-01

Full Text Available Asymmetric Michael addition of the enamine derived from 2,2-dimethylcyclopentanecarbox-aldehyde and (S-prolinol methyl ether to nitroethylene afforded the adduct of 75-76% ee, which finally yielded enantiomerically pure (+-polyzonimine, a nitrogen-containing spirocyclic compound isolated from the defensive glands of a milliped, Polyzonium rosalbum. By converting (+-polyzonimine into (4S,5R,6S-(+-nitropolyzonamine, the hitherto uncertain absolute configuration of the former was established as S.

Parametric Bayesian Estimation of Differential Entropy and Relative Entropy

Directory of Open Access Journals (Sweden)

Maya Gupta

2010-04-01

Full Text Available Given iid samples drawn from a distribution with known parametric form, we propose the minimization of expected Bregman divergence to form Bayesian estimates of differential entropy and relative entropy, and derive such estimators for the uniform, Gaussian, Wishart, and inverse Wishart distributions. Additionally, formulas are given for a log gamma Bregman divergence and the differential entropy and relative entropy for the Wishart and inverse Wishart. The results, as always with Bayesian estimates, depend on the accuracy of the prior parameters, but example simulations show that the performance can be substantially improved compared to maximum likelihood or state-of-the-art nonparametric estimators.

Entropy? Honest!

Directory of Open Access Journals (Sweden)

Tommaso Toffoli

2016-06-01

Full Text Available Here we deconstruct, and then in a reasoned way reconstruct, the concept of “entropy of a system”, paying particular attention to where the randomness may be coming from. We start with the core concept of entropy as a count associated with a description; this count (traditionally expressed in logarithmic form for a number of good reasons is in essence the number of possibilities—specific instances or “scenarios”—that match that description. Very natural (and virtually inescapable generalizations of the idea of description are the probability distribution and its quantum mechanical counterpart, the density operator. We track the process of dynamically updating entropy as a system evolves. Three factors may cause entropy to change: (1 the system’s internal dynamics; (2 unsolicited external influences on it; and (3 the approximations one has to make when one tries to predict the system’s future state. The latter task is usually hampered by hard-to-quantify aspects of the original description, limited data storage and processing resource, and possibly algorithmic inadequacy. Factors 2 and 3 introduce randomness—often huge amounts of it—into one’s predictions and accordingly degrade them. When forecasting, as long as the entropy bookkeping is conducted in an honest fashion, this degradation will always lead to an entropy increase. To clarify the above point we introduce the notion of honest entropy, which coalesces much of what is of course already done, often tacitly, in responsible entropy-bookkeping practice. This notion—we believe—will help to fill an expressivity gap in scientific discourse. With its help, we shall prove that any dynamical system—not just our physical universe—strictly obeys Clausius’s original formulation of the second law of thermodynamics if and only if it is invertible. Thus this law is a tautological property of invertible systems!

EEG entropy measures in anesthesia

Science.gov (United States)

Liang, Zhenhu; Wang, Yinghua; Sun, Xue; Li, Duan; Voss, Logan J.; Sleigh, Jamie W.; Hagihira, Satoshi; Li, Xiaoli

2015-01-01

Highlights: ► Twelve entropy indices were systematically compared in monitoring depth of anesthesia and detecting burst suppression.► Renyi permutation entropy performed best in tracking EEG changes associated with different anesthesia states.► Approximate Entropy and Sample Entropy performed best in detecting burst suppression. Objective: Entropy algorithms have been widely used in analyzing EEG signals during anesthesia. However, a systematic comparison of these entropy algorithms in assessing anesthesia drugs' effect is lacking. In this study, we compare the capability of 12 entropy indices for monitoring depth of anesthesia (DoA) and detecting the burst suppression pattern (BSP), in anesthesia induced by GABAergic agents. Methods: Twelve indices were investigated, namely Response Entropy (RE) and State entropy (SE), three wavelet entropy (WE) measures [Shannon WE (SWE), Tsallis WE (TWE), and Renyi WE (RWE)], Hilbert-Huang spectral entropy (HHSE), approximate entropy (ApEn), sample entropy (SampEn), Fuzzy entropy, and three permutation entropy (PE) measures [Shannon PE (SPE), Tsallis PE (TPE) and Renyi PE (RPE)]. Two EEG data sets from sevoflurane-induced and isoflurane-induced anesthesia respectively were selected to assess the capability of each entropy index in DoA monitoring and BSP detection. To validate the effectiveness of these entropy algorithms, pharmacokinetic/pharmacodynamic (PK/PD) modeling and prediction probability (Pk) analysis were applied. The multifractal detrended fluctuation analysis (MDFA) as a non-entropy measure was compared. Results: All the entropy and MDFA indices could track the changes in EEG pattern during different anesthesia states. Three PE measures outperformed the other entropy indices, with less baseline variability, higher coefficient of determination (R2) and prediction probability, and RPE performed best; ApEn and SampEn discriminated BSP best. Additionally, these entropy measures showed an advantage in computation

Relation Entropy and Transferable Entropy Think of Aggregation on Group Decision Making

Institute of Scientific and Technical Information of China (English)

CHENG Qi-yue; QIU Wan-hua; LIU Xiao-feng

2002-01-01

In this paper, aggregation question based on group decision making and a single decision making is studied. The theory of entropy is applied to the sets pair analysis. The system of relation entropy and the transferable entropy notion are put. The character is studied. An potential by the relation entropy and transferable entropy are defined. It is the consistency measure on the group between a single decision making. We gained a new aggregation effective definition on the group misjudge.

RNA Thermodynamic Structural Entropy.

Directory of Open Access Journals (Sweden)

Juan Antonio Garcia-Martin

Full Text Available Conformational entropy for atomic-level, three dimensional biomolecules is known experimentally to play an important role in protein-ligand discrimination, yet reliable computation of entropy remains a difficult problem. Here we describe the first two accurate and efficient algorithms to compute the conformational entropy for RNA secondary structures, with respect to the Turner energy model, where free energy parameters are determined from UV absorption experiments. An algorithm to compute the derivational entropy for RNA secondary structures had previously been introduced, using stochastic context free grammars (SCFGs. However, the numerical value of derivational entropy depends heavily on the chosen context free grammar and on the training set used to estimate rule probabilities. Using data from the Rfam database, we determine that both of our thermodynamic methods, which agree in numerical value, are substantially faster than the SCFG method. Thermodynamic structural entropy is much smaller than derivational entropy, and the correlation between length-normalized thermodynamic entropy and derivational entropy is moderately weak to poor. In applications, we plot the structural entropy as a function of temperature for known thermoswitches, such as the repression of heat shock gene expression (ROSE element, we determine that the correlation between hammerhead ribozyme cleavage activity and total free energy is improved by including an additional free energy term arising from conformational entropy, and we plot the structural entropy of windows of the HIV-1 genome. Our software RNAentropy can compute structural entropy for any user-specified temperature, and supports both the Turner'99 and Turner'04 energy parameters. It follows that RNAentropy is state-of-the-art software to compute RNA secondary structure conformational entropy. Source code is available at https://github.com/clotelab/RNAentropy/; a full web server is available at http

RNA Thermodynamic Structural Entropy.

Science.gov (United States)

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

Entropy generation minimization: A practical approach for performance evaluation of temperature cascaded co-generation plants

KAUST Repository

Myat, Aung; Thu, Kyaw; Kim, Youngdeuk; Saha, Bidyut Baran; Ng, K. C.

2012-01-01

We present a practical tool that employs entropy generation minimization (EGM) approach for an in-depth performance evaluation of a co-generation plant with a temperature-cascaded concept. Co-generation plant produces useful effect production sequentially, i.e., (i) electricity from the micro-turbines, (ii) low pressure steam at 250 °C or about 8-10 bars, (iii) cooling capacity of 4 refrigeration tones (Rtons) and (iv) dehumidification of outdoor air for air conditioned space. The main objective is to configure the most efficient configuration of producing power and heat. We employed entropy generation minimization (EGM) which reflects to minimize the dissipative losses and maximize the cycle efficiency of the individual thermally activated systems. The minimization of dissipative losses or EGM is performed in two steps namely, (i) adjusting heat source temperatures for the heat-fired cycles and (ii) the use of Genetic Algorithm (GA), to seek out the sensitivity of heat transfer areas, flow rates of working fluids, inlet temperatures of heat sources and coolant, etc., over the anticipated range of operation to achieve maximum efficiency. With EGM equipped with GA, we verified that the local minimization of entropy generation individually at each of the heat-activated processes would lead to the maximum efficiency of the system. © 2012.

Entropy generation minimization: A practical approach for performance evaluation of temperature cascaded co-generation plants

KAUST Repository

Myat, Aung

2012-10-01

We present a practical tool that employs entropy generation minimization (EGM) approach for an in-depth performance evaluation of a co-generation plant with a temperature-cascaded concept. Co-generation plant produces useful effect production sequentially, i.e., (i) electricity from the micro-turbines, (ii) low pressure steam at 250 °C or about 8-10 bars, (iii) cooling capacity of 4 refrigeration tones (Rtons) and (iv) dehumidification of outdoor air for air conditioned space. The main objective is to configure the most efficient configuration of producing power and heat. We employed entropy generation minimization (EGM) which reflects to minimize the dissipative losses and maximize the cycle efficiency of the individual thermally activated systems. The minimization of dissipative losses or EGM is performed in two steps namely, (i) adjusting heat source temperatures for the heat-fired cycles and (ii) the use of Genetic Algorithm (GA), to seek out the sensitivity of heat transfer areas, flow rates of working fluids, inlet temperatures of heat sources and coolant, etc., over the anticipated range of operation to achieve maximum efficiency. With EGM equipped with GA, we verified that the local minimization of entropy generation individually at each of the heat-activated processes would lead to the maximum efficiency of the system. © 2012.

EEG entropy measures in anesthesia

Directory of Open Access Journals (Sweden)

Zhenhu eLiang

2015-02-01

Full Text Available Objective: Entropy algorithms have been widely used in analyzing EEG signals during anesthesia. However, a systematic comparison of these entropy algorithms in assessing anesthesia drugs’ effect is lacking. In this study, we compare the capability of twelve entropy indices for monitoring depth of anesthesia (DoA and detecting the burst suppression pattern (BSP, in anesthesia induced by GA-BAergic agents.Methods: Twelve indices were investigated, namely Response Entropy (RE and State entropy (SE, three wavelet entropy (WE measures (Shannon WE (SWE, Tsallis WE (TWE and Renyi WE (RWE, Hilbert-Huang spectral entropy (HHSE, approximate entropy (ApEn, sample entropy (SampEn, Fuzzy entropy, and three permutation entropy (PE measures (Shannon PE (SPE, Tsallis PE (TPE and Renyi PE (RPE. Two EEG data sets from sevoflurane-induced and isoflu-rane-induced anesthesia respectively were selected to assess the capability of each entropy index in DoA monitoring and BSP detection. To validate the effectiveness of these entropy algorithms, phar-macokinetic / pharmacodynamic (PK/PD modeling and prediction probability analysis were applied. The multifractal detrended fluctuation analysis (MDFA as a non-entropy measure was compared.Results: All the entropy and MDFA indices could track the changes in EEG pattern during different anesthesia states. Three PE measures outperformed the other entropy indices, with less baseline vari-ability, higher coefficient of determination and prediction probability, and RPE performed best; ApEn and SampEn discriminated BSP best. Additionally, these entropy measures showed an ad-vantage in computation efficiency compared with MDFA.Conclusion: Each entropy index has its advantages and disadvantages in estimating DoA. Overall, it is suggested that the RPE index was a superior measure.Significance: Investigating the advantages and disadvantages of these entropy indices could help improve current clinical indices for monitoring DoA.

Informational Entropy and Bridge Scour Estimation under Complex Hydraulic Scenarios

Science.gov (United States)

Pizarro, Alonso; Link, Oscar; Fiorentino, Mauro; Samela, Caterina; Manfreda, Salvatore

2017-04-01

Bridges are important for society because they allow social, cultural and economic connectivity. Flood events can compromise the safety of bridge piers up to the complete collapse. The Bridge Scour phenomena has been described by empirical formulae deduced from hydraulic laboratory experiments. The range of applicability of such models is restricted by the specific hydraulic conditions or flume geometry used for their derivation (e.g., water depth, mean flow velocity, pier diameter and sediment properties). We seek to identify a general formulation able to capture the main dynamic of the process in order to cover a wide range of hydraulic and geometric configuration, allowing to extend our analysis in different contexts. Therefore, exploiting the Principle of Maximum Entropy (POME) and applying it on the recently proposed dimensionless Effective flow work, W*, we derived a simple model characterized by only one parameter. The proposed Bridge Scour Entropic (BRISENT) model shows good performances under complex hydraulic conditions as well as under steady-state flow. Moreover, the model was able to capture the evolution of scour in several hydraulic configurations even if the model contains only one parameter. Furthermore, results show that the model parameter is controlled by the geometric configurations of the experiment. This offers a possible strategy to obtain a priori model parameter calibration. The BRISENT model represents a good candidate for estimating the time-dependent scour depth under complex hydraulic scenarios. The authors are keen to apply this idea for describing the scour behavior during a real flood event. Keywords: Informational entropy, Sediment transport, Bridge pier scour, Effective flow work.

Three faces of entropy for complex systems: Information, thermodynamics, and the maximum entropy principle

Science.gov (United States)

Thurner, Stefan; Corominas-Murtra, Bernat; Hanel, Rudolf

2017-09-01

There are at least three distinct ways to conceptualize entropy: entropy as an extensive thermodynamic quantity of physical systems (Clausius, Boltzmann, Gibbs), entropy as a measure for information production of ergodic sources (Shannon), and entropy as a means for statistical inference on multinomial processes (Jaynes maximum entropy principle). Even though these notions represent fundamentally different concepts, the functional form of the entropy for thermodynamic systems in equilibrium, for ergodic sources in information theory, and for independent sampling processes in statistical systems, is degenerate, H (p ) =-∑ipilogpi . For many complex systems, which are typically history-dependent, nonergodic, and nonmultinomial, this is no longer the case. Here we show that for such processes, the three entropy concepts lead to different functional forms of entropy, which we will refer to as SEXT for extensive entropy, SIT for the source information rate in information theory, and SMEP for the entropy functional that appears in the so-called maximum entropy principle, which characterizes the most likely observable distribution functions of a system. We explicitly compute these three entropy functionals for three concrete examples: for Pólya urn processes, which are simple self-reinforcing processes, for sample-space-reducing (SSR) processes, which are simple history dependent processes that are associated with power-law statistics, and finally for multinomial mixture processes.

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.

Nonequilibrium entropies

International Nuclear Information System (INIS)

Maes, Christian

2012-01-01

In contrast to the quite unique entropy concept useful for systems in (local) thermodynamic equilibrium, there is a variety of quite distinct nonequilibrium entropies, reflecting different physical points. We disentangle these entropies as they relate to heat, fluctuations, response, time asymmetry, variational principles, monotonicity, volume contraction or statistical forces. However, not all of those extensions yield state quantities as understood thermodynamically. At the end we sketch how aspects of dynamical activity can take over for obtaining an extended Clausius relation.

Ising model on tangled chain - 1: Free energy and entropy

International Nuclear Information System (INIS)

Mejdani, R.

1993-04-01

In this paper we have considered an Ising model defined on tangled chain, in which more bonds have been added to those of pure Ising chain. to understand their competition, particularly between ferromagnetic and antiferromagnetic bonds, we have studied, using the transfer matrix method, some simple analytical calculations and an iterative algorithm, the behaviour of the free energy and entropy, particularly in the zero-field and zero temperature limit, for different configurations of the ferromagnetic tangled chain and different types of addition interaction (ferromagnetic or antiferromagnetic). We found that the condition J=J' between the ferromagnetic interaction J along the chain and the antiferromagnetic interaction J' across the chain is somewhat as a ''transition-region'' condition for this behaviour. Our results indicate also the existence of non-zero entropy at zero temperature. (author). 17 refs, 8 figs

The entropy function for the black holes of Nariai class

International Nuclear Information System (INIS)

Cho, Jin-Ho; Nam, Soonkeon

2008-01-01

Based on the fact that the near horizon geometry of the extremal Schwarzschild-de Sitter black holes is Nariai geometry, we define the black holes of Nariai class as the configuration whose near-horizon geometry is factorized as two dimensional de Sitter space-time and some compact topology, that is Nariai geometry. We extend the entropy function formalism to the case of the black holes of Nariai class. The conventional entropy function (for the extremal black holes) is defined as Legendre transformation of Lagrangian density, thus the 'Routhian density', over two dimensional anti-de Sitter. As for the black holes of Nariai class, it is defined as minus 'Routhian density' over two dimensional de Sitter space-time. We found an exact agreement of the result with Bekenstein-Hawking entropy. The higher order corrections are nontrivial only when the space-time dimension is over four, that is, d>4. There is a subtlety as regards the temperature of the black holes of Nariai class. We show that in order to be consistent with the near horizon geometry, the temperature should be non-vanishing despite the extremality of the black holes

Fluctuation theorems in feedback-controlled open quantum systems: Quantum coherence and absolute irreversibility

Science.gov (United States)

Murashita, Yûto; Gong, Zongping; Ashida, Yuto; Ueda, Masahito

2017-10-01

The thermodynamics of quantum coherence has attracted growing attention recently, where the thermodynamic advantage of quantum superposition is characterized in terms of quantum thermodynamics. We investigate the thermodynamic effects of quantum coherent driving in the context of the fluctuation theorem. We adopt a quantum-trajectory approach to investigate open quantum systems under feedback control. In these systems, the measurement backaction in the forward process plays a key role, and therefore the corresponding time-reversed quantum measurement and postselection must be considered in the backward process, in sharp contrast to the classical case. The state reduction associated with quantum measurement, in general, creates a zero-probability region in the space of quantum trajectories of the forward process, which causes singularly strong irreversibility with divergent entropy production (i.e., absolute irreversibility) and hence makes the ordinary fluctuation theorem break down. In the classical case, the error-free measurement ordinarily leads to absolute irreversibility, because the measurement restricts classical paths to the region compatible with the measurement outcome. In contrast, in open quantum systems, absolute irreversibility is suppressed even in the presence of the projective measurement due to those quantum rare events that go through the classically forbidden region with the aid of quantum coherent driving. This suppression of absolute irreversibility exemplifies the thermodynamic advantage of quantum coherent driving. Absolute irreversibility is shown to emerge in the absence of coherent driving after the measurement, especially in systems under time-delayed feedback control. We show that absolute irreversibility is mitigated by increasing the duration of quantum coherent driving or decreasing the delay time of feedback control.

Regenerator optimization of a Closed Brayton Cycle via entropy generation minimization

International Nuclear Information System (INIS)

Araújo, Élvis Falcão de; Ribeiro, Guilherme Borges; Guimarães, Lamartine N. F.

2017-01-01

This paper aims the numerical study of the heat transfer and fluid flow of a Closed Brayton Cycle (CBC) regenerator that is part of TERRA microreactor. This regenerator consists in a cross flow heat exchanger, where heat transfer occurs between internal fluid flow in radial tubes and external fluid flow passing perpendicularly to the tubes, which are disposed in a symmetrical cylindrical set where the number of tubes in the axial and radial directions can vary. In the simulations, mass flow inlet is varied for a fixed geometry. The fluid flow solution is provided by a commercial CFD solver and the entropy generation number calculation is later computed for optimization purposes. As a result, the entropy minimization method provides the regenerator configuration that enables the highest energy conversion efficiency. (author)

Regenerator optimization of a Closed Brayton Cycle via entropy generation minimization

Energy Technology Data Exchange (ETDEWEB)

Araújo, Élvis Falcão de; Ribeiro, Guilherme Borges; Guimarães, Lamartine N. F., E-mail: falcao@ieav.cta.br, E-mail: gbribeiro@ieav.cta.br, E-mail: guimarae@ieav.cta.br [Instituto de Estudos Avançacados (IEAv), São José dos Campos, SP (Brazil). Div. de Energia Nuclear

2017-07-01

This paper aims the numerical study of the heat transfer and fluid flow of a Closed Brayton Cycle (CBC) regenerator that is part of TERRA microreactor. This regenerator consists in a cross flow heat exchanger, where heat transfer occurs between internal fluid flow in radial tubes and external fluid flow passing perpendicularly to the tubes, which are disposed in a symmetrical cylindrical set where the number of tubes in the axial and radial directions can vary. In the simulations, mass flow inlet is varied for a fixed geometry. The fluid flow solution is provided by a commercial CFD solver and the entropy generation number calculation is later computed for optimization purposes. As a result, the entropy minimization method provides the regenerator configuration that enables the highest energy conversion efficiency. (author)

The holographic entropy cone

Energy Technology Data Exchange (ETDEWEB)

Bao, Ning [Institute for Quantum Information and Matter, California Institute of Technology,Pasadena, CA 91125 (United States); Walter Burke Institute for Theoretical Physics, California Institute of Technology,452-48, Pasadena, CA 91125 (United States); Nezami, Sepehr [Stanford Institute for Theoretical Physics, Stanford University,Stanford, CA 94305 (United States); Ooguri, Hirosi [Walter Burke Institute for Theoretical Physics, California Institute of Technology,452-48, Pasadena, CA 91125 (United States); Kavli Institute for the Physics and Mathematics of the Universe, University of Tokyo,Kashiwa 277-8583 (Japan); Stoica, Bogdan [Walter Burke Institute for Theoretical Physics, California Institute of Technology,452-48, Pasadena, CA 91125 (United States); Sully, James [Theory Group, SLAC National Accelerator Laboratory, Stanford University,Menlo Park, CA 94025 (United States); Walter, Michael [Stanford Institute for Theoretical Physics, Stanford University,Stanford, CA 94305 (United States)

2015-09-21

We initiate a systematic enumeration and classification of entropy inequalities satisfied by the Ryu-Takayanagi formula for conformal field theory states with smooth holographic dual geometries. For 2, 3, and 4 regions, we prove that the strong subadditivity and the monogamy of mutual information give the complete set of inequalities. This is in contrast to the situation for generic quantum systems, where a complete set of entropy inequalities is not known for 4 or more regions. We also find an infinite new family of inequalities applicable to 5 or more regions. The set of all holographic entropy inequalities bounds the phase space of Ryu-Takayanagi entropies, defining the holographic entropy cone. We characterize this entropy cone by reducing geometries to minimal graph models that encode the possible cutting and gluing relations of minimal surfaces. We find that, for a fixed number of regions, there are only finitely many independent entropy inequalities. To establish new holographic entropy inequalities, we introduce a combinatorial proof technique that may also be of independent interest in Riemannian geometry and graph theory.

The holographic entropy cone

International Nuclear Information System (INIS)

Bao, Ning; Nezami, Sepehr; Ooguri, Hirosi; Stoica, Bogdan; Sully, James; Walter, Michael

2015-01-01

We initiate a systematic enumeration and classification of entropy inequalities satisfied by the Ryu-Takayanagi formula for conformal field theory states with smooth holographic dual geometries. For 2, 3, and 4 regions, we prove that the strong subadditivity and the monogamy of mutual information give the complete set of inequalities. This is in contrast to the situation for generic quantum systems, where a complete set of entropy inequalities is not known for 4 or more regions. We also find an infinite new family of inequalities applicable to 5 or more regions. The set of all holographic entropy inequalities bounds the phase space of Ryu-Takayanagi entropies, defining the holographic entropy cone. We characterize this entropy cone by reducing geometries to minimal graph models that encode the possible cutting and gluing relations of minimal surfaces. We find that, for a fixed number of regions, there are only finitely many independent entropy inequalities. To establish new holographic entropy inequalities, we introduce a combinatorial proof technique that may also be of independent interest in Riemannian geometry and graph theory.

Inhomogeneity of epidemic spreading with entropy-based infected clusters.

Science.gov (United States)

Wen-Jie, Zhou; Xing-Yuan, Wang

2013-12-01

Considering the difference in the sizes of the infected clusters in the dynamic complex networks, the normalized entropy based on infected clusters (δ*) is proposed to characterize the inhomogeneity of epidemic spreading. δ* gives information on the variability of the infected clusters in the system. We investigate the variation in the inhomogeneity of the distribution of the epidemic with the absolute velocity v of moving agent, the infection density ρ, and the interaction radius r. By comparing δ* in the dynamic networks with δH* in homogeneous mode, the simulation experiments show that the inhomogeneity of epidemic spreading becomes smaller with the increase of v, ρ, r.

On the Conditional Rényi Entropy

NARCIS (Netherlands)

S. Fehr (Serge); S. Berens (Stefan)

2014-01-01

htmlabstractThe Rényi entropy of general order unifies the well-known Shannon entropy with several other entropy notions, like the min-entropy or the collision entropy. In contrast to the Shannon entropy, there seems to be no commonly accepted definition for the conditional Rényi entropy: several

Mosher Amides: Determining the Absolute Stereochemistry of Optically-Active Amines

Science.gov (United States)

Allen, Damian A.; Tomaso, Anthony E., Jr.; Priest, Owen P.; Hindson, David F.; Hurlburt, Jamie L.

2008-01-01

The use of chiral reagents for the derivatization of optically-active amines and alcohols for the purpose of determining their enantiomeric purity or absolute configuration is a tool used by many chemists. Among the techniques used, Mosher's amide and Mosher's ester analyses are among the most reliable and one of the most often used. Despite this,…

Tsallis-like entropies in quantum scattering

International Nuclear Information System (INIS)

Ion, D.B.; Ion, M.L.

1998-01-01

In this work, the following entropies in quantum scattering are defined: the informational angular entropy, S θ ; Tsallis-like angular entropies, S q (θ); the angular momentum entropy, S L ; the Tsallis-like angular momentum entropies, S q (L); the angle-angular momentum entropy, S θL . These entropies are defined as natural measures of the uncertainties corresponding to the distribution probabilities. If we are interested in obtaining a measure of uncertainty of the simultaneous realization of the probability distributions, than, we have to calculate the entropy corresponding to these distributions. The expression of angle-angular momentum entropy is given. The relation between the Tsallis entropies and the angle-angular momentum entropy is derived

Entropy for Mechanically Vibrating Systems

Science.gov (United States)

Tufano, Dante

The research contained within this thesis deals with the subject of entropy as defined for and applied to mechanically vibrating systems. This work begins with an overview of entropy as it is understood in the fields of classical thermodynamics, information theory, statistical mechanics, and statistical vibroacoustics. Khinchin's definition of entropy, which is the primary definition used for the work contained in this thesis, is introduced in the context of vibroacoustic systems. The main goal of this research is to to establish a mathematical framework for the application of Khinchin's entropy in the field of statistical vibroacoustics by examining the entropy context of mechanically vibrating systems. The introduction of this thesis provides an overview of statistical energy analysis (SEA), a modeling approach to vibroacoustics that motivates this work on entropy. The objective of this thesis is given, and followed by a discussion of the intellectual merit of this work as well as a literature review of relevant material. Following the introduction, an entropy analysis of systems of coupled oscillators is performed utilizing Khinchin's definition of entropy. This analysis develops upon the mathematical theory relating to mixing entropy, which is generated by the coupling of vibroacoustic systems. The mixing entropy is shown to provide insight into the qualitative behavior of such systems. Additionally, it is shown that the entropy inequality property of Khinchin's entropy can be reduced to an equality using the mixing entropy concept. This equality can be interpreted as a facet of the second law of thermodynamics for vibroacoustic systems. Following this analysis, an investigation of continuous systems is performed using Khinchin's entropy. It is shown that entropy analyses using Khinchin's entropy are valid for continuous systems that can be decomposed into a finite number of modes. The results are shown to be analogous to those obtained for simple oscillators

Entropy of the electroencephalogram as applied in the M-Entropy S ...

African Journals Online (AJOL)

Background: It has been suggested that spectral entropy of the electroencephalogram as applied in the M-Entropy S/5TM Module (GE Healthcare) does not detect the effects of nitrous oxide (N2O). The aim of this study was to investigate the effect on entropy by graded increases in N2O concentrations in the presence of a ...

Surface single-molecule dynamics controlled by entropy at low temperatures

Science.gov (United States)

Gehrig, J. C.; Penedo, M.; Parschau, M.; Schwenk, J.; Marioni, M. A.; Hudson, E. W.; Hug, H. J.

2017-02-01

Configuration transitions of individual molecules and atoms on surfaces are traditionally described using an Arrhenius equation with energy barrier and pre-exponential factor (attempt rate) parameters. Characteristic parameters can vary even for identical systems, and pre-exponential factors sometimes differ by orders of magnitude. Using low-temperature scanning tunnelling microscopy (STM) to measure an individual dibutyl sulfide molecule on Au(111), we show that the differences arise when the relative position of tip apex and molecule changes by a fraction of the molecule size. Altering the tip position on that scale modifies the transition's barrier and attempt rate in a highly correlated fashion, which results in a single-molecular enthalpy-entropy compensation. Conversely, appropriately positioning the STM tip allows selecting the operating point on the compensation line and modifying the transition rates. The results highlight the need to consider entropy in transition rates of single molecules, even at low temperatures.

Entropy of Baker's Transformation

Institute of Scientific and Technical Information of China (English)

栾长福

2003-01-01

Four theorems about four different kinds of entropies for Baker's transformation are presented. The Kolmogorov entropy of Baker's transformation is sensitive to the initial flips by the time. The topological entropy of Baker's transformation is found to be log k. The conditions for the state of Baker's transformation to be forbidden are also derived. The relations among the Shanonn, Kolmogorov, topological and Boltzmann entropies are discussed in details.

The Dynameomics Entropy Dictionary: A Large-Scale Assessment of Conformational Entropy across Protein Fold Space.

Science.gov (United States)

Towse, Clare-Louise; Akke, Mikael; Daggett, Valerie

2017-04-27

Molecular dynamics (MD) simulations contain considerable information with regard to the motions and fluctuations of a protein, the magnitude of which can be used to estimate conformational entropy. Here we survey conformational entropy across protein fold space using the Dynameomics database, which represents the largest existing data set of protein MD simulations for representatives of essentially all known protein folds. We provide an overview of MD-derived entropies accounting for all possible degrees of dihedral freedom on an unprecedented scale. Although different side chains might be expected to impose varying restrictions on the conformational space that the backbone can sample, we found that the backbone entropy and side chain size are not strictly coupled. An outcome of these analyses is the Dynameomics Entropy Dictionary, the contents of which have been compared with entropies derived by other theoretical approaches and experiment. As might be expected, the conformational entropies scale linearly with the number of residues, demonstrating that conformational entropy is an extensive property of proteins. The calculated conformational entropies of folding agree well with previous estimates. Detailed analysis of specific cases identifies deviations in conformational entropy from the average values that highlight how conformational entropy varies with sequence, secondary structure, and tertiary fold. Notably, α-helices have lower entropy on average than do β-sheets, and both are lower than coil regions.

The maximum entropy production and maximum Shannon information entropy in enzyme kinetics

Science.gov (United States)

Dobovišek, Andrej; Markovič, Rene; Brumen, Milan; Fajmut, Aleš

2018-04-01

We demonstrate that the maximum entropy production principle (MEPP) serves as a physical selection principle for the description of the most probable non-equilibrium steady states in simple enzymatic reactions. A theoretical approach is developed, which enables maximization of the density of entropy production with respect to the enzyme rate constants for the enzyme reaction in a steady state. Mass and Gibbs free energy conservations are considered as optimization constraints. In such a way computed optimal enzyme rate constants in a steady state yield also the most uniform probability distribution of the enzyme states. This accounts for the maximal Shannon information entropy. By means of the stability analysis it is also demonstrated that maximal density of entropy production in that enzyme reaction requires flexible enzyme structure, which enables rapid transitions between different enzyme states. These results are supported by an example, in which density of entropy production and Shannon information entropy are numerically maximized for the enzyme Glucose Isomerase.

Entropy production in a cell and reversal of entropy flow as an anticancer therapy

Institute of Scientific and Technical Information of China (English)

Liao-fu LUO

2009-01-01

The entropy production rate of cancer cells is always higher than healthy cells in the case where no external field is applied. Different entropy production between two kinds of cells determines the direction of entropy flow among cells. The entropy flow is the carrier of information flow. The entropy flow from cancerous cells to healthy cells takes along the harmful information of cancerous cells, propagating its toxic action to healthy tissues. We demonstrate that a low-frequency and low- intensity electromagnetic field or ultrasound irradiation may increase the entropy production rate of a cell in normal tissue than that in cancer and consequently re- verse the direction of entropy current between two kinds of cells. The modification of the PH value of cells may also cause the reversal of the direction of entropy flow between healthy and cancerous cells. Therefore, the bio- logical tissue under the irradiation of an electromagnetic field or ultrasound or under the appropriate change of cell acidity can avoid the propagation of harmful infor- marion from cancer cells. We suggest that this entropy mechanism possibly provides a basis for a novel approach to anticancer therapy.

Isolation and Absolute Configuration of Boehmenan from Durio affinis Becc.

Directory of Open Access Journals (Sweden)

Rudiyansyah

2014-03-01

Full Text Available Boehmenan (1 is a lignan which has two feruloyl moieties at C-9 and C-9"' respectively. The structural characterization of (+-boehmenan was confirmed by 1H-NMR, 13C NMR and HRESIMS as well as by direct comparison with the literature. CD measurements established a 7S' , 8R' configuration. Cytotoxicity evaluation showed that boehmenan is moderately active against the T47D cell line with IC 50 13.7 m g/mL and shows weak activity against the HeLa cancer cell line with IC 50 93.5 m g/mL. Boehmenan is also non-cytotoxic to the Vero cell line. From this study, boehmenan X and erythro-carolignan E were also obtained.

The different paths to entropy

International Nuclear Information System (INIS)

Benguigui, L

2013-01-01

In order to understand how the complex concept of entropy emerged, we propose a trip into the past, reviewing the works of Clausius, Boltzmann, Gibbs and Planck. In particular, since Gibbs's work is not very well known we present a detailed analysis, recalling the three definitions of entropy that Gibbs gives. The introduction of entropy in quantum mechanics gives in a compact form all the classical definitions of entropy. Perhaps one of the most important aspects of entropy is to see it as a thermodynamic potential like the others proposed by Callen. The calculation of fluctuations in thermodynamic quantities is thus naturally related to entropy. We close with some remarks on entropy and irreversibility. (paper)

ENTROPY - OUR BEST FRIEND

Directory of Open Access Journals (Sweden)

Urban Kordes

2005-10-01

Full Text Available The paper tries to tackle the question of connection between entropy and the living. Definitions of life as the phenomenon that defies entropy are overviewed and the conclusion is reached that life is in a way dependant on entropy - it couldn't exist without it. Entropy is a sort of medium, a fertile soil, that gives life possibility to blossom. Paper ends with presenting some consequences for the field of artificial intelligence.

On quantum Rényi entropies

DEFF Research Database (Denmark)

Müller-Lennert, Martin; Dupont-Dupuis, Fréderic; Szehr, Oleg

2013-01-01

The Rényi entropies constitute a family of information measures that generalizes the well-known Shannon entropy, inheriting many of its properties. They appear in the form of unconditional and conditional entropies, relative entropies, or mutual information, and have found many applications in in...

Entanglement entropy of ABJM theory and entropy of topological black hole

Science.gov (United States)

Nian, Jun; Zhang, Xinyu

2017-07-01

In this paper we discuss the supersymmetric localization of the 4D N = 2 offshell gauged supergravity on the background of the AdS4 neutral topological black hole, which is the gravity dual of the ABJM theory defined on the boundary {S}^1× H^2 . We compute the large- N expansion of the supergravity partition function. The result gives the black hole entropy with the logarithmic correction, which matches the previous result of the entanglement entropy of the ABJM theory up to some stringy effects. Our result is consistent with the previous on-shell one-loop computation of the logarithmic correction to black hole entropy. It provides an explicit example of the identification of the entanglement entropy of the boundary conformal field theory with the bulk black hole entropy beyond the leading order given by the classical Bekenstein-Hawking formula, which consequently tests the AdS/CFT correspondence at the subleading order.

Entropy-Stabilized Oxides

Science.gov (United States)

2015-09-29

antiferroelectrics. Phys. Rev. Lett. 110, 017603 (2013). 22. Cantor , B., Chang, I., Knight, P. & Vincent, A. Microstructural development in equiatomic...Science 345, 1153–1158 (2014). 24. Gali, A. & George , E. Tensile properties of high- and medium-entropy alloys. Intermetallics 39, 74–78 (2013). 25...148–153 (2014). 26. Otto, F., Yang, Y., Bei, H. & George , E. Relative effects of enthalpy and entropy on the phase stability of equiatomic high-entropy

Transplanckian entanglement entropy

International Nuclear Information System (INIS)

Chang, Darwin; Chu, C.-S.; Lin Fengli

2004-01-01

The entanglement entropy of the event horizon is known to be plagued by the UV divergence due to the infinitely blue-shifted near horizon modes. In this Letter we calculate the entanglement entropy using the transplanckian dispersion relation, which has been proposed to model the quantum gravity effects. We show that, very generally, the entropy is rendered UV finite due to the suppression of high energy modes effected by the transplanckian dispersion relation

Thermostatistical aspects of generalized entropies

International Nuclear Information System (INIS)

Fa, K.S.; Lenzi, E.K.

2004-01-01

We investigate the properties concerning a class of generalized entropies given by S q,r =k{1-[Σ i p i q ] r }/[r(q-1)] which include Tsallis' entropy (r=1), the usual Boltzmann-Gibbs entropy (q=1), Renyi's entropy (r=0) and normalized Tsallis' entropy (r=-1). In order to obtain the generalized thermodynamic relations we use the laws of thermodynamics and considering the hypothesis that the joint probability of two independent systems is given by p ij A c upB =p i A p j B . We show that the transmutation which occurs from Tsallis' entropy to Renyi's entropy also occur with S q,r . In this scenario, we also analyze the generalized variance, covariance and correlation coefficient of a non-interacting system by using extended optimal Lagrange multiplier approach. We show that the correlation coefficient tends to zero in the thermodynamic limit. However, Renyi's entropy related to this non-interacting system presents a certain degree of non-extensivity

Large-scale behaviour of local and entanglement entropy of the free Fermi gas at any temperature

Science.gov (United States)

Leschke, Hajo; Sobolev, Alexander V.; Spitzer, Wolfgang

2016-07-01

The leading asymptotic large-scale behaviour of the spatially bipartite entanglement entropy (EE) of the free Fermi gas infinitely extended in multidimensional Euclidean space at zero absolute temperature, T = 0, is by now well understood. Here, we present and discuss the first rigorous results for the corresponding EE of thermal equilibrium states at T> 0. The leading large-scale term of this thermal EE turns out to be twice the first-order finite-size correction to the infinite-volume thermal entropy (density). Not surprisingly, this correction is just the thermal entropy on the interface of the bipartition. However, it is given by a rather complicated integral derived from a semiclassical trace formula for a certain operator on the underlying one-particle Hilbert space. But in the zero-temperature limit T\\downarrow 0, the leading large-scale term of the thermal EE considerably simplifies and displays a {ln}(1/T)-singularity which one may identify with the known logarithmic enhancement at T = 0 of the so-called area-law scaling. birthday of the ideal Fermi gas.

Some remarks on conditional entropy

NARCIS (Netherlands)

Nijst, A.G.P.M.

1969-01-01

Using a definition of conditional entropy given by Hanen and Neveu [5, 10, 11] we discuss in this paper some properties of conditional entropy and mean entropy, in particular an integral representation of conditional entropy (§ 2), and the decomposition theorem of the KolmogorovSina¯i invariant (§

Entropy, matter, and cosmology.

Science.gov (United States)

Prigogine, I; Géhéniau, J

1986-09-01

The role of irreversible processes corresponding to creation of matter in general relativity is investigated. The use of Landau-Lifshitz pseudotensors together with conformal (Minkowski) coordinates suggests that this creation took place in the early universe at the stage of the variation of the conformal factor. The entropy production in this creation process is calculated. It is shown that these dissipative processes lead to the possibility of cosmological models that start from empty conditions and gradually build up matter and entropy. Gravitational entropy takes a simple meaning as associated to the entropy that is necessary to produce matter. This leads to an extension of the third law of thermodynamics, as now the zero point of entropy becomes the space-time structure out of which matter is generated. The theory can be put into a convenient form using a supplementary "C" field in Einstein's field equations. The role of the C field is to express the coupling between gravitation and matter leading to irreversible entropy production.

Relations Among Some Fuzzy Entropy Formulae

Institute of Scientific and Technical Information of China (English)

卿铭

2004-01-01

Fuzzy entropy has been widely used to analyze and design fuzzy systems, and many fuzzy entropy formulae have been proposed. For further in-deepth analysis of fuzzy entropy, the axioms and some important formulae of fuzzy entropy are introduced. Some equivalence results among these fuzzy entropy formulae are proved, and it is shown that fuzzy entropy is a special distance measurement.

Entropy and Digital Installation

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Susan Ballard

2005-01-01

Full Text Available This paper examines entropy as a process which introduces ideas of distributed materiality to digital installation. Beginning from an analysis of entropy as both force and probability measure within information theory and it’s extension in Ruldof Arnheim’s text ‘Entropy and Art” it develops an argument for the positive rather thannegative forces of entropy. The paper centres on a discussion of two recent works by New Zealand artists Ronnie van Hout (“On the Run”, Wellington City Gallery, NZ, 2004 and Alex Monteith (“Invisible Cities”, Physics Room Contemporary Art Space, Christchurch, NZ, 2004. Ballard suggests that entropy, rather than being a hindrance to understanding or a random chaotic force, discloses a necessary and material politics of noise present in digital installation.

Misuse of thermodynamic entropy in economics

International Nuclear Information System (INIS)

Kovalev, Andrey V.

2016-01-01

The direct relationship between thermodynamic entropy and economic scarcity is only valid for a thermodynamically isolated economy. References to the second law of thermodynamics in economics within the context of scarcity ignore the fact that the earth is not an isolated system. The earth interacts with external sources and sinks of entropy and the resulting total entropy fluctuates around a constant. Even if the mankind finally proves unable to recycle industrial waste and close the technological cycle, the economic disruption caused by the depletion of natural resources may happen while the total thermodynamic entropy of the ecosystem remains essentially at the present level, because the transfer of chemically refined products may not increase significantly the total entropy, but it may decrease their recyclability. The inutility of industrial waste is not connected with its entropy, which may be exemplified with the case of alumina production. The case also demonstrates that industrially generated entropy is discharged into surroundings without being accumulated in ‘thermodynamically unavailable matter’. Material entropy, as a measure of complexity and economic dispersal of resources, can be a recyclability metric, but it is not a thermodynamic parameter, and its growth is not equivalent to the growth of thermodynamic entropy. - Highlights: • Entropy cannot be used as a measure of economic scarcity. • There is no anthropogenic entropy separate from the entropy produced naturally. • Inutility of industrial waste is not connected with its thermodynamic entropy. • Industrially generated entropy may or may not be accumulated in industrial waste. • Recyclability is more important than thermodynamic entropy of a product.

Frenetic Bounds on the Entropy Production

Science.gov (United States)

Maes, Christian

2017-10-01

We give a systematic derivation of positive lower bounds for the expected entropy production (EP) rate in classical statistical mechanical systems obeying a dynamical large deviation principle. The logic is the same for the return to thermodynamic equilibrium as it is for steady nonequilibria working under the condition of local detailed balance. We recover there recently studied "uncertainty" relations for the EP, appearing in studies about the effectiveness of mesoscopic machines. In general our refinement of the positivity of the expected EP rate is obtained in terms of a positive and even function of the expected current(s) which measures the dynamical activity in the system, a time-symmetric estimate of the changes in the system's configuration. Also underdamped diffusions can be included in the analysis.

How multiplicity determines entropy and the derivation of the maximum entropy principle for complex systems.

Science.gov (United States)

Hanel, Rudolf; Thurner, Stefan; Gell-Mann, Murray

2014-05-13

The maximum entropy principle (MEP) is a method for obtaining the most likely distribution functions of observables from statistical systems by maximizing entropy under constraints. The MEP has found hundreds of applications in ergodic and Markovian systems in statistical mechanics, information theory, and statistics. For several decades there has been an ongoing controversy over whether the notion of the maximum entropy principle can be extended in a meaningful way to nonextensive, nonergodic, and complex statistical systems and processes. In this paper we start by reviewing how Boltzmann-Gibbs-Shannon entropy is related to multiplicities of independent random processes. We then show how the relaxation of independence naturally leads to the most general entropies that are compatible with the first three Shannon-Khinchin axioms, the (c,d)-entropies. We demonstrate that the MEP is a perfectly consistent concept for nonergodic and complex statistical systems if their relative entropy can be factored into a generalized multiplicity and a constraint term. The problem of finding such a factorization reduces to finding an appropriate representation of relative entropy in a linear basis. In a particular example we show that path-dependent random processes with memory naturally require specific generalized entropies. The example is to our knowledge the first exact derivation of a generalized entropy from the microscopic properties of a path-dependent random process.

Entropy: Order or Information

Science.gov (United States)

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.)

Antidiarrheal Thymol Derivatives from Ageratina glabrata. Structure and Absolute Configuration of 10-Benzoyloxy-8,9-epoxy-6-hydroxythymol Isobutyrate

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Celia Bustos-Brito

2016-09-01

Full Text Available Chemical investigation of the leaves from Ageratina glabrata yielded four new thymol derivatives, namely: 10-benzoyloxy-8,9-dehydro-6-hydroxythymol isobutyrate (4, 10-benzoyloxy-8,9-dehydrothymol (5, 10-benzoyloxythymol (6 and 10-benzoyloxy-6,8-dihydroxy-9-isobutyryl-oxythymol (7. In addition, (8S-10-benzoyloxy-8,9-epoxy-6-hydroxythymol isobutyrate (1, together with other two already known thymol derivatives identified as 10-benzoyloxy-8,9-epoxy-6-methoxythymol isobutyrate (2 and 10-benzoyloxy-8,9-epoxythymol isobutyrate (3 were also obtained. In this paper, we report the structures and complete assignments of the 1H and 13C-NMR data of compounds 1–7, and the absolute configuration for compound 1, unambiguously established by single crystal X-ray diffraction, and evaluation of the Flack parameter. The in vitro antiprotozoal assay showed that compound 1 and its derivative 1a were the most potent antiamoebic and antigiardial compounds. Both compounds showed selectivity and good antiamoebic activity comparable to emetine and metronidazole, respectively, two antiprotozoal drugs used as positive controls. In relation to anti-propulsive effect, compound 1 and 1a showed inhibitory activity, with activities comparable to quercetin and compound 9, two natural antipropulsive compounds used as positive controls. These data suggest that compound 1 may play an important role in antidiarrheal properties of Ageratina glabrata.

Entropy-based financial asset pricing.

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Mihály Ormos

Full Text Available We investigate entropy as a financial risk measure. Entropy explains the equity premium of securities and portfolios in a simpler way and, at the same time, with higher explanatory power than the beta parameter of the capital asset pricing model. For asset pricing we define the continuous entropy as an alternative measure of risk. Our results show that entropy decreases in the function of the number of securities involved in a portfolio in a similar way to the standard deviation, and that efficient portfolios are situated on a hyperbola in the expected return-entropy system. For empirical investigation we use daily returns of 150 randomly selected securities for a period of 27 years. Our regression results show that entropy has a higher explanatory power for the expected return than the capital asset pricing model beta. Furthermore we show the time varying behavior of the beta along with entropy.

Entropy-based financial asset pricing.

Science.gov (United States)

Ormos, Mihály; Zibriczky, Dávid

2014-01-01

We investigate entropy as a financial risk measure. Entropy explains the equity premium of securities and portfolios in a simpler way and, at the same time, with higher explanatory power than the beta parameter of the capital asset pricing model. For asset pricing we define the continuous entropy as an alternative measure of risk. Our results show that entropy decreases in the function of the number of securities involved in a portfolio in a similar way to the standard deviation, and that efficient portfolios are situated on a hyperbola in the expected return-entropy system. For empirical investigation we use daily returns of 150 randomly selected securities for a period of 27 years. Our regression results show that entropy has a higher explanatory power for the expected return than the capital asset pricing model beta. Furthermore we show the time varying behavior of the beta along with entropy.

The residual entropy of Shastry-Sutherland lattice of rare-earth tetraborides

Energy Technology Data Exchange (ETDEWEB)

Novikov, V.V., E-mail: vvnovikov@mail.ru [Bryansk Physical Laboratory, Petrovsky Bryansk State University, 14, Bezhitskaja St., 241036, Bryansk (Russian Federation); Matovnikov, A.V.; Mitroshenkov, N.V. [Bryansk Physical Laboratory, Petrovsky Bryansk State University, 14, Bezhitskaja St., 241036, Bryansk (Russian Federation); Tolstosheev, A.K. [Bryansk State Technical University, 7, Bulvar 50-letiya Oktyabrya, 241035, Bryansk (Russian Federation)

2016-05-05

The experimental temperature dependence of thulium tetraboride specific heat C{sub p}(T) and other heat capacity data for other RE-tetraborides were investigated in the 2–300 K temperature interval. Anomalies of C{sub p}(T) dependence of TmB{sub 4} at T{sub N1} = 9.6 K and T{sub N2} = 11.4 K due to the antiferromagnetic ordering have been revealed. The ground state of the ion Tm{sup 3+} was confirmed as a doublet. The diffuse anomaly of C{sub p}(T) is attributed to the Schottky contribution to the specific heat of the tetraboride, which is caused by the influence of the crystal electric field (CEF). The presence of the residual (zero-point) entropy S{sub 0} of the magnetic moments system of Tm{sup 3+} ions, due to frustration of the Shastry-Sutherland lattice, is detected. As a measure of the frustration of the system, a new characteristic of frustrated systems, the entropy frustration figure of merit, the value of which depends on the zero-point entropy of the system, is introduced: f{sub S} = S{sub 0}/ΔS{sub m} {sub max}, where ΔS{sub m} {sub max} is the maximum value of entropy change of the boride magnetic subsystem. For TmB{sub 4} and tetraborides of Gd, Tb, Dy, Ho, and Er, f{sub s} values determined from thermal measurements, and f = θ{sub c-w}/T{sub N} (θ{sub c-w} denotes the Curie-Weiss temperature; T{sub N} is Neel temperature), calculated according to the magnetic measurement data, are practically identical. - Highlights: • The specific heat of tulium tetraboride at 2–300 K was experimentally investigated. • The nature of the ground state is established. • The Schottky contribution to the specific heat of tetraboride is identified. • The frustration figures of merit of RB{sub 4} correspond to their entropy at absolute zero.

Entropy of Iterated Function Systems and Their Relations with Black Holes and Bohr-Like Black Holes Entropies

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Christian Corda

2018-01-01

Full Text Available In this paper we consider the metric entropies of the maps of an iterated function system deduced from a black hole which are known the Bekenstein–Hawking entropies and its subleading corrections. More precisely, we consider the recent model of a Bohr-like black hole that has been recently analysed in some papers in the literature, obtaining the intriguing result that the metric entropies of a black hole are created by the metric entropies of the functions, created by the black hole principal quantum numbers, i.e., by the black hole quantum levels. We present a new type of topological entropy for general iterated function systems based on a new kind of the inverse of covers. Then the notion of metric entropy for an Iterated Function System ( I F S is considered, and we prove that these definitions for topological entropy of IFS’s are equivalent. It is shown that this kind of topological entropy keeps some properties which are hold by the classic definition of topological entropy for a continuous map. We also consider average entropy as another type of topological entropy for an I F S which is based on the topological entropies of its elements and it is also an invariant object under topological conjugacy. The relation between Axiom A and the average entropy is investigated.

Quantum thermodynamics: Microscopic foundations of entropy and of entropy generation by irreversibility

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Beretta, Gian Paolo

2008-02-01

Full Text Available What is the physical significance of entropy? What is the physical origin of irreversibility? Do entropy and irreversibility exist only for complex and macroscopic systems? Most physicists still accept and teach that the rationalization of these fundamental questions is given by Statistical Mechanics. Indeed, for everyday laboratory physics, the mathematical formalism of Statistical Mechanics (canonical and grand-canonical, Boltzmann, Bose-Einstein and Fermi-Dirac distributions allows a successful description of the thermodynamic equilibrium properties of matter, including entropy values. However, as already recognized by Schrodinger in 1936, Statistical Mechanics is impaired by conceptual ambiguities and logical inconsistencies, both in its explanation of the meaning of entropy and in its implications on the concept of state of a system. An alternative theory has been developed by Gyftopoulos, Hatsopoulos and the present author to eliminate these stumbling conceptual blocks while maintaining the mathematical formalism so successful in applications. To resolve both the problem of the meaning of entropy and that of the origin of irreversibility we have built entropy and irreversibility into the laws of microscopic physics. The result is a theory, that we call Quantum Thermodynamics, that has all the necessary features to combine Mechanics and Thermodynamics uniting all the successful results of both theories, eliminating the logical inconsistencies of Statistical Mechanics and the paradoxes on irreversibility, and providing an entirely new perspective on the microscopic origin of irreversibility, nonlinearity (therefore including chaotic behavior and maximal-entropy-generation nonequilibrium dynamics. In this paper we discuss the background and formalism of Quantum Thermodynamics including its nonlinear equation of motion and the main general results. Our objective is to show in a not-too-technical manner that this theory provides indeed a

Holographic charged Rényi entropies

Science.gov (United States)

Belin, Alexandre; Hung, Ling-Yan; Maloney, Alexander; Matsuura, Shunji; Myers, Robert C.; Sierens, Todd

2013-12-01

We construct a new class of entanglement measures by extending the usual definition of Rényi entropy to include a chemical potential. These charged Rényi entropies measure the degree of entanglement in different charge sectors of the theory and are given by Euclidean path integrals with the insertion of a Wilson line encircling the entangling surface. We compute these entropies for a spherical entangling surface in CFT's with holographic duals, where they are related to entropies of charged black holes with hyperbolic horizons. We also compute charged Rényi entropies in free field theories.

Entropy of quasiblack holes

International Nuclear Information System (INIS)

Lemos, Jose P. S.; Zaslavskii, Oleg B.

2010-01-01

We trace the origin of the black hole entropy S, replacing a black hole by a quasiblack hole. Let the boundary of a static body approach its own gravitational radius, in such a way that a quasihorizon forms. We show that if the body is thermal with the temperature taking the Hawking value at the quasihorizon limit, it follows, in the nonextremal case, from the first law of thermodynamics that the entropy approaches the Bekenstein-Hawking value S=A/4. In this setup, the key role is played by the surface stresses on the quasihorizon and one finds that the entropy comes from the quasihorizon surface. Any distribution of matter inside the surface leads to the same universal value for the entropy in the quasihorizon limit. This can be of some help in the understanding of black hole entropy. Other similarities between black holes and quasiblack holes such as the mass formulas for both objects had been found previously. We also discuss the entropy for extremal quasiblack holes, a more subtle issue.

Possible extended forms of thermodynamic entropy

International Nuclear Information System (INIS)

Sasa, Shin-ichi

2014-01-01

Thermodynamic entropy is determined by a heat measurement through the Clausius equality. The entropy then formalizes a fundamental limitation of operations by the second law of thermodynamics. The entropy is also expressed as the Shannon entropy of the microscopic degrees of freedom. Whenever an extension of thermodynamic entropy is attempted, we must pay special attention to how its three different aspects just mentioned are altered. In this paper, we discuss possible extensions of the thermodynamic entropy. (paper)

Monotonicity of the von Neumann entropy expressed as a function of R\\'enyi entropies

OpenAIRE

Fannes, Mark

2013-01-01

The von Neumann entropy of a density matrix of dimension d, expressed in terms of the first d-1 integer order R\\'enyi entropies, is monotonically increasing in R\\'enyi entropies of even order and decreasing in those of odd order.

More dimensions: Less entropy

International Nuclear Information System (INIS)

Kolb, E.W.; Lindley, D.; Seckel, D.

1984-01-01

For a cosmological model with d noncompact and D compact spatial dimensions and symmetry R 1 x S/sup d/ x S/sup D/, we calculate the entropy produced in d dimensions due to the compactification of D dimensions and show it too small to be of cosmological interest. Although insufficient entropy is produced in the model we study, the contraction of extra dimensions does lead to entropy production. We discuss modifications of our assumptions, including changing our condition for decoupling of the extra dimensions, which may lead to a large entropy production and change our conclusions

Black hole thermodynamical entropy

International Nuclear Information System (INIS)

Tsallis, Constantino; Cirto, Leonardo J.L.

2013-01-01

As early as 1902, Gibbs pointed out that systems whose partition function diverges, e.g. gravitation, lie outside the validity of the Boltzmann-Gibbs (BG) theory. Consistently, since the pioneering Bekenstein-Hawking results, physically meaningful evidence (e.g., the holographic principle) has accumulated that the BG entropy S BG of a (3+1) black hole is proportional to its area L 2 (L being a characteristic linear length), and not to its volume L 3 . Similarly it exists the area law, so named because, for a wide class of strongly quantum-entangled d-dimensional systems, S BG is proportional to lnL if d=1, and to L d-1 if d>1, instead of being proportional to L d (d ≥ 1). These results violate the extensivity of the thermodynamical entropy of a d-dimensional system. This thermodynamical inconsistency disappears if we realize that the thermodynamical entropy of such nonstandard systems is not to be identified with the BG additive entropy but with appropriately generalized nonadditive entropies. Indeed, the celebrated usefulness of the BG entropy is founded on hypothesis such as relatively weak probabilistic correlations (and their connections to ergodicity, which by no means can be assumed as a general rule of nature). Here we introduce a generalized entropy which, for the Schwarzschild black hole and the area law, can solve the thermodynamic puzzle. (orig.)

Entropy-Corrected Holographic Dark Energy

International Nuclear Information System (INIS)

Wei Hao

2009-01-01

The holographic dark energy (HDE) is now an interesting candidate of dark energy, which has been studied extensively in the literature. In the derivation of HDE, the black hole entropy plays an important role. In fact, the entropy-area relation can be modified due to loop quantum gravity or other reasons. With the modified entropy-area relation, we propose the so-called 'entropy-corrected holographic dark energy' (ECHDE) in the present work. We consider many aspects of ECHDE and find some interesting results. In addition, we briefly consider the so-called 'entropy-corrected agegraphic dark energy' (ECADE). (geophysics, astronomy, and astrophysics)

Understanding Atmospheric Behaviour in Terms of Entropy: A Review of Applications of the Second Law of Thermodynamics to Meteorology

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Donghai Wang

2011-01-01

Full Text Available The concept of entropy and its relevant principles, mainly the principle of maximum entropy production (MEP, the effect of negative entropy flow (NEF on the organization of atmospheric systems and the principle of the Second Law of thermodynamics, as well as their applications to atmospheric sciences, are reviewed. Some formulations of sub-grid processes such as diffusion parameterization schemes in computational geophysical fluid dynamics that can be improved based on full-irreversibility are also discussed, although they have not yet been systematically subjected to scrutiny from the perspective of the entropy budgets. A comparative investigation shows that the principle of MEP applies to the entropy production of macroscopic fluxes and determines the most probable state, that is, a system may choose a development meta-stable trajectory with a smaller production since entropy production behavior involves many specific dynamical and thermodynamic processes in the atmosphere and the extremal principles only provide a general insight into the overall configuration of the atmosphere. In contrast to the principle of MEP, the analysis of NEF is able to provide a new insight into the mechanism responsible for the evolution of a weather system as well as a new approach to predicting its track and intensity trend.

Variations mechanism in entropy of wave height field and its relation with thermodynamic entropy

Institute of Scientific and Technical Information of China (English)

无

2006-01-01

This paper gives a brief description of annual period and seasonal variation in the wave height field entropy in the northeastern Pacific. A calculation of the quantity of the, received by lithosphere systems in the northern hemisphere is introduced. The wave heat field entropy is compared with the difference in the quantity of the sun's radiation heat. Analysis on the transfer method, period and lag of this seasonal variation led to the conclusion that the annual period and seasonal variation in the entropy of the wave height field in the Northwestern Pacific is due to the seasonal variation of the sun's radiation heat. Furthermore, the inconsistency between thermodynamic entropy and information entropy was studied.

On unified-entropy characterization of quantum channels

International Nuclear Information System (INIS)

Rastegin, A E

2012-01-01

We consider properties of quantum channels with the use of unified entropies. Extremal unravelings of quantum channel with respect to these entropies are examined. The concept of map entropy is extended in terms of the unified entropies. The map (q, s)-entropy is naturally defined as the unified (q, s)-entropy of a rescaled dynamical matrix of given quantum channel. Inequalities of Fannes type are obtained for introduced entropies in terms of both the trace and Frobenius norms of difference between corresponding dynamical matrices. Additivity properties of introduced map entropies are discussed. The known inequality of Lindblad with the entropy exchange is generalized to many of the unified entropies. For the tensor product of a pair of quantum channels, we derive a two-sided estimate on the output entropy of a maximally entangled input state. (paper)

Maximum Entropy Fundamentals

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F. Topsøe

2001-09-01

Full Text Available Abstract: In its modern formulation, the Maximum Entropy Principle was promoted by E.T. Jaynes, starting in the mid-fifties. The principle dictates that one should look for a distribution, consistent with available information, which maximizes the entropy. However, this principle focuses only on distributions and it appears advantageous to bring information theoretical thinking more prominently into play by also focusing on the "observer" and on coding. This view was brought forward by the second named author in the late seventies and is the view we will follow-up on here. It leads to the consideration of a certain game, the Code Length Game and, via standard game theoretical thinking, to a principle of Game Theoretical Equilibrium. This principle is more basic than the Maximum Entropy Principle in the sense that the search for one type of optimal strategies in the Code Length Game translates directly into the search for distributions with maximum entropy. In the present paper we offer a self-contained and comprehensive treatment of fundamentals of both principles mentioned, based on a study of the Code Length Game. Though new concepts and results are presented, the reading should be instructional and accessible to a rather wide audience, at least if certain mathematical details are left aside at a rst reading. The most frequently studied instance of entropy maximization pertains to the Mean Energy Model which involves a moment constraint related to a given function, here taken to represent "energy". This type of application is very well known from the literature with hundreds of applications pertaining to several different elds and will also here serve as important illustration of the theory. But our approach reaches further, especially regarding the study of continuity properties of the entropy function, and this leads to new results which allow a discussion of models with so-called entropy loss. These results have tempted us to speculate over

Information Entropy Production of Maximum Entropy Markov Chains from Spike Trains

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Cofré, Rodrigo; Maldonado, Cesar

2018-01-01

We consider the maximum entropy Markov chain inference approach to characterize the collective statistics of neuronal spike trains, focusing on the statistical properties of the inferred model. We review large deviations techniques useful in this context to describe properties of accuracy and convergence in terms of sampling size. We use these results to study the statistical fluctuation of correlations, distinguishability and irreversibility of maximum entropy Markov chains. We illustrate these applications using simple examples where the large deviation rate function is explicitly obtained for maximum entropy models of relevance in this field.

Compressibility and rarefaction effects on entropy and entropy generation in micro/nano Couette flow using DSMC

International Nuclear Information System (INIS)

Ejtehadi, Omid; Esfahani, Javad Abolfazli; Roohi, Ehsan

2012-01-01

In the present work, compressible flow of argon gas in the famous problem of Couette flow in micro/nano-scale is considered and numerically analyzed using the direct simulation Monte Carlo (DSMC) method. The effects of compressibility and rarefaction on entropy and entropy generation in terms of viscous dissipation and thermal diffusion are studied in a wide range of Mach and Knudsen numbers and the observed physics are discussed. In this regard, we computed entropy by using its kinetic theory formulation in a microscopic way while the entropy generation distribution is achieved by applying a semi-microscopic approach and thoroughly free from equilibrium assumptions. The results of our simulations demonstrated that the entropy profiles are in accordance with the temperature profiles. It is also illustrated that the increase of Mach number will result in non-uniform entropy profiles with increase in the vicinity of the central regions of the channel. Moreover, generation of entropy in all regions of the domain stages clear growth. By contrast, increasing the Knudsen number has inverse effects such as: uniform entropy profiles and a falling off in entropy generation amount throughout the channel.

Entropy in Biology

Indian Academy of Sciences (India)

During the process of ageing, the balance shifts in the direction of anarchy. Death is ... tion of life and the laws of statistieal physics and entropy, both of which ... capable of doing work. ... defined by Ludwig Boltzmann in 1877, the entropy of the.

Entropy Generation and Human Aging: Lifespan Entropy and Effect of Physical Activity Level

Science.gov (United States)

Silva, Carlos; Annamalai, Kalyan

2008-06-01

The first and second laws of thermodynamics were applied to biochemical reactions typical of human metabolism. An open-system model was used for a human body. Energy conservation, availability and entropy balances were performed to obtain the entropy generated for the main food components. Quantitative results for entropy generation were obtained as a function of age using the databases from the U.S. Food and Nutrition Board (FNB) and Centers for Disease Control and Prevention (CDC), which provide energy requirements and food intake composition as a function of age, weight and stature. Numerical integration was performed through human lifespan for different levels of physical activity. Results were presented and analyzed. Entropy generated over the lifespan of average individuals (natural death) was found to be 11,404 kJ/ºK per kg of body mass with a rate of generation three times higher on infants than on the elderly. The entropy generated predicts a life span of 73.78 and 81.61 years for the average U.S. male and female individuals respectively, which are values that closely match the average lifespan from statistics (74.63 and 80.36 years). From the analysis of the effect of different activity levels, it is shown that entropy generated increases with physical activity, suggesting that exercise should be kept to a “healthy minimum” if entropy generation is to be minimized.

Preimage entropy dimension of topological dynamical systems

OpenAIRE

Liu, Lei; Zhou, Xiaomin; Zhou, Xiaoyao

2014-01-01

We propose a new definition of preimage entropy dimension for continuous maps on compact metric spaces, investigate fundamental properties of the preimage entropy dimension, and compare the preimage entropy dimension with the topological entropy dimension. The defined preimage entropy dimension holds various basic properties of topological entropy dimension, for example, the preimage entropy dimension of a subsystem is bounded by that of the original system and topologically conjugated system...

On S-mixing entropy of quantum channels

Science.gov (United States)

Mukhamedov, Farrukh; Watanabe, Noboru

2018-06-01

In this paper, an S-mixing entropy of quantum channels is introduced as a generalization of Ohya's S-mixing entropy. We investigate several properties of the introduced entropy. Moreover, certain relations between the S-mixing entropy and the existing map and output entropies of quantum channels are investigated as well. These relations allowed us to find certain connections between separable states and the introduced entropy. Hence, there is a sufficient condition to detect entangled states. Moreover, several properties of the introduced entropy are investigated. Besides, entropies of qubit and phase-damping channels are calculated.

Maximum Quantum Entropy Method

OpenAIRE

Sim, Jae-Hoon; Han, Myung Joon

2018-01-01

Maximum entropy method for analytic continuation is extended by introducing quantum relative entropy. This new method is formulated in terms of matrix-valued functions and therefore invariant under arbitrary unitary transformation of input matrix. As a result, the continuation of off-diagonal elements becomes straightforward. Without introducing any further ambiguity, the Bayesian probabilistic interpretation is maintained just as in the conventional maximum entropy method. The applications o...

Assignment of absolute stereostructures through quantum mechanics electronic and vibrational circular dichroism calculations.

Science.gov (United States)

Dai, Peng; Jiang, Nan; Tan, Ren-Xiang

2016-01-01

Elucidation of absolute configuration of chiral molecules including structurally complex natural products remains a challenging problem in organic chemistry. A reliable method for assigning the absolute stereostructure is to combine the experimental circular dichroism (CD) techniques such as electronic and vibrational CD (ECD and VCD), with quantum mechanics (QM) ECD and VCD calculations. The traditional QM methods as well as their continuing developments make them more applicable with accuracy. Taking some chiral natural products with diverse conformations as examples, this review describes the basic concepts and new developments of QM approaches for ECD and VCD calculations in solution and solid states.

Entropy: From Thermodynamics to Hydrology

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Demetris Koutsoyiannis

2014-02-01

Full Text Available Some known results from statistical thermophysics as well as from hydrology are revisited from a different perspective trying: (a to unify the notion of entropy in thermodynamic and statistical/stochastic approaches of complex hydrological systems and (b to show the power of entropy and the principle of maximum entropy in inference, both deductive and inductive. The capability for deductive reasoning is illustrated by deriving the law of phase change transition of water (Clausius-Clapeyron from scratch by maximizing entropy in a formal probabilistic frame. However, such deductive reasoning cannot work in more complex hydrological systems with diverse elements, yet the entropy maximization framework can help in inductive inference, necessarily based on data. Several examples of this type are provided in an attempt to link statistical thermophysics with hydrology with a unifying view of entropy.

Entropy Evolution and Uncertainty Estimation with Dynamical Systems

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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.

All Inequalities for the Relative Entropy

Science.gov (United States)

Ibinson, Ben; Linden, Noah; Winter, Andreas

2007-01-01

The relative entropy of two n-party quantum states is an important quantity exhibiting, for example, the extent to which the two states are different. The relative entropy of the states formed by reducing two n-party states to a smaller number m of parties is always less than or equal to the relative entropy of the two original n-party states. This is the monotonicity of relative entropy. Using techniques from convex geometry, we prove that monotonicity under restrictions is the only general inequality satisfied by quantum relative entropies. In doing so we make a connection to secret sharing schemes with general access structures: indeed, it turns out that the extremal rays of the cone defined by monotonicity are populated by classical secret sharing schemes. A surprising outcome is that the structure of allowed relative entropy values of subsets of multiparty states is much simpler than the structure of allowed entropy values. And the structure of allowed relative entropy values (unlike that of entropies) is the same for classical probability distributions and quantum states.

Algebraic entropy for algebraic maps

International Nuclear Information System (INIS)

Hone, A N W; Ragnisco, Orlando; Zullo, Federico

2016-01-01

We propose an extension of the concept of algebraic entropy, as introduced by Bellon and Viallet for rational maps, to algebraic maps (or correspondences) of a certain kind. The corresponding entropy is an index of the complexity of the map. The definition inherits the basic properties from the definition of entropy for rational maps. We give an example with positive entropy, as well as two examples taken from the theory of Bäcklund transformations. (letter)

Determination of the absolute configurations of natural products via density functional theory calculations of optical rotation, electronic circular dichroism, and vibrational circular dichroism: the cytotoxic sesquiterpene natural products quadrone, suberosenone, suberosanone, and suberosenol A acetate.

Science.gov (United States)

Stephens, P J; McCann, D M; Devlin, F J; Smith, A B

2006-07-01

The determination of the absolute configurations (ACs) of chiral molecules using the chiroptical techniques of optical rotation (OR), electronic circular dichroism (ECD), and vibrational circular dichroism (VCD) has been revolutionized by the development of density functional theory (DFT) methods for the prediction of these properties. Here, we demonstrate the significance of these advances for the stereochemical characterization of natural products. Time-dependent DFT (TDDFT) calculations of the specific rotations, [alpha](D), of four cytotoxic natural products, quadrone (1), suberosenone (2), suberosanone (3), and suberosenol A acetate (4), are used to assign their ACs. TDDFT calculations of the ECD of 1 are used to assign its AC. The VCD spectrum of 1 is reported and also used, together with DFT calculations, to assign its AC. The ACs of 1 derived from its [alpha](D), ECD, and VCD are identical and in agreement with the AC previously determined via total synthesis. The previously undetermined ACs of 2-4, derived from their [alpha](D) values, have absolute configurations of their tricyclic cores identical to that of 1. Further studies of the ACs of these molecules using ECD and, especially, VCD are recommended to establish more definitively this finding. Our studies of the OR, ECD, and VCD of quadrone are the first to utilize DFT calculations of all three properties for the determination of the AC of a chiral natural product molecule.

Weighted fractional permutation entropy and fractional sample entropy for nonlinear Potts financial dynamics

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.

Weighted fractional permutation entropy and fractional sample entropy for nonlinear Potts financial dynamics

International Nuclear Information System (INIS)

Xu, Kaixuan; Wang, Jun

2017-01-01

In this paper, recently introduced permutation entropy and sample entropy are further developed to the fractional cases, weighted fractional permutation entropy (WFPE) and fractional sample entropy (FSE). The fractional order generalization of information entropy is utilized in the above two complexity approaches, to detect the statistical characteristics of fractional order information in complex systems. The effectiveness analysis of proposed methods on the synthetic data and the real-world data reveals that tuning the fractional order allows a high sensitivity and more accurate characterization to the signal evolution, which is useful in describing the dynamics of complex systems. Moreover, the numerical research on nonlinear complexity behaviors is compared between the returns series of Potts financial model and the actual stock markets. And the empirical results confirm the feasibility of the proposed model. - Highlights: • Two new entropy approaches for estimation of nonlinear complexity are proposed for the financial market. • Effectiveness analysis of proposed methods is presented and their respective features are studied. • Empirical research of proposed analysis on seven world financial market indices. • Numerical simulation of Potts financial dynamics is preformed for nonlinear complexity behaviors.

Nonsymmetric entropy I: basic concepts and results

OpenAIRE

Liu, Chengshi

2006-01-01

A new concept named nonsymmetric entropy which generalizes the concepts of Boltzman's entropy and shannon's entropy, was introduced. Maximal nonsymmetric entropy principle was proven. Some important distribution laws were derived naturally from maximal nonsymmetric entropy principle.

Statistical mechanical theory of liquid entropy

International Nuclear Information System (INIS)

Wallace, D.C.

1993-01-01

The multiparticle correlation expansion for the entropy of a classical monatomic liquid is presented. This entropy expresses the physical picture in which there is no free particle motion, but rather, each atom moves within a cage formed by its neighbors. The liquid expansion, including only pair correlations, gives an excellent account of the experimental entropy of most liquid metals, of liquid argon, and the hard sphere liquid. The pair correlation entropy is well approximated by a universal function of temperature. Higher order correlation entropy, due to n-particle irreducible correlations for n≥3, is significant in only a few liquid metals, and its occurrence suggests the presence of n-body forces. When the liquid theory is applied to the study of melting, the author discovers the important classification of normal and anomalous melting, according to whether there is not or is a significant change in the electronic structure upon melting, and he discovers the universal disordering entropy for melting of a monatomic crystal. Interesting directions for future research are: extension to include orientational correlations of molecules, theoretical calculation of the entropy of water, application to the entropy of the amorphous state, and correlational entropy of compressed argon. The author clarifies the relation among different entropy expansions in the recent literature

Entropy and equilibrium via games of complexity

Science.gov (United States)

Topsøe, Flemming

2004-09-01

It is suggested that thermodynamical equilibrium equals game theoretical equilibrium. Aspects of this thesis are discussed. The philosophy is consistent with maximum entropy thinking of Jaynes, but goes one step deeper by deriving the maximum entropy principle from an underlying game theoretical principle. The games introduced are based on measures of complexity. Entropy is viewed as minimal complexity. It is demonstrated that Tsallis entropy ( q-entropy) and Kaniadakis entropy ( κ-entropy) can be obtained in this way, based on suitable complexity measures. A certain unifying effect is obtained by embedding these measures in a two-parameter family of entropy functions.

Enthalpy–entropy compensation

Indian Academy of Sciences (India)

Enthalpy–entropy compensation is the name given to the correlation sometimes observed between the estimates of the enthalpy and entropy of a reaction obtained from temperature-dependence data. Although the mainly artefactual nature of this correlation has been known for many years, the subject enjoys periodical ...

Linear entropy and collapse–revival phenomenon for a general formalism N-type four-level atom interacting with a single-mode field

Science.gov (United States)

Eied, A. A.

2018-05-01

In this paper, the linear entropy and collapse-revival phenomenon through the relation ( -{\\bar{n}}) in a system of N-configuration four-level atom interacting with a single-mode field with additional forms of nonlinearities of both the field and the intensity-dependent atom-field coupling functional are investigated. A factorization of the initial density operator is assumed, considering the field to be initially in a squeezed coherent states and the atom initially in its most upper excited state. The dynamical behavior of the linear entropy and the time evolution of ( -{\\bar{n}}) are analyzed. In particular, the effects of the mean photon number, detuning, Kerr-like medium and the intensity-dependent coupling functional on the entropy and the evolution of ( -{\\bar{n}}) are examined.

Multivariate refined composite multiscale entropy analysis

International Nuclear Information System (INIS)

Humeau-Heurtier, Anne

2016-01-01

Multiscale entropy (MSE) has become a prevailing method to quantify signals complexity. MSE relies on sample entropy. However, MSE may yield imprecise complexity estimation at large scales, because sample entropy does not give precise estimation of entropy when short signals are processed. A refined composite multiscale entropy (RCMSE) has therefore recently been proposed. Nevertheless, RCMSE is for univariate signals only. The simultaneous analysis of multi-channel (multivariate) data often over-performs studies based on univariate signals. We therefore introduce an extension of RCMSE to multivariate data. Applications of multivariate RCMSE to simulated processes reveal its better performances over the standard multivariate MSE. - Highlights: • Multiscale entropy quantifies data complexity but may be inaccurate at large scale. • A refined composite multiscale entropy (RCMSE) has therefore recently been proposed. • Nevertheless, RCMSE is adapted to univariate time series only. • We herein introduce an extension of RCMSE to multivariate data. • It shows better performances than the standard multivariate multiscale entropy.

On holographic defect entropy

International Nuclear Information System (INIS)

Estes, John; Jensen, Kristan; O’Bannon, Andy; Tsatis, Efstratios; Wrase, Timm

2014-01-01

We study a number of (3+1)- and (2+1)-dimensional defect and boundary conformal field theories holographically dual to supergravity theories. In all cases the defects or boundaries are planar, and the defects are codimension-one. Using holography, we compute the entanglement entropy of a (hemi-)spherical region centered on the defect (boundary). We define defect and boundary entropies from the entanglement entropy by an appropriate background subtraction. For some (3+1)-dimensional theories we find evidence that the defect/boundary entropy changes monotonically under certain renormalization group flows triggered by operators localized at the defect or boundary. This provides evidence that the g-theorem of (1+1)-dimensional field theories generalizes to higher dimensions

Entropy Generation and Human Aging: Lifespan Entropy and Effect of Physical Activity Level

Directory of Open Access Journals (Sweden)

Kalyan Annamalai

2008-06-01

Full Text Available The first and second laws of thermodynamics were applied to biochemical reactions typical of human metabolism. An open-system model was used for a human body. Energy conservation, availability and entropy balances were performed to obtain the entropy generated for the main food components. Quantitative results for entropy generation were obtained as a function of age using the databases from the U.S. Food and Nutrition Board (FNB and Centers for Disease Control and Prevention (CDC, which provide energy requirements and food intake composition as a function of age, weight and stature. Numerical integration was performed through human lifespan for different levels of physical activity. Results were presented and analyzed. Entropy generated over the lifespan of average individuals (natural death was found to be 11,404 kJ/ºK per kg of body mass with a rate of generation three times higher on infants than on the elderly. The entropy generated predicts a life span of 73.78 and 81.61 years for the average U.S. male and female individuals respectively, which are values that closely match the average lifespan from statistics (74.63 and 80.36 years. From the analysis of the effect of different activity levels, it is shown that entropy generated increases with physical activity, suggesting that exercise should be kept to a “healthy minimum” if entropy generation is to be minimized.

Entropy and cosmology.

Science.gov (United States)

Zucker, M. H.

This paper is a critical analysis and reassessment of entropic functioning as it applies to the question of whether the ultimate fate of the universe will be determined in the future to be "open" (expanding forever to expire in a big chill), "closed" (collapsing to a big crunch), or "flat" (balanced forever between the two). The second law of thermodynamics declares that entropy can only increase and that this principle extends, inevitably, to the universe as a whole. This paper takes the position that this extension is an unwarranted projection based neither on experience nonfact - an extrapolation that ignores the powerful effect of a gravitational force acting within a closed system. Since it was originally presented by Clausius, the thermodynamic concept of entropy has been redefined in terms of "order" and "disorder" - order being equated with a low degree of entropy and disorder with a high degree. This revised terminology more subjective than precise, has generated considerable confusion in cosmology in several critical instances. For example - the chaotic fireball of the big bang, interpreted by Stephen Hawking as a state of disorder (high entropy), is infinitely hot and, thermally, represents zero entropy (order). Hawking, apparently focusing on the disorderly "chaotic" aspect, equated it with a high degree of entropy - overlooking the fact that the universe is a thermodynamic system and that the key factor in evaluating the big-bang phenomenon is the infinitely high temperature at the early universe, which can only be equated with zero entropy. This analysis resolves this confusion and reestablishes entropy as a cosmological function integrally linked to temperature. The paper goes on to show that, while all subsystems contained within the universe require external sources of energization to have their temperatures raised, this requirement does not apply to the universe as a whole. The universe is the only system that, by itself can raise its own

Entropy maximization

Indian Academy of Sciences (India)

Abstract. 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 f that satisfy. ∫ fhi dμ = λi for i = 1, 2,...,...k the maximizer of entropy is an f0 that is pro- portional to exp(. ∑ ci hi ) for some choice of ci . An extension of this to a continuum of.

Excess Entropy and Diffusivity

Indian Academy of Sciences (India)

First page Back Continue Last page Graphics. Excess Entropy and Diffusivity. Excess entropy scaling of diffusivity (Rosenfeld,1977). Analogous relationships also exist for viscosity and thermal conductivity.

Entropy in molecular recognition by proteins.

Science.gov (United States)

Caro, José A; Harpole, Kyle W; Kasinath, Vignesh; Lim, Jackwee; Granja, Jeffrey; Valentine, Kathleen G; Sharp, Kim A; Wand, A Joshua

2017-06-20

Molecular recognition by proteins is fundamental to molecular biology. Dissection of the thermodynamic energy terms governing protein-ligand interactions has proven difficult, with determination of entropic contributions being particularly elusive. NMR relaxation measurements have suggested that changes in protein conformational entropy can be quantitatively obtained through a dynamical proxy, but the generality of this relationship has not been shown. Twenty-eight protein-ligand complexes are used to show a quantitative relationship between measures of fast side-chain motion and the underlying conformational entropy. We find that the contribution of conformational entropy can range from favorable to unfavorable, which demonstrates the potential of this thermodynamic variable to modulate protein-ligand interactions. For about one-quarter of these complexes, the absence of conformational entropy would render the resulting affinity biologically meaningless. The dynamical proxy for conformational entropy or "entropy meter" also allows for refinement of the contributions of solvent entropy and the loss in rotational-translational entropy accompanying formation of high-affinity complexes. Furthermore, structure-based application of the approach can also provide insight into long-lived specific water-protein interactions that escape the generic treatments of solvent entropy based simply on changes in accessible surface area. These results provide a comprehensive and unified view of the general role of entropy in high-affinity molecular recognition by proteins.

Improvements in absolute seismometer sensitivity calibration using local earth gravity measurements

Science.gov (United States)

Anthony, Robert E.; Ringler, Adam; Wilson, David

2018-01-01

The ability to determine both absolute and relative seismic amplitudes is fundamentally limited by the accuracy and precision with which scientists are able to calibrate seismometer sensitivities and characterize their response. Currently, across the Global Seismic Network (GSN), errors in midband sensitivity exceed 3% at the 95% confidence interval and are the least‐constrained response parameter in seismic recording systems. We explore a new methodology utilizing precise absolute Earth gravity measurements to determine the midband sensitivity of seismic instruments. We first determine the absolute sensitivity of Kinemetrics EpiSensor accelerometers to 0.06% at the 99% confidence interval by inverting them in a known gravity field at the Albuquerque Seismological Laboratory (ASL). After the accelerometer is calibrated, we install it in its normal configuration next to broadband seismometers and subject the sensors to identical ground motions to perform relative calibrations of the broadband sensors. Using this technique, we are able to determine the absolute midband sensitivity of the vertical components of Nanometrics Trillium Compact seismometers to within 0.11% and Streckeisen STS‐2 seismometers to within 0.14% at the 99% confidence interval. The technique enables absolute calibrations from first principles that are traceable to National Institute of Standards and Technology (NIST) measurements while providing nearly an order of magnitude more precision than step‐table calibrations.

q-entropy for symbolic dynamical systems

International Nuclear Information System (INIS)

Zhao, Yun; Pesin, Yakov

2015-01-01

For symbolic dynamical systems we use the Carathéodory construction as described in (Pesin 1997 Dimension Theory in Dynamical Systems, ConTemporary Views and Applications (Chicago: University of Chicago Press)) to introduce the notions of q-topological and q-metric entropies. We describe some basic properties of these entropies and in particular, discuss relations between q-metric entropy and local metric entropy. Both q-topological and q-metric entropies are new invariants respectively under homeomorphisms and metric isomorphisms of dynamical systems. (paper)

Transfer entropy in physical systems and the arrow of time

Science.gov (United States)

Spinney, Richard E.; Lizier, Joseph T.; Prokopenko, Mikhail

2016-08-01

Recent developments have cemented the realization that many concepts and quantities in thermodynamics and information theory are shared. In this paper, we consider a highly relevant quantity in information theory and complex systems, the transfer entropy, and explore its thermodynamic role by considering the implications of time reversal upon it. By doing so we highlight the role of information dynamics on the nuanced question of observer perspective within thermodynamics by relating the temporal irreversibility in the information dynamics to the configurational (or spatial) resolution of the thermodynamics. We then highlight its role in perhaps the most enduring paradox in modern physics, the manifestation of a (thermodynamic) arrow of time. We find that for systems that process information such as those undergoing feedback, a robust arrow of time can be formulated by considering both the apparent physical behavior which leads to conventional entropy production and the information dynamics which leads to a quantity we call the information theoretic arrow of time. We also offer an interpretation in terms of optimal encoding of observed physical behavior.

Entropy Maximization

Indian Academy of Sciences (India)

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 ∫ f h i d = i for i = 1 , 2 , … , … k the maximizer of entropy is an f 0 that is proportional to exp ⁡ ( ∑ c i h i ) for some choice of c i . An extension of this to a continuum of ...

Entropy evaporated by a black hole

International Nuclear Information System (INIS)

Zurek, W.H.

1982-01-01

It is shown that the entropy of the radiation evaporated by an uncharged, nonrotating black hole into vacuum in the course of its lifetime is approximately (4/3) times the initial entropy of this black hole. Also considered is a thermodynamically reversible process in which an increase of black-hole entropy is equal to the decrease of the entropy of its surroundings. Implications of these results for the generalized second law of thermodynamics and for the interpretation of black-hole entropy are pointed out

Entropy and transverse section reconstruction

International Nuclear Information System (INIS)

Gullberg, G.T.

1976-01-01

A new approach to the reconstruction of a transverse section using projection data from multiple views incorporates the concept of maximum entropy. The principle of maximizing information entropy embodies the assurance of minimizing bias or prejudice in the reconstruction. Using maximum entropy is a necessary condition for the reconstructed image. This entropy criterion is most appropriate for 3-D reconstruction of objects from projections where the system is underdetermined or the data are limited statistically. This is the case in nuclear medicine time limitations in patient studies do not yield sufficient projections

Entropy and optimality in river deltas

Science.gov (United States)

Tejedor, Alejandro; Longjas, Anthony; Edmonds, Douglas A.; Zaliapin, Ilya; Georgiou, Tryphon T.; Rinaldo, Andrea; Foufoula-Georgiou, Efi

2017-10-01

The form and function of river deltas is intricately linked to the evolving structure of their channel networks, which controls how effectively deltas are nourished with sediments and nutrients. Understanding the coevolution of deltaic channels and their flux organization is crucial for guiding maintenance strategies of these highly stressed systems from a range of anthropogenic activities. To date, however, a unified theory explaining how deltas self-organize to distribute water and sediment up to the shoreline remains elusive. Here, we provide evidence for an optimality principle underlying the self-organized partition of fluxes in delta channel networks. By introducing a suitable nonlocal entropy rate (nER) and by analyzing field and simulated deltas, we suggest that delta networks achieve configurations that maximize the diversity of water and sediment flux delivery to the shoreline. We thus suggest that prograding deltas attain dynamically accessible optima of flux distributions on their channel network topologies, thus effectively decoupling evolutionary time scales of geomorphology and hydrology. When interpreted in terms of delta resilience, high nER configurations reflect an increased ability to withstand perturbations. However, the distributive mechanism responsible for both diversifying flux delivery to the shoreline and dampening possible perturbations might lead to catastrophic events when those perturbations exceed certain intensity thresholds.

Dynamical entropy for infinite quantum systems

International Nuclear Information System (INIS)

Hudetz, T.

1990-01-01

We review the recent physical application of the so-called Connes-Narnhofer-Thirring entropy, which is the successful quantum mechanical generalization of the classical Kolmogorov-Sinai entropy and, by its very conception, is a dynamical entropy for infinite quantum systems. We thus comparingly review also the physical applications of the classical dynamical entropy for infinite classical systems. 41 refs. (Author)

Entropy Generation Across Earth's Bow Shock

Science.gov (United States)

Parks, George K.; McCarthy, Michael; Fu, Suiyan; Lee E. s; Cao, Jinbin; Goldstein, Melvyn L.; Canu, Patrick; Dandouras, Iannis S.; Reme, Henri; Fazakerley, Andrew;

Topological entropy of continuous functions on topological spaces

International Nuclear Information System (INIS)

Liu Lei; Wang Yangeng; Wei Guo

2009-01-01

Adler, Konheim and McAndrew introduced the concept of topological entropy of a continuous mapping for compact dynamical systems. Bowen generalized the concept to non-compact metric spaces, but Walters indicated that Bowen's entropy is metric-dependent. We propose a new definition of topological entropy for continuous mappings on arbitrary topological spaces (compactness, metrizability, even axioms of separation not necessarily required), investigate fundamental properties of the new entropy, and compare the new entropy with the existing ones. The defined entropy generates that of Adler, Konheim and McAndrew and is metric-independent for metrizable spaces. Yet, it holds various basic properties of Adler, Konheim and McAndrew's entropy, e.g., the entropy of a subsystem is bounded by that of the original system, topologically conjugated systems have a same entropy, the entropy of the induced hyperspace system is larger than or equal to that of the original system, and in particular this new entropy coincides with Adler, Konheim and McAndrew's entropy for compact systems

Problems in black-hole entropy interpretation

International Nuclear Information System (INIS)

Liberati, S.

1997-01-01

In this work some proposals for black-hole entropy interpretation are exposed and investigated. In particular, the author will firstly consider the so-called 'entanglement entropy' interpretation, in the framework of the brick wall model and the divergence problem arising in the one-loop calculations of various thermodynamical quantities, like entropy, internal energy and heat capacity. It is shown that the assumption of equality of entanglement entropy and Bekenstein-Hawking one appears to give inconsistent results. These will be a starting point for a different interpretation of black.hole entropy based on peculiar topological structures of manifolds with 'intrinsic' thermodynamical features. It is possible to show an exact relation between black-hole gravitational entropy and topology of these Euclidean space-times. the expression for the Euler characteristic, through the Gauss-Bonnet integral, and the one for entropy for gravitational instantons are proposed in a form which makes the relation between these self-evident. Using this relation he propose a generalization of the Bekenstein-Hawking entropy in which the former and Euler characteristic are related in the equation S = χA / 8. Finally, he try to expose some conclusions and hypotheses about possible further development of this research

Gyrokinetic Statistical Absolute Equilibrium and Turbulence

International Nuclear Information System (INIS)

Zhu, Jian-Zhou; Hammett, Gregory W.

2011-01-01

A paradigm based on the absolute equilibrium of Galerkin-truncated inviscid systems to aid in understanding turbulence (T.-D. Lee, 'On some statistical properties of hydrodynamical and magnetohydrodynamical fields,' Q. Appl. Math. 10, 69 (1952)) is taken to study gyrokinetic plasma turbulence: A finite set of Fourier modes of the collisionless gyrokinetic equations are kept and the statistical equilibria are calculated; possible implications for plasma turbulence in various situations are discussed. For the case of two spatial and one velocity dimension, in the calculation with discretization also of velocity v with N grid points (where N + 1 quantities are conserved, corresponding to an energy invariant and N entropy-related invariants), the negative temperature states, corresponding to the condensation of the generalized energy into the lowest modes, are found. This indicates a generic feature of inverse energy cascade. Comparisons are made with some classical results, such as those of Charney-Hasegawa-Mima in the cold-ion limit. There is a universal shape for statistical equilibrium of gyrokinetics in three spatial and two velocity dimensions with just one conserved quantity. Possible physical relevance to turbulence, such as ITG zonal flows, and to a critical balance hypothesis are also discussed.

Gyrokinetic statistical absolute equilibrium and turbulence

International Nuclear Information System (INIS)

Zhu Jianzhou; Hammett, Gregory W.

2010-01-01

A paradigm based on the absolute equilibrium of Galerkin-truncated inviscid systems to aid in understanding turbulence [T.-D. Lee, Q. Appl. Math. 10, 69 (1952)] is taken to study gyrokinetic plasma turbulence: a finite set of Fourier modes of the collisionless gyrokinetic equations are kept and the statistical equilibria are calculated; possible implications for plasma turbulence in various situations are discussed. For the case of two spatial and one velocity dimension, in the calculation with discretization also of velocity v with N grid points (where N+1 quantities are conserved, corresponding to an energy invariant and N entropy-related invariants), the negative temperature states, corresponding to the condensation of the generalized energy into the lowest modes, are found. This indicates a generic feature of inverse energy cascade. Comparisons are made with some classical results, such as those of Charney-Hasegawa-Mima in the cold-ion limit. There is a universal shape for statistical equilibrium of gyrokinetics in three spatial and two velocity dimensions with just one conserved quantity. Possible physical relevance to turbulence, such as ITG zonal flows, and to a critical balance hypothesis are also discussed.

Absolute risk, absolute risk reduction and relative risk

Directory of Open Access Journals (Sweden)

Jose Andres Calvache

2012-12-01

Full Text Available This article illustrates the epidemiological concepts of absolute risk, absolute risk reduction and relative risk through a clinical example. In addition, it emphasizes the usefulness of these concepts in clinical practice, clinical research and health decision-making process.

Gravitational entropies in LTB dust models

International Nuclear Information System (INIS)

Sussman, Roberto A; Larena, Julien

2014-01-01

We consider generic Lemaître–Tolman–Bondi (LTB) dust models to probe the gravitational entropy proposals of Clifton, Ellis and Tavakol (CET) and of Hosoya and Buchert (HB). We also consider a variant of the HB proposal based on a suitable quasi-local scalar weighted average. We show that the conditions for entropy growth for all proposals are directly related to a negative correlation of similar fluctuations of the energy density and Hubble scalar. While this correlation is evaluated locally for the CET proposal, it must be evaluated in a non-local domain dependent manner for the two HB proposals. By looking at the fulfilment of these conditions at the relevant asymptotic limits we are able to provide a well grounded qualitative description of the full time evolution and radial asymptotic scaling of the three entropies in generic models. The following rigorous analytic results are obtained for the three proposals: (i) entropy grows when the density growing mode is dominant, (ii) all ever-expanding hyperbolic models reach a stable terminal equilibrium characterized by an inhomogeneous entropy maximum in their late time evolution; (iii) regions with decaying modes and collapsing elliptic models exhibit unstable equilibria associated with an entropy minimum (iv) near singularities the CET entropy diverges while the HB entropies converge; (v) the CET entropy converges for all models in the radial asymptotic range, whereas the HB entropies only converge for models asymptotic to a Friedmann–Lemaître–Robertson–Walker background. The fact that different independent proposals yield fairly similar conditions for entropy production, time evolution and radial scaling in generic LTB models seems to suggest that their common notion of a ‘gravitational entropy’ may be a theoretically robust concept applicable to more general spacetimes. (paper)

Information Entropy Production of Maximum Entropy Markov Chains from Spike Trains

Directory of Open Access Journals (Sweden)

Rodrigo Cofré

2018-01-01

Full Text Available The spiking activity of neuronal networks follows laws that are not time-reversal symmetric; the notion of pre-synaptic and post-synaptic neurons, stimulus correlations and noise correlations have a clear time order. Therefore, a biologically realistic statistical model for the spiking activity should be able to capture some degree of time irreversibility. We use the thermodynamic formalism to build a framework in the context maximum entropy models to quantify the degree of time irreversibility, providing an explicit formula for the information entropy production of the inferred maximum entropy Markov chain. We provide examples to illustrate our results and discuss the importance of time irreversibility for modeling the spike train statistics.

Enthalpy-entropy compensation in protein unfolding

Institute of Scientific and Technical Information of China (English)

无

2000-01-01

Enthalpy-entropy compensation was found to be a universal law in protein unfolding based on over 3 000 experimental data. Water molecular reorganization accompanying the protein unfolding was suggested as the origin of the enthalpy-entropy compensation in protein unfolding. It is indicated that the enthalpy-entropy compensation constitutes the physical foundation that satisfies the biological need of the small free energy changes in protein unfolding, without the sacrifice of the bio-diversity of proteins. The enthalpy-entropy compensation theory proposed herein also provides valuable insights into the Privalov's puzzle of enthalpy and entropy convergence in protein unfolding.

Entropy inequalities from reflection positivity

International Nuclear Information System (INIS)

Casini, H

2010-01-01

We investigate the question of whether the entropy and the Renyi entropies of the vacuum state reduced to a region of space can be represented in terms of correlators in quantum field theory. In this case, the positivity relations for the correlators are mapped into inequalities for the entropies. We write them using a real-time version of reflection positivity, which can be generalized to general quantum systems. Using this generalization we can prove an infinite sequence of inequalities which are obeyed by the Renyi entropies of integer index. There is one independent inequality involving any number of different subsystems. In quantum field theory the inequalities acquire a simple geometrical form and are consistent with the integer index Renyi entropies being given by vacuum expectation values of twisting operators in the Euclidean formulation. Several possible generalizations and specific examples are analyzed

The Entropy of Co-Compact Open Covers

Directory of Open Access Journals (Sweden)

Steven Bourquin

2013-06-01

Full Text Available Co-compact entropy is introduced as an invariant of topological conjugation for perfect mappings defined on any Hausdorff space (compactness and metrizability are not necessarily required. This is achieved through the consideration of co-compact covers of the space. The advantages of co-compact entropy include: (1 it does not require the space to be compact and, thus, generalizes Adler, Konheim and McAndrew’s topological entropy of continuous mappings on compact dynamical systems; and (2 it is an invariant of topological conjugation, compared to Bowen’s entropy, which is metric-dependent. Other properties of co-compact entropy are investigated, e.g., the co-compact entropy of a subsystem does not exceed that of the whole system. For the linear system, (R; f, defined by f(x = 2x, the co-compact entropy is zero, while Bowen’s entropy for this system is at least log 2. More generally, it is found that co-compact entropy is a lower bound of Bowen’s entropies, and the proof of this result also generates the Lebesgue Covering Theorem to co-compact open covers of non-compact metric spaces.

On Thermodynamic Interpretation of Transfer Entropy

Directory of Open Access Journals (Sweden)

Don C. Price

2013-02-01

Full Text Available We propose a thermodynamic interpretation of transfer entropy near equilibrium, using a specialised Boltzmann’s principle. The approach relates conditional probabilities to the probabilities of the corresponding state transitions. This in turn characterises transfer entropy as a difference of two entropy rates: the rate for a resultant transition and another rate for a possibly irreversible transition within the system affected by an additional source. We then show that this difference, the local transfer entropy, is proportional to the external entropy production, possibly due to irreversibility. Near equilibrium, transfer entropy is also interpreted as the difference in equilibrium stabilities with respect to two scenarios: a default case and the case with an additional source. Finally, we demonstrated that such a thermodynamic treatment is not applicable to information flow, a measure of causal effect.

Entropy type complexity of quantum processes

International Nuclear Information System (INIS)

Watanabe, Noboru

2014-01-01

von Neumann entropy represents the amount of information in the quantum state, and this was extended by Ohya for general quantum systems [10]. Umegaki first defined the quantum relative entropy for σ-finite von Neumann algebras, which was extended by Araki, and Uhlmann, for general von Neumann algebras and *-algebras, respectively. In 1983 Ohya introduced the quantum mutual entropy by using compound states; this describes the amount of information correctly transmitted through the quantum channel, which was also extended by Ohya for general quantum systems. In this paper, we briefly explain Ohya's S-mixing entropy and the quantum mutual entropy for general quantum systems. By using structure equivalent class, we will introduce entropy type functionals based on quantum information theory to improve treatment for the Gaussian communication process. (paper)

Notes on entanglement entropy in string theory

International Nuclear Information System (INIS)

He, Song; Numasawa, Tokiro; Takayanagi, Tadashi; Watanabe, Kento

2015-01-01

In this paper, we study the conical entropy in string theory in the simplest setup of dividing the nine dimensional space into two halves. This corresponds to the leading quantum correction to the horizon entropy in string theory on the Rindler space. This entropy is also called the conical entropy and includes surface term contributions. We first derive a new simple formula of the conical entropy for any free higher spin fields. Then we apply this formula to computations of conical entropy in open and closed superstring. In our analysis of closed string, we study the twisted conical entropy defined by making use of string theory on Melvin backgrounds. This quantity is easier to calculate owing to the folding trick. Our analysis shows that the conical entropy in closed superstring is UV finite owing to the string scale cutoff.

Entropy and Entropy Production: Old Misconceptions and New Breakthroughs

Directory of Open Access Journals (Sweden)

Leonid M. Martyushev

2013-03-01

Full Text Available Persistent misconceptions existing for dozens of years and influencing progress in various fields of science are sometimes encountered in the scientific and especially, the popular-science literature. The present brief review deals with two such interrelated misconceptions (misunderstandings. The first misunderstanding: entropy is a measure of disorder. This is an old and very common opinion. The second misconception is that the entropy production minimizes in the evolution of nonequilibrium systems. However, as it has recently become clear, evolution (progress in Nature demonstrates the opposite, i.e., maximization of the entropy production. The principal questions connected with this maximization are considered herein. The two misconceptions mentioned above can lead to the apparent contradiction between the conclusions of modern thermodynamics and the basic conceptions of evolution existing in biology. In this regard, the analysis of these issues seems extremely important and timely as it contributes to the deeper understanding of the laws of development of the surrounding World and the place of humans in it.

A Note on Quantum Entropy

International Nuclear Information System (INIS)

Hansen, Frank

2016-01-01

Incremental information, as measured by the quantum entropy, is increasing when two ensembles are united. This result was proved by Lieb and Ruskai, and it is the foundation for the proof of strong subadditivity of quantum entropy. We present a truly elementary proof of this fact in the context of the broader family of matrix entropies introduced by Chen and Tropp.

A Note on Quantum Entropy

Energy Technology Data Exchange (ETDEWEB)

Hansen, Frank, E-mail: frank.hansen@m.tohoku.ac.jp [Tohoku University, Institute for Excellence in Higher Education (Japan)

2016-06-15

Incremental information, as measured by the quantum entropy, is increasing when two ensembles are united. This result was proved by Lieb and Ruskai, and it is the foundation for the proof of strong subadditivity of quantum entropy. We present a truly elementary proof of this fact in the context of the broader family of matrix entropies introduced by Chen and Tropp.

Entropy function and universality of entropy-area relation for small black holes

International Nuclear Information System (INIS)

Cai Ronggen; Chen, C.-M.; Maeda, Kei-ichi; Ohta, Nobuyoshi; Pang Dawei

2008-01-01

We discuss the entropy-area relation for the small black holes with higher curvature corrections by using the entropy function formalism and field redefinition method. We show that the entropy S BH of the small black hole is proportional to its horizon area A. In particular, we find a universal result that S BH =A/2G, the ratio is 2 times of Bekenstein-Hawking entropy-area formula in many cases of physical interest. In four dimensions, the universal relation is always true irrespective of the coefficients of the higher-order terms if the dilaton couplings are the same, which is the case for string effective theory, while in five dimensions, the relation again holds irrespective of the overall coefficient if the higher-order corrections are in the GB combination. We also discuss how this result generalizes to known physically interesting cases with Lovelock correction terms in various dimensions, and possible implications of the universal relation.

Entropy Production of Stars

Directory of Open Access Journals (Sweden)

Leonid M. Martyushev

2015-06-01

Full Text Available The entropy production (inside the volume bounded by a photosphere of main-sequence stars, subgiants, giants, and supergiants is calculated based on B–V photometry data. A non-linear inverse relationship of thermodynamic fluxes and forces as well as an almost constant specific (per volume entropy production of main-sequence stars (for 95% of stars, this quantity lies within 0.5 to 2.2 of the corresponding solar magnitude is found. The obtained results are discussed from the perspective of known extreme principles related to entropy production.

Superheterodyne configuration for two-wavelength interferometry applied to absolute distance measurement

International Nuclear Information System (INIS)

Le Floch, Sebastien; Salvade, Yves; Droz, Nathalie; Mitouassiwou, Rostand; Favre, Patrick

2010-01-01

We present a new superheterodyne technique for long-distance measurements by two-wavelength interferometry (TWI). While conventional systems use two acousto-optic modulators to generate two different heterodyne frequencies, here the two frequencies result from synchronized sweeps of optical and radio frequencies. A distributed feedback laser source is injected in an intensity modulator that is driven at the half-wave voltage mode. A radio-frequency signal is applied to this intensity modulator to generate two optical sidebands around the optical carrier. This applied radio frequency consists of a digital ramp between 13 and 15 GHz, with 1 ms duration and with an accuracy of better than 1 ppm. Simultaneously, the laser source is frequency modulated by a current modulation that is synchronized on the radio-frequency ramp as well as on a triangle waveform. These two frequency-swept optical signals at the output of the modulator illuminate a Michelson interferometer and create two distinct distance-dependent heterodyne frequencies on the photodetector. The superheterodyne signal is then detected and bandpass filtered to retrieve the absolute distance measurement. Experiments between 1 and 15 m confirm the validity of this new concept, leading to a distance accuracy of ± 50 μm for a 1 ms acquisition time.

Weak entropy inequalities and entropic convergence

Institute of Scientific and Technical Information of China (English)

2008-01-01

A criterion for algebraic convergence of the entropy is presented and an algebraic convergence result for the entropy of an exclusion process is improved. A weak entropy inequality is considered and its relationship to entropic convergence is discussed.

Relative entropy and the RG flow

Energy Technology Data Exchange (ETDEWEB)

Casini, Horacio; Testé, Eduardo; Torroba, Gonzalo [Centro Atómico Bariloche and CONICET,S.C. de Bariloche, Río Negro, R8402AGP (Argentina)

2017-03-16

We consider the relative entropy between vacuum states of two different theories: a conformal field theory (CFT), and the CFT perturbed by a relevant operator. By restricting both states to the null Cauchy surface in the causal domain of a sphere, we make the relative entropy equal to the difference of entanglement entropies. As a result, this difference has the positivity and monotonicity properties of relative entropy. From this it follows a simple alternative proof of the c-theorem in d=2 space-time dimensions and, for d>2, the proof that the coefficient of the area term in the entanglement entropy decreases along the renormalization group (RG) flow between fixed points. We comment on the regimes of convergence of relative entropy, depending on the space-time dimensions and the conformal dimension Δ of the perturbation that triggers the RG flow.

Large Field Inflation and Gravitational Entropy

DEFF Research Database (Denmark)

Kaloper, Nemanja; Kleban, Matthew; Lawrence, Albion

2016-01-01

species will lead to a violation of the covariant entropy bound at large $N$. If so, requiring the validity of the covariant entropy bound could limit the number of light species and their couplings, which in turn could severely constrain axion-driven inflation. Here we show that there is no such problem...... entropy of de Sitter or near-de Sitter backgrounds at leading order. Working in detail with $N$ scalar fields in de Sitter space, renormalized to one loop order, we show that the gravitational entropy automatically obeys the covariant entropy bound. Furthermore, while the axion decay constant is a strong...... in this light, and show that they are perfectly consistent with the covariant entropy bound. Thus, while quantum gravity might yet spoil large field inflation, holographic considerations in the semiclassical theory do not obstruct it....

Entropy Budget for Hawking Evaporation

Directory of Open Access Journals (Sweden)

Ana Alonso-Serrano

2017-07-01

Full Text Available Blackbody radiation, emitted from a furnace and described by a Planck spectrum, contains (on average an entropy of 3 . 9 ± 2 . 5 bits per photon. Since normal physical burning is a unitary process, this amount of entropy is compensated by the same amount of “hidden information” in correlations between the photons. The importance of this result lies in the posterior extension of this argument to the Hawking radiation from black holes, demonstrating that the assumption of unitarity leads to a perfectly reasonable entropy/information budget for the evaporation process. In order to carry out this calculation, we adopt a variant of the “average subsystem” approach, but consider a tripartite pure system that includes the influence of the rest of the universe, and which allows “young” black holes to still have a non-zero entropy; which we identify with the standard Bekenstein entropy.

The dynamical entropy of quantum systems

International Nuclear Information System (INIS)

Connes, A.; Narnhofer, H.; Thirring, W.

1987-01-01

The definition of the dynamical entropy for automorphisms of C * - algebras is represented. Several properties are discussed; especially it is argued that the entropy of the shift can be shown in special cases to be equal with the entropy density. (Author)

Spontaneous entropy decrease and its statistical formula

OpenAIRE

Xing, Xiu-San

2007-01-01

Why can the world resist the law of entropy increase and produce self-organizing structure? Does the entropy of an isolated system always only increase and never decrease? Can be thermodymamic degradation and self-organizing evolution united? How to unite? In this paper starting out from nonequilibrium entropy evolution equation we proved that a new entropy decrease could spontaneously emerge in nonequilibrium system with internal attractive interaction. This new entropy decrease coexists wit...

Optimal paths of piston motion of irreversible diesel cycle for minimum entropy generation

Directory of Open Access Journals (Sweden)

Ge Yanlin

2011-01-01

Full Text Available A Diesel cycle heat engine with internal and external irreversibility’s of heat transfer and friction, in which the finite rate of combustion is considered and the heat transfer between the working fluid and the environment obeys Newton’s heat transfer law [q≈ Δ(T], is studied in this paper. Optimal piston motion trajectories for minimizing entropy generation per cycle are derived for the fixed total cycle time and fuel consumed per cycle. Optimal control theory is applied to determine the optimal piston motion trajectories for the cases of with piston acceleration constraint on each stroke and the optimal distribution of the total cycle time among the strokes. The optimal piston motion with acceleration constraint for each stroke consists of three segments, including initial maximum acceleration and final maximum deceleration boundary segments, respectively. Numerical examples for optimal configurations are provided, and the results obtained are compared with those obtained when maximizing the work output with Newton’s heat transfer law. The results also show that optimizing the piston motion trajectories could reduce engine entropy generation by more than 20%. This is primarily due to the decrease in entropy generation caused by heat transfer loss on the initial portion of the power stroke.

Using entropy measures to characterize human locomotion.

Science.gov (United States)

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 versus cosmological horizon entropy

International Nuclear Information System (INIS)

Davis, Tamara M; Davies, P C W; Lineweaver, Charles H

2003-01-01

The generalized second law of thermodynamics states that entropy always increases when all event horizons are attributed with an entropy proportional to their area. We test the generalized second law by investigating the change in entropy when dust, radiation and black holes cross a cosmological event horizon. We generalize for flat, open and closed Friedmann-Robertson-Walker universes by using numerical calculations to determine the cosmological horizon evolution. In most cases, the loss of entropy from within the cosmological horizon is more than balanced by an increase in cosmological event horizon entropy, maintaining the validity of the generalized second law of thermodynamics. However, an intriguing set of open universe models shows an apparent entropy decrease when black holes disappear over the cosmological event horizon. We anticipate that this apparent violation of the generalized second law will disappear when solutions are available for black holes embedded in arbitrary backgrounds

Entropy of uremia and dialysis technology.

Science.gov (United States)

Ronco, Claudio

2013-01-01

The second law of thermodynamics applies with local exceptions to patient history and therapy interventions. Living things preserve their low level of entropy throughout time because they receive energy from their surroundings in the form of food. They gain their order at the expense of disordering the nutrients they consume. Death is the thermodynamically favored state: it represents a large increase in entropy as molecular structure yields to chaos. The kidney is an organ dissipating large amounts of energy to maintain the level of entropy of the organism as low as possible. Diseases, and in particular uremia, represent conditions of rapid increase in entropy. Therapeutic strategies are oriented towards a reduction in entropy or at least a decrease in the speed of entropy increase. Uremia is a process accelerating the trend towards randomness and disorder (increase in entropy). Dialysis is a factor external to the patient that tends to reduce the level of entropy caused by kidney disease. Since entropy can only increase in closed systems, energy and work must be spent to limit the entropy of uremia. This energy should be adapted to the system (patient) and be specifically oriented and personalized. This includes a multidimensional effort to achieve an adequate dialysis that goes beyond small molecular weight solute clearance. It includes a biological plan for recovery of homeostasis and a strategy towards long-term rehabilitation of the patient. Such objectives can be achieved with a combination of technology and innovation to answer specific questions that are still present after 60 years of dialysis history. This change in the individual bioentropy may represent a local exception to natural trends as the patient could be considered an isolated universe responding to the classic laws of thermodynamics. Copyright © 2013 S. Karger AG, Basel.

Time Dependence of Entropy Flux and Entropy Production of a Dissipative Dynamical System Driven by Non-Gaussian Noise

International Nuclear Information System (INIS)

Guo Yongfeng; Xu Wei; Li Dongxi; Xie Wenxian

2008-01-01

A stochastic dissipative dynamical system driven by non-Gaussian noise is investigated. A general approximate Fokker-Planck equation of the system is derived through a path-integral approach. Based on the definition of Shannon's information entropy, the exact time dependence of entropy flux and entropy production of the system is calculated both in the absence and in the presence of non-equilibrium constraint. The present calculation can be used to interpret the interplay of the dissipative constant and non-Gaussian noise on the entropy flux and entropy production

Calculations of the magnetic entropy change in amorphous through a microscopic anisotropic model: Applications to Dy{sub 70}Zr{sub 30} and DyCo{sub 3.4} alloys

Energy Technology Data Exchange (ETDEWEB)

Ranke, P. J. von, E-mail: von.ranke@uol.com.br; Nóbrega, E. P.; Ribeiro, P. O.; Alvarenga, T. S. T.; Lopes, P. H. O.; Sousa, V. S. R. de; Oliveira, N. A. de [Instituto de Física, Universidade do Estado do Rio de Janeiro—UERJ, Rua São Francisco Xavier, 524, 20550-013 Rio de Janeiro (Brazil); Caldas, A. [Sociedade Unificada de Ensino Superior e Cultura, SUESC, 20211-351 Rio de Janeiro (Brazil); Alho, B. P. [Instituto de Aplicação Fernando Rodrigues da Silveira, Universidade do Estado do Rio de Janeiro, Rua Santa Alexandrina, 288, 20260-232 Rio de Janeiro (Brazil); Carvalho, G. [Laboratório Nacional de Luz Sincroton—LNLS, 13083-970 Campinas, São Paulo (Brazil); Magnus, A.

2014-10-14

We report theoretical investigations on the magnetocaloric effect, described by the magnetic entropy change in rare earth—transition metal amorphous systems. The model includes the local anisotropy on the rare earth ions in Harris-Plischke-Zuckermann assumptions. The transition metals ions are treated in terms of itinerant electron ferromagnetism and the magnetic moment of rare earth ions is coupled to the polarized d-band by a local exchange interaction. The magnetocaloric effect was calculated in DyCo{sub 3.4} system, which presents amorphous sperimagnetic configuration. The calculations predict higher refrigerant capacity in the amorphous DyCo{sub 3.4} than in DyCo{sub 2} crystal, highlighting the importance of amorphous magnetocaloric materials. Our calculation of the magnetocaloric effect in Dy{sub 70}Zr{sub 30}, which presents amorphous asperomagnetic configuration, is in good agreement with the experimental result. Furthermore, magnetic entropy changes associated with crystal-amorphous configurations change are estimated.

Information-theoretical aspects of quantum-mechanical entropy

International Nuclear Information System (INIS)

Wehrl, A.

1990-01-01

Properties of the quantum ( = von Neumann) entropy S(ρ) -k Trρ lnρ, ρ being a compact operator, are proved first, and differences against the classical case, e.g. the Shannon entropy, are worked out. The main result is on the strong subadditivity of this quantum entropy. Then another entropy, a function not of the state but of the dynamics of the system, is considered as a quantum analogue of the classical Kolmogorov-Sinai-entropy. An attempt in defining such a quantity had only recently sucess in a paper of Connes, Narnhofer and Thirring. A definition of this entropy is given. 34 refs

Algorithmic randomness and physical entropy

International Nuclear Information System (INIS)

Zurek, W.H.

1989-01-01

Algorithmic randomness provides a rigorous, entropylike measure of disorder of an individual, microscopic, definite state of a physical system. It is defined by the size (in binary digits) of the shortest message specifying the microstate uniquely up to the assumed resolution. Equivalently, algorithmic randomness can be expressed as the number of bits in the smallest program for a universal computer that can reproduce the state in question (for instance, by plotting it with the assumed accuracy). In contrast to the traditional definitions of entropy, algorithmic randomness can be used to measure disorder without any recourse to probabilities. Algorithmic randomness is typically very difficult to calculate exactly but relatively easy to estimate. In large systems, probabilistic ensemble definitions of entropy (e.g., coarse-grained entropy of Gibbs and Boltzmann's entropy H=lnW, as well as Shannon's information-theoretic entropy) provide accurate estimates of the algorithmic entropy of an individual system or its average value for an ensemble. One is thus able to rederive much of thermodynamics and statistical mechanics in a setting very different from the usual. Physical entropy, I suggest, is a sum of (i) the missing information measured by Shannon's formula and (ii) of the algorithmic information content---algorithmic randomness---present in the available data about the system. This definition of entropy is essential in describing the operation of thermodynamic engines from the viewpoint of information gathering and using systems. These Maxwell demon-type entities are capable of acquiring and processing information and therefore can ''decide'' on the basis of the results of their measurements and computations the best strategy for extracting energy from their surroundings. From their internal point of view the outcome of each measurement is definite

Entropy of network ensembles

Science.gov (United States)

Bianconi, Ginestra

2009-03-01

In this paper we generalize the concept of random networks to describe network ensembles with nontrivial features by a statistical mechanics approach. This framework is able to describe undirected and directed network ensembles as well as weighted network ensembles. These networks might have nontrivial community structure or, in the case of networks embedded in a given space, they might have a link probability with a nontrivial dependence on the distance between the nodes. These ensembles are characterized by their entropy, which evaluates the cardinality of networks in the ensemble. In particular, in this paper we define and evaluate the structural entropy, i.e., the entropy of the ensembles of undirected uncorrelated simple networks with given degree sequence. We stress the apparent paradox that scale-free degree distributions are characterized by having small structural entropy while they are so widely encountered in natural, social, and technological complex systems. We propose a solution to the paradox by proving that scale-free degree distributions are the most likely degree distribution with the corresponding value of the structural entropy. Finally, the general framework we present in this paper is able to describe microcanonical ensembles of networks as well as canonical or hidden-variable network ensembles with significant implications for the formulation of network-constructing algorithms.

Entropy Production in Stochastics

Directory of Open Access Journals (Sweden)

Demetris Koutsoyiannis

2017-10-01

Full Text Available While the modern definition of entropy is genuinely probabilistic, in entropy production the classical thermodynamic definition, as in heat transfer, is typically used. Here we explore the concept of entropy production within stochastics and, particularly, two forms of entropy production in logarithmic time, unconditionally (EPLT or conditionally on the past and present having been observed (CEPLT. We study the theoretical properties of both forms, in general and in application to a broad set of stochastic processes. A main question investigated, related to model identification and fitting from data, is how to estimate the entropy production from a time series. It turns out that there is a link of the EPLT with the climacogram, and of the CEPLT with two additional tools introduced here, namely the differenced climacogram and the climacospectrum. In particular, EPLT and CEPLT are related to slopes of log-log plots of these tools, with the asymptotic slopes at the tails being most important as they justify the emergence of scaling laws of second-order characteristics of stochastic processes. As a real-world application, we use an extraordinary long time series of turbulent velocity and show how a parsimonious stochastic model can be identified and fitted using the tools developed.

Does black-hole entropy make sense

International Nuclear Information System (INIS)

Wilkins, D.

1979-01-01

Bekenstein and Hawking saved the second law of thermodynamics near a black hole by assigning to the hole an entropy Ssub(h) proportional to the area of its event horizon. It is tempting to assume that Ssub(h) possesses all the features commonly associated with the physical entropy. Kundt has shown, however, that Ssub(h) violates several reasonable physical expectations. This criticism is reviewed, augmenting it as follows: (a) Ssub(h) is a badly behaved state function requiring knowledge of the hole's future history; and (b) close analogs of event horizons in other space-times do not possess an 'entropy'. These questions are also discussed: (c) Is Ssub(h) suitable for all regions of a black-hole space-time. And (b) should Ssub(h) be attributed to the exterior of a white hole. One can retain Ssub(h) for the interior (respectively, exterior) of a black (respectively, white) hole, but is rejected as contrary to the information-theoretic derivation of horizon entropy given by Berkenstein. The total entropy defined by Kundt (all ordinary entropy on space-section cutting through the hole, no horizon term) and that of Bekenstein-Hawking (ordinary entropy outside horizon plus horizon term) appear to be complementary concepts with separate domains of validity. In the most natural choice, an observer inside a black hole will use Kundt's entropy, and one remaining outside that of Bekenstein-Hawking. (author)

Applications of Entropy in Finance: A Review

Directory of Open Access Journals (Sweden)

Guanqun Tong

2013-11-01

Full Text Available Although the concept of entropy is originated from thermodynamics, its concepts and relevant principles, especially the principles of maximum entropy and minimum cross-entropy, have been extensively applied in finance. In this paper, we review the concepts and principles of entropy, as well as their applications in the field of finance, especially in portfolio selection and asset pricing. Furthermore, we review the effects of the applications of entropy and compare them with other traditional and new methods.

Wavelet entropy characterization of elevated intracranial pressure.

Science.gov (United States)

Xu, Peng; Scalzo, Fabien; Bergsneider, Marvin; Vespa, Paul; Chad, Miller; Hu, Xiao

2008-01-01

Intracranial Hypertension (ICH) often occurs for those patients with traumatic brain injury (TBI), stroke, tumor, etc. Pathology of ICH is still controversial. In this work, we used wavelet entropy and relative wavelet entropy to study the difference existed between normal and hypertension states of ICP for the first time. The wavelet entropy revealed the similar findings as the approximation entropy that entropy during ICH state is smaller than that in normal state. Moreover, with wavelet entropy, we can see that ICH state has the more focused energy in the low wavelet frequency band (0-3.1 Hz) than the normal state. The relative wavelet entropy shows that the energy distribution in the wavelet bands between these two states is actually different. Based on these results, we suggest that ICH may be formed by the re-allocation of oscillation energy within brain.

Entropy of international trades

Science.gov (United States)

Oh, Chang-Young; Lee, D.-S.

2017-05-01

The organization of international trades is highly complex under the collective efforts towards economic profits of participating countries given inhomogeneous resources for production. Considering the trade flux as the probability of exporting a product from a country to another, we evaluate the entropy of the world trades in the period 1950-2000. The trade entropy has increased with time, and we show that it is mainly due to the extension of trade partnership. For a given number of trade partners, the mean trade entropy is about 60% of the maximum possible entropy, independent of time, which can be regarded as a characteristic of the trade fluxes' heterogeneity and is shown to be derived from the scaling and functional behaviors of the universal trade-flux distribution. The correlation and time evolution of the individual countries' gross-domestic products and the number of trade partners show that most countries achieved their economic growth partly by extending their trade relationship.

Curvature Entropy for Curved Profile Generation

Directory of Open Access Journals (Sweden)

Koichiro Sato

2012-03-01

Full Text Available In a curved surface design, the overall shape features that emerge from combinations of shape elements are important. However, controlling the features of the overall shape in curved profiles is difficult using conventional microscopic shape information such as dimension. Herein two types of macroscopic shape information, curvature entropy and quadrature curvature entropy, quantitatively represent the features of the overall shape. The curvature entropy is calculated by the curvature distribution, and represents the complexity of a shape (one of the overall shape features. The quadrature curvature entropy is an improvement of the curvature entropy by introducing a Markov process to evaluate the continuity of a curvature and to approximate human cognition of the shape. Additionally, a shape generation method using a genetic algorithm as a calculator and the entropy as a shape generation index is presented. Finally, the applicability of the proposed method is demonstrated using the side view of an automobile as a design example.

Gradient Dynamics and Entropy Production Maximization

Science.gov (United States)

Janečka, Adam; Pavelka, Michal

2018-01-01

We compare two methods for modeling dissipative processes, namely gradient dynamics and entropy production maximization. Both methods require similar physical inputs-how energy (or entropy) is stored and how it is dissipated. Gradient dynamics describes irreversible evolution by means of dissipation potential and entropy, it automatically satisfies Onsager reciprocal relations as well as their nonlinear generalization (Maxwell-Onsager relations), and it has statistical interpretation. Entropy production maximization is based on knowledge of free energy (or another thermodynamic potential) and entropy production. It also leads to the linear Onsager reciprocal relations and it has proven successful in thermodynamics of complex materials. Both methods are thermodynamically sound as they ensure approach to equilibrium, and we compare them and discuss their advantages and shortcomings. In particular, conditions under which the two approaches coincide and are capable of providing the same constitutive relations are identified. Besides, a commonly used but not often mentioned step in the entropy production maximization is pinpointed and the condition of incompressibility is incorporated into gradient dynamics.

Entropy is in Flux V3.4

Science.gov (United States)

Kadanoff, Leo P.

2017-05-01

The science of thermodynamics was put together in the Nineteenth Century to describe large systems in equilibrium. One part of thermodynamics defines entropy for equilibrium systems and demands an ever-increasing entropy for non-equilibrium ones. Since thermodynamics does not define entropy out of equilibrium, pure thermodynamics cannot follow the details of how this increase occurs. However, starting with the work of Ludwig Boltzmann in 1872, and continuing to the present day, various models of non-equilibrium behavior have been put together with the specific aim of generalizing the concept of entropy to non-equilibrium situations. This kind of entropy has been termed kinetic entropy to distinguish it from the thermodynamic variety. Knowledge of kinetic entropy started from Boltzmann's insight about his equation for the time dependence of gaseous systems. In this paper, his result is stated as a definition of kinetic entropy in terms of a local equation for the entropy density. This definition is then applied to Landau's theory of the Fermi liquid thereby giving the kinetic entropy within that theory. The dynamics of many condensed matter systems including Fermi liquids, low temperature superfluids, and ordinary metals lend themselves to the definition of kinetic entropy. In fact, entropy has been defined and used for a wide variety of situations in which a condensed matter system has been allowed to relax for a sufficient period so that the very most rapid fluctuations have been ironed out. One of the broadest applications of non-equilibrium analysis considers quantum degenerate systems using Martin-Schwinger Green's functions (Phys Rev 115:1342-1373, 1959) as generalized Wigner functions, g^({p},ω ,{R},T). This paper describes once again how the quantum kinetic equations for these functions give locally defined conservation laws for mass momentum and energy. In local thermodynamic equilibrium, this kinetic theory enables a reasonable definition of the density

Algebraic entropy for differential-delay equations

OpenAIRE

Viallet, Claude M.

2014-01-01

We extend the definition of algebraic entropy to a class of differential-delay equations. The vanishing of the entropy, as a structural property of an equation, signals its integrability. We suggest a simple way to produce differential-delay equations with vanishing entropy from known integrable differential-difference equations.

The Wehrl entropy has Gaussian optimizers

DEFF Research Database (Denmark)

De Palma, Giacomo

2018-01-01

We determine the minimum Wehrl entropy among the quantum states with a given von Neumann entropy and prove that it is achieved by thermal Gaussian states. This result determines the relation between the von Neumann and the Wehrl entropies. The key idea is proving that the quantum-classical channel...

Single Particle Entropy in Heated Nuclei

International Nuclear Information System (INIS)

Guttormsen, M.; Chankova, R.; Hjorth-Jensen, M.; Rekstad, J.; Siem, S.; Sunde, A. C.; Syed, N. U. H.; Agvaanluvsan, U.; Schiller, A.; Voinov, A.

2006-01-01

The thermal motion of single particles represents the largest contribution to level density (or entropy) in atomic nuclei. The concept of single particle entropy is presented and shown to be an approximate extensive (additive) quantity for mid-shell nuclei. A few applications of single particle entropy are demonstrated

BiEntropy for Python v. 1.0

Energy Technology Data Exchange (ETDEWEB)

2018-03-15

This Python package provides high-performance implementations of the functions and examples presented in "BiEntropy - The Approximate Entropy of a Finite Binary String" by Grenville J. Croll, presented at ANPA 34 in 2013. https://arxiv.org/abs/1305.0954 According to the paper, BiEntropy is "a simple algorithm which computes the approximate entropy of a finite binary string of arbitrary length" using "a weighted average of the Shannon Entropies of the string and all but the last binary derivative of the string."

Nonextensive entropies derived from Gauss' principle

International Nuclear Information System (INIS)

Wada, Tatsuaki

2011-01-01

Gauss' principle in statistical mechanics is generalized for a q-exponential distribution in nonextensive statistical mechanics. It determines the associated stochastic and statistical nonextensive entropies which satisfy Greene-Callen principle concerning on the equivalence between microcanonical and canonical ensembles. - Highlights: → Nonextensive entropies are derived from Gauss' principle and ensemble equivalence. → Gauss' principle is generalized for a q-exponential distribution. → I have found the condition for satisfying Greene-Callen principle. → The associated statistical q-entropy is found to be normalized Tsallis entropy.

Entanglement entropy in top-down models

Energy Technology Data Exchange (ETDEWEB)

Jones, Peter A.R.; Taylor, Marika [Mathematical Sciences and STAG Research Centre, University of Southampton,Highfield, Southampton, SO17 1BJ (United Kingdom)

2016-08-26

We explore holographic entanglement entropy in ten-dimensional supergravity solutions. It has been proposed that entanglement entropy can be computed in such top-down models using minimal surfaces which asymptotically wrap the compact part of the geometry. We show explicitly in a wide range of examples that the holographic entanglement entropy thus computed agrees with the entanglement entropy computed using the Ryu-Takayanagi formula from the lower-dimensional Einstein metric obtained from reduction over the compact space. Our examples include not only consistent truncations but also cases in which no consistent truncation exists and Kaluza-Klein holography is used to identify the lower-dimensional Einstein metric. We then give a general proof, based on the Lewkowycz-Maldacena approach, of the top-down entanglement entropy formula.

Entanglement entropy in top-down models

International Nuclear Information System (INIS)

Jones, Peter A.R.; Taylor, Marika

2016-01-01

We explore holographic entanglement entropy in ten-dimensional supergravity solutions. It has been proposed that entanglement entropy can be computed in such top-down models using minimal surfaces which asymptotically wrap the compact part of the geometry. We show explicitly in a wide range of examples that the holographic entanglement entropy thus computed agrees with the entanglement entropy computed using the Ryu-Takayanagi formula from the lower-dimensional Einstein metric obtained from reduction over the compact space. Our examples include not only consistent truncations but also cases in which no consistent truncation exists and Kaluza-Klein holography is used to identify the lower-dimensional Einstein metric. We then give a general proof, based on the Lewkowycz-Maldacena approach, of the top-down entanglement entropy formula.

Encasing the Absolutes

Directory of Open Access Journals (Sweden)

Uroš Martinčič

2014-05-01

Full Text Available The paper explores the issue of structure and case in English absolute constructions, whose subjects are deduced by several descriptive grammars as being in the nominative case due to its supposed neutrality in terms of register. This deduction is countered by systematic accounts presented within the framework of the Minimalist Program which relate the case of absolute constructions to specific grammatical factors. Each proposal is shown as an attempt of analysing absolute constructions as basic predication structures, either full clauses or small clauses. I argue in favour of the small clause approach due to its minimal reliance on transformations and unique stipulations. Furthermore, I propose that small clauses project a singular category, and show that the use of two cases in English absolute constructions can be accounted for if they are analysed as depictive phrases, possibly selected by prepositions. The case of the subject in absolutes is shown to be a result of syntactic and non-syntactic factors. I thus argue in accordance with Minimalist goals that syntactic case does not exist, attributing its role in absolutes to other mechanisms.

Credal Networks under Maximum Entropy

OpenAIRE

Lukasiewicz, Thomas

2013-01-01

We apply the principle of maximum entropy to select a unique joint probability distribution from the set of all joint probability distributions specified by a credal network. In detail, we start by showing that the unique joint distribution of a Bayesian tree coincides with the maximum entropy model of its conditional distributions. This result, however, does not hold anymore for general Bayesian networks. We thus present a new kind of maximum entropy models, which are computed sequentially. ...

Holographic entanglement entropy and cyclic cosmology

Science.gov (United States)

Frampton, Paul H.

2018-06-01

We discuss a cyclic cosmology in which the visible universe, or introverse, is all that is accessible to an observer while the extroverse represents the total spacetime originating from the time when the dark energy began to dominate. It is argued that entanglement entropy of the introverse is the more appropriate quantity to render infinitely cyclic, rather than the entropy of the total universe. Since vanishing entanglement entropy implies disconnected spacetimes, at the turnaround when the introverse entropy is zero the disconnected extroverse can be jettisoned with impunity.

Entropy as a measure of diffusion

International Nuclear Information System (INIS)

Aghamohammadi, Amir; Fatollahi, Amir H.; Khorrami, Mohammad; Shariati, Ahmad

2013-01-01

The time variation of entropy, as an alternative to the variance, is proposed as a measure of the diffusion rate. It is shown that for linear and time-translationally invariant systems having a large-time limit for the density, at large times the entropy tends exponentially to a constant. For systems with no stationary density, at large times the entropy is logarithmic with a coefficient specifying the speed of the diffusion. As an example, the large-time behaviors of the entropy and the variance are compared for various types of fractional-derivative diffusions.

Entropy as a measure of diffusion

Energy Technology Data Exchange (ETDEWEB)

Aghamohammadi, Amir, E-mail: mohamadi@alzahra.ac.ir; Fatollahi, Amir H., E-mail: fath@alzahra.ac.ir; Khorrami, Mohammad, E-mail: mamwad@mailaps.org; Shariati, Ahmad, E-mail: shariati@mailaps.org

2013-10-15

The time variation of entropy, as an alternative to the variance, is proposed as a measure of the diffusion rate. It is shown that for linear and time-translationally invariant systems having a large-time limit for the density, at large times the entropy tends exponentially to a constant. For systems with no stationary density, at large times the entropy is logarithmic with a coefficient specifying the speed of the diffusion. As an example, the large-time behaviors of the entropy and the variance are compared for various types of fractional-derivative diffusions.

A Modified Entropy Generation Number for Heat Exchangers

Institute of Scientific and Technical Information of China (English)

无

1996-01-01

This paper demonstrates the difference between the entropy generation number method proposed by Bejian and the method of entropy generation per unit amount of heat transferred in analyzing the ther-modynamic performance of heat exchangers,points out the reason for leading to the above difference.A modified entropy generation number for evaluating the irreversibility of heat exchangers is proposed which is in consistent with the entropy generation per unit amount of heat transferred in entropy generation analysis.The entropy generated by friction is also investigated.Results show that when the entropy generated by friction in heat exchangers in taken into account,there is a minimum total entropy generation number while the NTU and the ratio of heat capacity rates vary.The existence of this minimum is the prerequisite of heat exchanger optimization.

Entropy of charged dilaton-axion black hole

International Nuclear Information System (INIS)

Ghosh, Tanwi; SenGupta, Soumitra

2008-01-01

Using the brick wall method, the entropy of the charged dilaton-axion black hole is determined for both asymptotically flat and nonflat cases. The entropy turns out to be proportional to the horizon area of the black hole confirming the Bekenstein-Hawking area-entropy formula for black holes. The leading order logarithmic corrections to the entropy are also derived for such black holes.

Towards operational interpretations of generalized entropies

Science.gov (United States)

Topsøe, Flemming

2010-12-01

The driving force behind our study has been to overcome the difficulties you encounter when you try to extend the clear and convincing operational interpretations of classical Boltzmann-Gibbs-Shannon entropy to other notions, especially to generalized entropies as proposed by Tsallis. Our approach is philosophical, based on speculations regarding the interplay between truth, belief and knowledge. The main result demonstrates that, accepting philosophically motivated assumptions, the only possible measures of entropy are those suggested by Tsallis - which, as we know, include classical entropy. This result constitutes, so it seems, a more transparent interpretation of entropy than previously available. However, further research to clarify the assumptions is still needed. Our study points to the thesis that one should never consider the notion of entropy in isolation - in order to enable a rich and technically smooth study, further concepts, such as divergence, score functions and descriptors or controls should be included in the discussion. This will clarify the distinction between Nature and Observer and facilitate a game theoretical discussion. The usefulness of this distinction and the subsequent exploitation of game theoretical results - such as those connected with the notion of Nash equilibrium - is demonstrated by a discussion of the Maximum Entropy Principle.

Towards operational interpretations of generalized entropies

International Nuclear Information System (INIS)

Topsoee, Flemming

2010-01-01

The driving force behind our study has been to overcome the difficulties you encounter when you try to extend the clear and convincing operational interpretations of classical Boltzmann-Gibbs-Shannon entropy to other notions, especially to generalized entropies as proposed by Tsallis. Our approach is philosophical, based on speculations regarding the interplay between truth, belief and knowledge. The main result demonstrates that, accepting philosophically motivated assumptions, the only possible measures of entropy are those suggested by Tsallis - which, as we know, include classical entropy. This result constitutes, so it seems, a more transparent interpretation of entropy than previously available. However, further research to clarify the assumptions is still needed. Our study points to the thesis that one should never consider the notion of entropy in isolation - in order to enable a rich and technically smooth study, further concepts, such as divergence, score functions and descriptors or controls should be included in the discussion. This will clarify the distinction between Nature and Observer and facilitate a game theoretical discussion. The usefulness of this distinction and the subsequent exploitation of game theoretical results - such as those connected with the notion of Nash equilibrium - is demonstrated by a discussion of the Maximum Entropy Principle.

Maximum Entropy in Drug Discovery

Directory of Open Access Journals (Sweden)

Chih-Yuan Tseng

2014-07-01

Full Text Available Drug discovery applies multidisciplinary approaches either experimentally, computationally or both ways to identify lead compounds to treat various diseases. While conventional approaches have yielded many US Food and Drug Administration (FDA-approved drugs, researchers continue investigating and designing better approaches to increase the success rate in the discovery process. In this article, we provide an overview of the current strategies and point out where and how the method of maximum entropy has been introduced in this area. The maximum entropy principle has its root in thermodynamics, yet since Jaynes’ pioneering work in the 1950s, the maximum entropy principle has not only been used as a physics law, but also as a reasoning tool that allows us to process information in hand with the least bias. Its applicability in various disciplines has been abundantly demonstrated. We give several examples of applications of maximum entropy in different stages of drug discovery. Finally, we discuss a promising new direction in drug discovery that is likely to hinge on the ways of utilizing maximum entropy.

A comparison of entropy balance and probability weighting methods to generalize observational cohorts to a population: a simulation and empirical example.

Science.gov (United States)

Harvey, Raymond A; Hayden, Jennifer D; Kamble, Pravin S; Bouchard, Jonathan R; Huang, Joanna C

2017-04-01

We compared methods to control bias and confounding in observational studies including inverse probability weighting (IPW) and stabilized IPW (sIPW). These methods often require iteration and post-calibration to achieve covariate balance. In comparison, entropy balance (EB) optimizes covariate balance a priori by calibrating weights using the target's moments as constraints. We measured covariate balance empirically and by simulation by using absolute standardized mean difference (ASMD), absolute bias (AB), and root mean square error (RMSE), investigating two scenarios: the size of the observed (exposed) cohort exceeds the target (unexposed) cohort and vice versa. The empirical application weighted a commercial health plan cohort to a nationally representative National Health and Nutrition Examination Survey target on the same covariates and compared average total health care cost estimates across methods. Entropy balance alone achieved balance (ASMD ≤ 0.10) on all covariates in simulation and empirically. In simulation scenario I, EB achieved the lowest AB and RMSE (13.64, 31.19) compared with IPW (263.05, 263.99) and sIPW (319.91, 320.71). In scenario II, EB outperformed IPW and sIPW with smaller AB and RMSE. In scenarios I and II, EB achieved the lowest mean estimate difference from the simulated population outcome ($490.05, $487.62) compared with IPW and sIPW, respectively. Empirically, only EB differed from the unweighted mean cost indicating IPW, and sIPW weighting was ineffective. Entropy balance demonstrated the bias-variance tradeoff achieving higher estimate accuracy, yet lower estimate precision, compared with IPW methods. EB weighting required no post-processing and effectively mitigated observed bias and confounding. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

High-entropy ejections from magnetized proto-neutron star winds: implications for heavy element nucleosynthesis

Science.gov (United States)

Thompson, Todd A.; ud-Doula, Asif

2018-06-01

Although initially thought to be promising for production of the r-process nuclei, standard models of neutrino-heated winds from proto-neutron stars (PNSs) do not reach the requisite neutron-to-seed ratio for production of the lanthanides and actinides. However, the abundance distribution created by the r-, rp-, or νp-processes in PNS winds depends sensitively on the entropy and dynamical expansion time-scale of the flow, which may be strongly affected by high magnetic fields. Here, we present results from magnetohydrodynamic simulations of non-rotating neutrino-heated PNS winds with strong dipole magnetic fields from 1014 to 1016 G, and assess their role in altering the conditions for nucleosynthesis. The strong field forms a closed zone and helmet streamer configuration at the equator, with episodic dynamical mass ejections in toroidal plasmoids. We find dramatically enhanced entropy in these regions and conditions favourable for third-peak r-process nucleosynthesis if the wind is neutron-rich. If instead the wind is proton-rich, the conditions will affect the abundances from the νp-process. We quantify the distribution of ejected matter in entropy and dynamical expansion time-scale, and the critical magnetic field strength required to affect the entropy. For B ≳1015 G, we find that ≳10-6 M⊙ and up to ˜10-5 M⊙ of high-entropy material is ejected per highly magnetized neutron star birth in the wind phase, providing a mechanism for prompt heavy element enrichment of the universe. Former binary companions identified within (magnetar-hosting) supernova remnants, the remnants themselves, and runaway stars may exhibit overabundances. We provide a comparison with a semi-analytic model of plasmoid eruption and discuss implications and extensions.

Time dependence of entropy flux and entropy production for a dynamical system driven by noises with coloured cross-correlation

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.

Topological nearly entropy

Science.gov (United States)

Gulamsarwar, Syazwani; Salleh, Zabidin

2017-08-01

The purpose of this paper is to generalize the notions of Adler's topological entropy along with their several fundamental properties. A function f : X → Y is said to be R-map if f-1 (V) is regular open in X for every regular open set V in Y. Thus, we initiated a notion of topological nearly entropy for topological R-dynamical systems which is based on nearly compact relative to the space by using R-map.

Quantum Statistical Entropy of Five-Dimensional Black Hole

Institute of Scientific and Technical Information of China (English)

ZHAO Ren; WU Yue-Qin; ZHANG Sheng-Li

2006-01-01

The generalized uncertainty relation is introduced to calculate quantum statistic entropy of a black hole.By using the new equation of state density motivated by the generalized uncertainty relation, we discuss entropies of Bose field and Fermi field on the background of the five-dimensional spacetime. In our calculation, we need not introduce cutoff. There is not the divergent logarithmic term as in the original brick-wall method. And it is obtained that the quantum statistic entropy corresponding to black hole horizon is proportional to the area of the horizon. Further it is shown that the entropy of black hole is the entropy of quantum state on the surface of horizon. The black hole's entropy is the intrinsic property of the black hole. The entropy is a quantum effect. It makes people further understand the quantum statistic entropy.

Quantum Statistical Entropy of Five-Dimensional Black Hole

International Nuclear Information System (INIS)

Zhao Ren; Zhang Shengli; Wu Yueqin

2006-01-01

The generalized uncertainty relation is introduced to calculate quantum statistic entropy of a black hole. By using the new equation of state density motivated by the generalized uncertainty relation, we discuss entropies of Bose field and Fermi field on the background of the five-dimensional spacetime. In our calculation, we need not introduce cutoff. There is not the divergent logarithmic term as in the original brick-wall method. And it is obtained that the quantum statistic entropy corresponding to black hole horizon is proportional to the area of the horizon. Further it is shown that the entropy of black hole is the entropy of quantum state on the surface of horizon. The black hole's entropy is the intrinsic property of the black hole. The entropy is a quantum effect. It makes people further understand the quantum statistic entropy.

Equipartition of entropy production as an approximation to the state of minimum entropy production in diabatic distillation

International Nuclear Information System (INIS)

Johannessen, Eivind; Rosjorde, Audun

2007-01-01

We show that the theorem of equipartition of entropy production is important for the understanding of the state of minimum entropy production in diabatic distillation. The theorem is not valid in a strictly mathematical sense. We explain why, when and in what sense this theorem is a good approximation to the optimal state in diabatic distillation. In order to make these predictions, we use a hypothesis for the state of minimum entropy production of an optimally controlled system, which was formulated on the basis of results of entropy production minimisation in chemical reactors. The hypothesis says that the state of minimum entropy production is characterised by approximately constant local entropy production and thermodynamic forces, given that there is sufficient freedom in the system. We present numerical results which are in agreement with the predictions. The results show that a column with constant tray entropy production in the stripping section and in the rectifying section is a good approximation to the optimal column, except when the total heat transfer area is low. The agreement between the two columns becomes better and better as the total heat transfer area and the number of trays increase. The fact that the predictions and the numerical results agree very well gives support to the validity of the hypothesis

Escort entropies and divergences and related canonical distribution

International Nuclear Information System (INIS)

Bercher, J.-F.

2011-01-01

We discuss two families of two-parameter entropies and divergences, derived from the standard Renyi and Tsallis entropies and divergences. These divergences and entropies are found as divergences or entropies of escort distributions. Exploiting the nonnegativity of the divergences, we derive the expression of the canonical distribution associated to the new entropies and a observable given as an escort-mean value. We show that this canonical distribution extends, and smoothly connects, the results obtained in nonextensive thermodynamics for the standard and generalized mean value constraints. -- Highlights: → Two-parameter entropies are derived from q-entropies and escort distributions. → The related canonical distribution is derived. → This connects and extends known results in nonextensive statistics.

Clausius entropy for arbitrary bifurcate null surfaces

International Nuclear Information System (INIS)

Baccetti, Valentina; Visser, Matt

2014-01-01

Jacobson’s thermodynamic derivation of the Einstein equations was originally applied only to local Rindler horizons. But at least some parts of that construction can usefully be extended to give meaningful results for arbitrary bifurcate null surfaces. As presaged in Jacobson’s original article, this more general construction sharply brings into focus the questions: is entropy objectively ‘real’? Or is entropy in some sense subjective and observer-dependent? These innocent questions open a Pandora’s box of often inconclusive debate. A consensus opinion, though certainly not universally held, seems to be that Clausius entropy (thermodynamic entropy, defined via a Clausius relation dS=đQ/T) should be objectively real, but that the ontological status of statistical entropy (Shannon or von Neumann entropy) is much more ambiguous, and much more likely to be observer-dependent. This question is particularly pressing when it comes to understanding Bekenstein entropy (black hole entropy). To perhaps further add to the confusion, we shall argue that even the Clausius entropy can often be observer-dependent. In the current article we shall conclusively demonstrate that one can meaningfully assign a notion of Clausius entropy to arbitrary bifurcate null surfaces—effectively defining a ‘virtual Clausius entropy’ for arbitrary ‘virtual (local) causal horizons’. As an application, we see that we can implement a version of the generalized second law (GSL) for this virtual Clausius entropy. This version of GSL can be related to certain (nonstandard) integral variants of the null energy condition. Because the concepts involved are rather subtle, we take some effort in being careful and explicit in developing our framework. In future work we will apply this construction to generalize Jacobson’s derivation of the Einstein equations. (paper)

Holographic entropy inequalities and gapped phases of matter

Energy Technology Data Exchange (ETDEWEB)

Bao, Ning [Institute for Quantum Information and Matter, California Institute of Technology,Pasadena, CA 91125 (United States); Walter Burke Institute for Theoretical Physics, California Institute of Technology,Pasadena, CA 91125 (United States); Cao, ChunJun [Walter Burke Institute for Theoretical Physics, California Institute of Technology,Pasadena, CA 91125 (United States); Walter, Michael [Stanford Institute for Theoretical Physics,Stanford University, Stanford, CA 94305 (United States); Wang, Zitao [Institute for Quantum Information and Matter, California Institute of Technology,Pasadena, CA 91125 (United States); Walter Burke Institute for Theoretical Physics, California Institute of Technology,Pasadena, CA 91125 (United States)

2015-09-29

We extend our studies of holographic entropy inequalities to gapped phases of matter. For any number of regions, we determine the linear entropy inequalities satisfied by systems in which the entanglement entropy satisfies an exact area law. In particular, we find that all holographic entropy inequalities are valid in such systems. In gapped systems with topological order, the “cyclic inequalities” derived recently for the holographic entanglement entropy generalize the Kitaev-Preskill formula for the topological entanglement entropy. Finally, we propose a candidate linear inequality for general 4-party quantum states.

Holographic entropy inequalities and gapped phases of matter

International Nuclear Information System (INIS)

Bao, Ning; Cao, ChunJun; Walter, Michael; Wang, Zitao

2015-01-01

We extend our studies of holographic entropy inequalities to gapped phases of matter. For any number of regions, we determine the linear entropy inequalities satisfied by systems in which the entanglement entropy satisfies an exact area law. In particular, we find that all holographic entropy inequalities are valid in such systems. In gapped systems with topological order, the “cyclic inequalities” derived recently for the holographic entanglement entropy generalize the Kitaev-Preskill formula for the topological entanglement entropy. Finally, we propose a candidate linear inequality for general 4-party quantum states.

Examples of Entropy-driven Ordering

Indian Academy of Sciences (India)

driven Ordering. Orientational ordering of long objects. Entropy of sliding increases. Freezing in hard-sphere systems. Vibrational entropy increases. Phase separation in hard-sphere binary mixtures with disparate sizes. More room for smaller ...

Receiver function estimated by maximum entropy deconvolution

Institute of Scientific and Technical Information of China (English)

吴庆举; 田小波; 张乃铃; 李卫平; 曾融生

2003-01-01

Maximum entropy deconvolution is presented to estimate receiver function, with the maximum entropy as the rule to determine auto-correlation and cross-correlation functions. The Toeplitz equation and Levinson algorithm are used to calculate the iterative formula of error-predicting filter, and receiver function is then estimated. During extrapolation, reflective coefficient is always less than 1, which keeps maximum entropy deconvolution stable. The maximum entropy of the data outside window increases the resolution of receiver function. Both synthetic and real seismograms show that maximum entropy deconvolution is an effective method to measure receiver function in time-domain.

Controlling the Shannon Entropy of Quantum Systems

Science.gov (United States)

Xing, Yifan; Wu, Jun

2013-01-01

This paper proposes a new quantum control method which controls the Shannon entropy of quantum systems. For both discrete and continuous entropies, controller design methods are proposed based on probability density function control, which can drive the quantum state to any target state. To drive the entropy to any target at any prespecified time, another discretization method is proposed for the discrete entropy case, and the conditions under which the entropy can be increased or decreased are discussed. Simulations are done on both two- and three-dimensional quantum systems, where division and prediction are used to achieve more accurate tracking. PMID:23818819

Controlling the Shannon Entropy of Quantum Systems

Directory of Open Access Journals (Sweden)

Yifan Xing

2013-01-01

Full Text Available This paper proposes a new quantum control method which controls the Shannon entropy of quantum systems. For both discrete and continuous entropies, controller design methods are proposed based on probability density function control, which can drive the quantum state to any target state. To drive the entropy to any target at any prespecified time, another discretization method is proposed for the discrete entropy case, and the conditions under which the entropy can be increased or decreased are discussed. Simulations are done on both two- and three-dimensional quantum systems, where division and prediction are used to achieve more accurate tracking.

Universal canonical entropy for gravitating systems

Indian Academy of Sciences (India)

Similar to this is the case of ref. [12] which also uses the saddle point approximation to express the microcanonical entropy in terms of the canonical entropy [12a]. Recalling that there is at least 'circumstantial' evidence that the microcanonical entropy has a 'universal' form [13–15], identical to that obtained in ref. [6] quoted.

Absolute advantage

NARCIS (Netherlands)

J.G.M. van Marrewijk (Charles)

2008-01-01

textabstractA country is said to have an absolute advantage over another country in the production of a good or service if it can produce that good or service using fewer real resources. Equivalently, using the same inputs, the country can produce more output. The concept of absolute advantage can

Angular momentum independence of the entropy sum and entropy product for AdS rotating black holes in all dimensions

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.

Dynamic Cross-Entropy.

Science.gov (United States)

Aur, Dorian; Vila-Rodriguez, Fidel

2017-01-01

Complexity measures for time series have been used in many applications to quantify the regularity of one dimensional time series, however many dynamical systems are spatially distributed multidimensional systems. We introduced Dynamic Cross-Entropy (DCE) a novel multidimensional complexity measure that quantifies the degree of regularity of EEG signals in selected frequency bands. Time series generated by discrete logistic equations with varying control parameter r are used to test DCE measures. Sliding window DCE analyses are able to reveal specific period doubling bifurcations that lead to chaos. A similar behavior can be observed in seizures triggered by electroconvulsive therapy (ECT). Sample entropy data show the level of signal complexity in different phases of the ictal ECT. The transition to irregular activity is preceded by the occurrence of cyclic regular behavior. A significant increase of DCE values in successive order from high frequencies in gamma to low frequencies in delta band reveals several phase transitions into less ordered states, possible chaos in the human brain. To our knowledge there are no reliable techniques able to reveal the transition to chaos in case of multidimensional times series. In addition, DCE based on sample entropy appears to be robust to EEG artifacts compared to DCE based on Shannon entropy. The applied technique may offer new approaches to better understand nonlinear brain activity. Copyright © 2016 Elsevier B.V. All rights reserved.

Entropy for the Complexity of Physiological Signal Dynamics.

Science.gov (United States)

Zhang, Xiaohua Douglas

2017-01-01

Recently, the rapid development of large data storage technologies, mobile network technology, and portable medical devices makes it possible to measure, record, store, and track analysis of biological dynamics. Portable noninvasive medical devices are crucial to capture individual characteristics of biological dynamics. The wearable noninvasive medical devices and the analysis/management of related digital medical data will revolutionize the management and treatment of diseases, subsequently resulting in the establishment of a new healthcare system. One of the key features that can be extracted from the data obtained by wearable noninvasive medical device is the complexity of physiological signals, which can be represented by entropy of biological dynamics contained in the physiological signals measured by these continuous monitoring medical devices. Thus, in this chapter I present the major concepts of entropy that are commonly used to measure the complexity of biological dynamics. The concepts include Shannon entropy, Kolmogorov entropy, Renyi entropy, approximate entropy, sample entropy, and multiscale entropy. I also demonstrate an example of using entropy for the complexity of glucose dynamics.

Constant conditional entropy and related hypotheses

International Nuclear Information System (INIS)

Ferrer-i-Cancho, Ramon; Dębowski, Łukasz; Moscoso del Prado Martín, Fermín

2013-01-01

Constant entropy rate (conditional entropies must remain constant as the sequence length increases) and uniform information density (conditional probabilities must remain constant as the sequence length increases) are two information theoretic principles that are argued to underlie a wide range of linguistic phenomena. Here we revise the predictions of these principles in the light of Hilberg’s law on the scaling of conditional entropy in language and related laws. We show that constant entropy rate (CER) and two interpretations for uniform information density (UID), full UID and strong UID, are inconsistent with these laws. Strong UID implies CER but the reverse is not true. Full UID, a particular case of UID, leads to costly uncorrelated sequences that are totally unrealistic. We conclude that CER and its particular cases are incomplete hypotheses about the scaling of conditional entropies. (letter)

On the fundamental equation of nonequilibrium statistical physics—Nonequilibrium entropy evolution equation and the formula for entropy production rate

Institute of Scientific and Technical Information of China (English)

无

2010-01-01

In this paper the author presents an overview on his own research works. More than ten years ago, we proposed a new fundamental equation of nonequilibrium statistical physics in place of the present Liouville equation. That is the stochastic velocity type’s Langevin equation in 6N dimensional phase space or its equivalent Liouville diffusion equation. This equation is time-reversed asymmetrical. It shows that the form of motion of particles in statistical thermodynamic systems has the drift-diffusion duality, and the law of motion of statistical thermodynamics is expressed by a superposition of both the law of dynamics and the stochastic velocity and possesses both determinism and probability. Hence it is different from the law of motion of particles in dynamical systems. The stochastic diffusion motion of the particles is the microscopic origin of macroscopic irreversibility. Starting from this fundamental equation the BBGKY diffusion equation hierarchy, the Boltzmann collision diffusion equation, the hydrodynamic equations such as the mass drift-diffusion equation, the Navier-Stokes equation and the thermal conductivity equation have been derived and presented here. What is more important, we first constructed a nonlinear evolution equation of nonequilibrium entropy density in 6N, 6 and 3 dimensional phase space, predicted the existence of entropy diffusion. This entropy evolution equation plays a leading role in nonequilibrium entropy theory, it reveals that the time rate of change of nonequilibrium entropy density originates together from its drift, diffusion and production in space. From this evolution equation, we presented a formula for entropy production rate (i.e. the law of entropy increase) in 6N and 6 dimensional phase space, proved that internal attractive force in nonequilibrium system can result in entropy decrease while internal repulsive force leads to another entropy increase, and derived a common expression for this entropy decrease rate or

On Equivalence of Nonequilibrium Thermodynamic and Statistical Entropies

Directory of Open Access Journals (Sweden)

Purushottam D. Gujrati

2015-02-01

Full Text Available We review the concept of nonequilibrium thermodynamic entropy and observables and internal variables as state variables, introduced recently by us, and provide a simple first principle derivation of additive statistical entropy, applicable to all nonequilibrium states by treating thermodynamics as an experimental science. We establish their numerical equivalence in several cases, which includes the most important case when the thermodynamic entropy is a state function. We discuss various interesting aspects of the two entropies and show that the number of microstates in the Boltzmann entropy includes all possible microstates of non-zero probabilities even if the system is trapped in a disjoint component of the microstate space. We show that negative thermodynamic entropy can appear from nonnegative statistical entropy.

Black hole entropy in the O(N) model

International Nuclear Information System (INIS)

Kabat, D.; Shenker, S.H.; Strassler, M.J.

1995-01-01

We consider corrections to the entropy of a black hole from an O(N)-invariant linear σ model. We obtain the entropy from a 1/N expansion of the partition function on a cone. The entropy arises from diagrams which are analogous to those introduced by Susskind and Uglum to explain black hole entropy in string theory. The interpretation of the σ-model entropy depends on scale. At short distances, it has a state counting interpretation, as the entropy of entanglement of the N fields φ a . In the infrared, the effective theory has a single composite field σ∼φ a φ a , and the state counting interpretation of the entropy is lost. copyright 1995 The American Physical Society

Entropy concentration and the empirical coding game

NARCIS (Netherlands)

Grünwald, P.D.

2008-01-01

We give a characterization of maximum entropy/minimum relative entropy inference by providing two 'strong entropy concentration' theorems. These theorems unify and generalize Jaynes''concentration phenomenon' and Van Campenhout and Cover's 'conditional limit theorem'. The theorems characterize

Logical entropy of quantum dynamical systems

Directory of Open Access Journals (Sweden)

Ebrahimzadeh Abolfazl

2016-01-01

Full Text Available This paper introduces the concepts of logical entropy and conditional logical entropy of hnite partitions on a quantum logic. Some of their ergodic properties are presented. Also logical entropy of a quantum dynamical system is dehned and ergodic properties of dynamical systems on a quantum logic are investigated. Finally, the version of Kolmogorov-Sinai theorem is proved.

Black hole entropy functions and attractor equations

International Nuclear Information System (INIS)

Lopes Cardoso, Gabriel; Wit, Bernard de; Mahapatra, Swapna

2007-01-01

The entropy and the attractor equations for static extremal black hole solutions follow from a variational principle based on an entropy function. In the general case such an entropy function can be derived from the reduced action evaluated in a near-horizon geometry. BPS black holes constitute special solutions of this variational principle, but they can also be derived directly from a different entropy function based on supersymmetry enhancement at the horizon. Both functions are consistent with electric/magnetic duality and for BPS black holes their corresponding OSV-type integrals give identical results at the semi-classical level. We clarify the relation between the two entropy functions and the corresponding attractor equations for N = 2 supergravity theories with higher-derivative couplings in four space-time dimensions. We discuss how non-holomorphic corrections will modify these entropy functions

Left-right entanglement entropy of Dp-branes

Energy Technology Data Exchange (ETDEWEB)

Zayas, Leopoldo A. Pando [The Abdus Salam International Centre for Theoretical Physics,Strada Costiera 11, 34014 Trieste (Italy); Michigan Center for Theoretical Physics, Randall Laboratory of Physics,The University of Michigan,450 Church Street, Ann Arbor, MI 48109-1120 (United States); Quiroz, Norma [Departamento de Ciencias Exactas, Tecnología y Metodología,Centro Universitario del Sur, Universidad de Guadalajara,Enrique Arreola Silva 883, C.P. 49000, Cd. Guzmán, Jalisco (Mexico)

2016-11-04

We compute the left-right entanglement entropy for Dp-branes in string theory. We employ the CFT approach to string theory Dp-branes, in particular, its presentation as coherent states of the closed string sector. The entanglement entropy is computed as the von Neumann entropy for a density matrix resulting from integration over the left-moving degrees of freedom. We discuss various crucial ambiguities related to sums over spin structures and argue that different choices capture different physics; however, we advance a themodynamic argument that seems to favor a particular choice of replica. We also consider Dp branes on compact dimensions and verify that the effects of T-duality act covariantly on the Dp brane entanglement entropy. We find that generically the left-right entanglement entropy provides a suitable generalization of boundary entropy and of the D-brane tension.

Shannon versus Kullback-Leibler entropies in nonequilibrium random motion

International Nuclear Information System (INIS)

Garbaczewski, Piotr

2005-01-01

We analyze dynamical properties of the Shannon information entropy of a continuous probability distribution, which is driven by a standard diffusion process. This entropy choice is confronted with another option, employing the conditional Kullback-Leibler entropy. Both entropies discriminate among various probability distributions, either statically or in the time domain. An asymptotic approach towards equilibrium is typically monotonic in terms of the Kullback entropy. The Shannon entropy time rate needs not to be positive and is a sensitive indicator of the power transfer processes (removal/supply) due to an active environment. In the case of Smoluchowski diffusions, the Kullback entropy time rate coincides with the Shannon entropy 'production' rate

On the way towards a generalized entropy maximization procedure

International Nuclear Information System (INIS)

Bagci, G. Baris; Tirnakli, Ugur

2009-01-01

We propose a generalized entropy maximization procedure, which takes into account the generalized averaging procedures and information gain definitions underlying the generalized entropies. This novel generalized procedure is then applied to Renyi and Tsallis entropies. The generalized entropy maximization procedure for Renyi entropies results in the exponential stationary distribution asymptotically for q element of (0,1] in contrast to the stationary distribution of the inverse power law obtained through the ordinary entropy maximization procedure. Another result of the generalized entropy maximization procedure is that one can naturally obtain all the possible stationary distributions associated with the Tsallis entropies by employing either ordinary or q-generalized Fourier transforms in the averaging procedure.

Entropy and black-hole thermodynamics

International Nuclear Information System (INIS)

Wald, R.M.

1979-01-01

The concept of entropy is examined with an eye toward gaining insight into the nature of black-hole thermodynamics. Definitions of entropy are given for ordinary classical and quantum-mechanical systems which lead to plausibility arguments for the ordinary laws of thermodynamics. The treatment of entropy for a classical system is in the spirit of the information-theory viewpoint, but by explicitly incorporating the coarse-grained observable into the definition of entropy, we eliminate any nonobjective features. The definition of entropy for a quantum-mechanical system is new, but directly parallels the classical treatment. We then apply these ideas to a self-gravitating quantum system which contains a black hole. Under some assumptions: which, although nontrivial, are by no means exotic: about the nature of such a system, it is seen that the same plausibility arguments which lead to the ordinary laws of thermodynamics for ordinary systems now lead to the laws of black-hole mechanics, including the generalized second law of thermodynamics. Thus, it appears perfectly plausible that black-hole thermodynamics is nothing more than ordinary thermodynamics applied to a self-gravitating quantum system

ENTROPY FLOW CHARACTERISTICS ANALYSIS OF TYPHOON MATSA (0509)

Institute of Scientific and Technical Information of China (English)

XU Hui; LIU Chong-jian

2008-01-01

The evolution of Typhoon Matsa (0509) is examined in terms of entropy flow through an entropy balance equation derived from the Gibbs relation, according to the second law of thermodynamics. The entropy flows in the various significant stages of (genesis, development and decaying) during its evolution are diagnosed based on the outputs of the PSU/NCAR mesoscale model (known as MM5). The results show that: (1) the vertical spatial distribution of entropy flow for Matsa is characterized by a predominantly negative entropy flow in a large portion of the troposphere and a positive flow in the upper levels; (2) the fields of entropy flows at the middle troposphere (500 hPa) show that the growth of the typhoon is greatly dependent on the negative entropy flows from its surroundings; and (3) the simulated centres of heavy rainfall associated with the typhoon match well with the zones of large negative entropy flows, suggesting that they may be a significant indicator for severe weather events.

Zero modes and entanglement entropy

Energy Technology Data Exchange (ETDEWEB)

Yazdi, Yasaman K. [Perimeter Institute for Theoretical Physics,31 Caroline St. N., Waterloo, ON, N2L 2Y5 (Canada); Department of Physics and Astronomy, University of Waterloo,200 University Avenue West, Waterloo, ON, N2L 3G1 (Canada)

2017-04-26

Ultraviolet divergences are widely discussed in studies of entanglement entropy. Also present, but much less understood, are infrared divergences due to zero modes in the field theory. In this note, we discuss the importance of carefully handling zero modes in entanglement entropy. We give an explicit example for a chain of harmonic oscillators in 1D, where a mass regulator is necessary to avoid an infrared divergence due to a zero mode. We also comment on a surprising contribution of the zero mode to the UV-scaling of the entanglement entropy.

Entropy Learning in Neural Network

Directory of Open Access Journals (Sweden)

Geok See Ng

2017-12-01

Full Text Available In this paper, entropy term is used in the learning phase of a neural network.  As learning progresses, more hidden nodes get into saturation.  The early creation of such hidden nodes may impair generalisation.  Hence entropy approach is proposed to dampen the early creation of such nodes.  The entropy learning also helps to increase the importance of relevant nodes while dampening the less important nodes.  At the end of learning, the less important nodes can then be eliminated to reduce the memory requirements of the neural network.

Shannon's information is not entropy

International Nuclear Information System (INIS)

Schiffer, M.

1990-01-01

In this letter we clear up the long-standing misidentification of Shannon's Information with Entropy. We show that Information, in contrast to Entropy, is not invariant under unitary transformations and that these quantities are only equivalent for representations consisting of Hamiltonian eigenstates. We illustrate this fact through a toy system consisting of a harmonic oscillator in a coherent state. It is further proved that the representations which maximize the information are those which are energy-eigenstates. This fact sets the entropy as an upper bound for Shannon's Information. (author)

Entanglement entropy and nonabelian gauge symmetry

International Nuclear Information System (INIS)

Donnelly, William

2014-01-01

Entanglement entropy has proven to be an extremely useful concept in quantum field theory. Gauge theories are of particular interest, but for these systems the entanglement entropy is not clearly defined because the physical Hilbert space does not factor as a tensor product according to regions of space. Here we review a definition of entanglement entropy that applies to abelian and nonabelian lattice gauge theories. This entanglement entropy is obtained by embedding the physical Hilbert space into a product of Hilbert spaces associated to regions with boundary. The latter Hilbert spaces include degrees of freedom on the entangling surface that transform like surface charges under the gauge symmetry. These degrees of freedom are shown to contribute to the entanglement entropy, and the form of this contribution is determined by the gauge symmetry. We test our definition using the example of two-dimensional Yang–Mills theory, and find that it agrees with the thermal entropy in de Sitter space, and with the results of the Euclidean replica trick. We discuss the possible implications of this result for more complicated gauge theories, including quantum gravity. (paper)

Topological entropy for induced hyperspace maps

International Nuclear Information System (INIS)

Canovas Pena, Jose S.; Lopez, Gabriel Soler

2006-01-01

Let (X,d) be a compact metric space and let f:X->X be continuous. Let K(X) be the family of compact subsets of X endowed with the Hausdorff metric and define the extension f-bar :K(X)->K(X) by f-bar (K)=f(K) for any K-bar K(X). We prove that the topological entropy of f-bar is greater or equal than the topological entropy of f, and this inequality can be strict. On the other hand, we prove that the topological entropy of f is positive if and only if the topological entropy of f-bar is also positive

Topological entropy for induced hyperspace maps

Energy Technology Data Exchange (ETDEWEB)

Canovas Pena, Jose S. [Departamento de Matematica Aplicada y Estadistica, Universidad Politecnica de Cartagena, 30203 Cartagena, Murcia (Spain)]. E-mail: Jose.canovas@upct.es; Lopez, Gabriel Soler [Departamento de Matematica Aplicada y Estadistica, Universidad Politecnica de Cartagena, 30203 Cartagena, Murcia (Spain)]. E-mail: Gabriel.soler@upct.es

2006-05-15

Let (X,d) be a compact metric space and let f:X->X be continuous. Let K(X) be the family of compact subsets of X endowed with the Hausdorff metric and define the extension f-bar :K(X)->K(X) by f-bar (K)=f(K) for any K-bar K(X). We prove that the topological entropy of f-bar is greater or equal than the topological entropy of f, and this inequality can be strict. On the other hand, we prove that the topological entropy of f is positive if and only if the topological entropy of f-bar is also positive.

Entropy statistics and information theory

NARCIS (Netherlands)

Frenken, K.; Hanusch, H.; Pyka, A.

2007-01-01

Entropy measures provide important tools to indicate variety in distributions at particular moments in time (e.g., market shares) and to analyse evolutionary processes over time (e.g., technical change). Importantly, entropy statistics are suitable to decomposition analysis, which renders the

Microscopic entropy and nonlocality

International Nuclear Information System (INIS)

Karpov, E.; Ordonets, G.; Petroskij, T.; Prigozhin, I.

2003-01-01

We have obtained a microscopic expression for entropy in terms of H function based on nonunitary Λ transformation which leads from the time evolution as a unitary group to a Markovian dynamics and unifies the reversible and irreversible aspects of quantum mechanics. This requires a new representation outside the Hilbert space. In terms of H, we show the entropy production and the entropy flow during the emission and absorption of radiation by an atom. Analyzing the time inversion experiment, we emphasize the importance of pre- and postcollisional correlations, which break the symmetry between incoming and outgoing waves. We consider the angle dependence of the H function in a three-dimensional situation. A model including virtual transitions is discussed in a subsequent paper

Maximum entropy methods

International Nuclear Information System (INIS)

Ponman, T.J.

1984-01-01

For some years now two different expressions have been in use for maximum entropy image restoration and there has been some controversy over which one is appropriate for a given problem. Here two further entropies are presented and it is argued that there is no single correct algorithm. The properties of the four different methods are compared using simple 1D simulations with a view to showing how they can be used together to gain as much information as possible about the original object. (orig.)

Entropy Generation in Thermal Radiative Loading of Structures with Distinct Heaters

Directory of Open Access Journals (Sweden)

Mohammad Yaghoub Abdollahzadeh Jamalabadi

2017-09-01

Full Text Available Thermal loading by radiant heaters is used in building heating and hot structure design applications. In this research, characteristics of the thermal radiative heating of an enclosure by a distinct heater are investigated from the second law of thermodynamics point of view. The governing equations of conservation of mass, momentum, and energy (fluid and solid are solved by the finite volume method and the semi-implicit method for pressure linked equations (SIMPLE algorithm. Radiant heaters are modeled by constant heat flux elements, and the lower wall is held at a constant temperature while the other boundaries are adiabatic. The thermal conductivity and viscosity of the fluid are temperature-dependent, which leads to complex partial differential equations with nonlinear coefficients. The parameter study is done based on the amount of thermal load (presented by heating number as well as geometrical configuration parameters, such as the aspect ratio of the enclosure and the radiant heater number. The results present the effect of thermal and geometrical parameters on entropy generation and the distribution field. Furthermore, the effect of thermal radiative heating on both of the components of entropy generation (viscous dissipation and heat dissipation is investigated.

Entropies of the automata networks with additive rule

Institute of Scientific and Technical Information of China (English)

Guo－qingGU; GeCHEN; 等

1996-01-01

The matrix presentation for automata networks with additive rule are described.A set of entropy theorems of additive automata network are proved and an analytic formula of its entropy is built.For example,we proved that the topological entropy is identically equal to metric entropy for an additive antomata network.

Specificity of foot configuration during bipedal stance in ballet dancers.

Science.gov (United States)

Casabona, Antonino; Leonardi, Giuseppa; Aimola, Ettore; La Grua, Giovanni; Polizzi, Cristina Maria; Cioni, Matteo; Valle, Maria Stella

2016-05-01

Learning highly specialized upright postures may be of benefit for more common as well as for novel stances. In this study, we asked whether this generalization occurs with foot configurations previously trained or depends on a generic increase in balance difficulty. We also explored the possibility that the benefit may concern not only the level of postural performance but also the structural organization of the upright standing. Ten elite professional ballet dancers were compared to ten untrained subjects, measuring the motion of the center of pressure (COP) across a set of five stances with different foot configurations. The balance stability was measured computing the area, the sway path, and the root mean square of the COP motion, whereas the structure of the postural control was assessed by compute approximate entropy, fractal dimension and the mean power frequency. The foot position included common and challenging stances, with the level of difficulty changed across the configurations. Among these conditions, only one foot configuration was familiar to the dancers. Statistically significant differences between the two groups, for all the parameters, were observed only for the stance with the foot position familiar to the dancers. Stability and structural parameters exhibited comparable differences. We concluded that the benefit from classical ballet is limited to a specific foot configuration, regardless of the level of stance difficulty or the component of postural control. Copyright © 2016 Elsevier B.V. All rights reserved.

Entropy Generation Analysis of Desalination Technologies

Directory of Open Access Journals (Sweden)

John H. Lienhard V

2011-09-01

Full Text Available Increasing global demand for fresh water is driving the development and implementation of a wide variety of seawater desalination technologies. Entropy generation analysis, and specifically, Second Law efficiency, is an important tool for illustrating the influence of irreversibilities within a system on the required energy input. When defining Second Law efficiency, the useful exergy output of the system must be properly defined. For desalination systems, this is the minimum least work of separation required to extract a unit of water from a feed stream of a given salinity. In order to evaluate the Second Law efficiency, entropy generation mechanisms present in a wide range of desalination processes are analyzed. In particular, entropy generated in the run down to equilibrium of discharge streams must be considered. Physical models are applied to estimate the magnitude of entropy generation by component and individual processes. These formulations are applied to calculate the total entropy generation in several desalination systems including multiple effect distillation, multistage flash, membrane distillation, mechanical vapor compression, reverse osmosis, and humidification-dehumidification. Within each technology, the relative importance of each source of entropy generation is discussed in order to determine which should be the target of entropy generation minimization. As given here, the correct application of Second Law efficiency shows which systems operate closest to the reversible limit and helps to indicate which systems have the greatest potential for improvement.

Logarithmic terms in entanglement entropies of 2D quantum critical points and Shannon entropies of spin chains.

Science.gov (United States)

Zaletel, Michael P; Bardarson, Jens H; Moore, Joel E

2011-07-08

Universal logarithmic terms in the entanglement entropy appear at quantum critical points (QCPs) in one dimension (1D) and have been predicted in 2D at QCPs described by 2D conformal field theories. The entanglement entropy in a strip geometry at such QCPs can be obtained via the "Shannon entropy" of a 1D spin chain with open boundary conditions. The Shannon entropy of the XXZ chain is found to have a logarithmic term that implies, for the QCP of the square-lattice quantum dimer model, a logarithm with universal coefficient ±0.25. However, the logarithm in the Shannon entropy of the transverse-field Ising model, which corresponds to entanglement in the 2D Ising conformal QCP, is found to have a singular dependence on the replica or Rényi index resulting from flows to different boundary conditions at the entanglement cut.

The Wigner-Yanase entropy is not subadditive

DEFF Research Database (Denmark)

Hansen, Frank

2007-01-01

Wigner and Yanase introduced in 1963 the Wigner-Yanase entropy defined as minus the skew information of a state with respect to a conserved observable. They proved that the Wigner-Yanase entropy is a concave function in the state and conjectured that it is subadditive with respect...... to the aggregation of possibly interacting subsystems. While this turned out to be true for the quantum-mechanical entropy, we negate the conjecture for the Wigner-Yanase entropy by providing a counter example....

Curvature Entropy for Curved Profile Generation

OpenAIRE

Ujiie, Yoshiki; Kato, Takeo; Sato, Koichiro; Matsuoka, Yoshiyuki

2012-01-01

In a curved surface design, the overall shape features that emerge from combinations of shape elements are important. However, controlling the features of the overall shape in curved profiles is difficult using conventional microscopic shape information such as dimension. Herein two types of macroscopic shape information, curvature entropy and quadrature curvature entropy, quantitatively represent the features of the overall shape. The curvature entropy is calculated by the curvature distribu...

Entanglement entropy in causal set theory

Science.gov (United States)

Sorkin, Rafael D.; Yazdi, Yasaman K.

2018-04-01

Entanglement entropy is now widely accepted as having deep connections with quantum gravity. It is therefore desirable to understand it in the context of causal sets, especially since they provide in a natural manner the UV cutoff needed to render entanglement entropy finite. Formulating a notion of entanglement entropy in a causal set is not straightforward because the type of canonical hypersurface-data on which its definition typically relies is not available. Instead, we appeal to the more global expression given in Sorkin (2012 (arXiv:1205.2953)) which, for a Gaussian scalar field, expresses the entropy of a spacetime region in terms of the field’s correlation function within that region (its ‘Wightman function’ W(x, x') ). Carrying this formula over to the causal set, one obtains an entropy which is both finite and of a Lorentz invariant nature. We evaluate this global entropy-expression numerically for certain regions (primarily order-intervals or ‘causal diamonds’) within causal sets of 1  +  1 dimensions. For the causal-set counterpart of the entanglement entropy, we obtain, in the first instance, a result that follows a (spacetime) volume law instead of the expected (spatial) area law. We find, however, that one obtains an area law if one truncates the commutator function (‘Pauli–Jordan operator’) and the Wightman function by projecting out the eigenmodes of the Pauli–Jordan operator whose eigenvalues are too close to zero according to a geometrical criterion which we describe more fully below. In connection with these results and the questions they raise, we also study the ‘entropy of coarse-graining’ generated by thinning out the causal set, and we compare it with what one obtains by similarly thinning out a chain of harmonic oscillators, finding the same, ‘universal’ behaviour in both cases.

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.

Analysis of the anomalous mean-field like properties of Gaussian core model in terms of entropy

Science.gov (United States)

Nandi, Manoj Kumar; Maitra Bhattacharyya, Sarika

2018-01-01

Studies of the Gaussian core model (GCM) have shown that it behaves like a mean-field model and the properties are quite different from standard glass former. In this work, we investigate the entropies, namely, the excess entropy (Sex) and the configurational entropy (Sc) and their different components to address these anomalies. Our study corroborates most of the earlier observations and also sheds new light on the high and low temperature dynamics. We find that unlike in standard glass former where high temperature dynamics is dominated by two-body correlation and low temperature by many-body correlations, in the GCM both high and low temperature dynamics are dominated by many-body correlations. We also find that the many-body entropy which is usually positive at low temperatures and is associated with activated dynamics is negative in the GCM suggesting suppression of activation. Interestingly despite the suppression of activation, the Adam-Gibbs (AG) relation that describes activated dynamics holds in the GCM, thus suggesting a non-activated contribution in AG relation. We also find an overlap between the AG relation and mode coupling power law regime leading to a power law behavior of Sc. From our analysis of this power law behavior, we predict that in the GCM the high temperature dynamics will disappear at dynamical transition temperature and below that there will be a transition to the activated regime. Our study further reveals that the activated regime in the GCM is quite narrow.

Definition of Nonequilibrium Entropy of General Systems

OpenAIRE

Mei, Xiaochun

1999-01-01

The definition of nonequilibrium entropy is provided for the general nonequilibrium processes by connecting thermodynamics with statistical physics, and the principle of entropy increment in the nonequilibrium processes is also proved in the paper. The result shows that the definition of nonequilibrium entropy is not unique.

Algebraic topological entropy

International Nuclear Information System (INIS)

Hudetz, T.

1989-01-01

As a 'by-product' of the Connes-Narnhofer-Thirring theory of dynamical entropy for (originally non-Abelian) nuclear C * -algebras, the well-known variational principle for topological entropy is eqivalently reformulated in purly algebraically defined terms for (separable) Abelian C * -algebras. This 'algebraic variational principle' should not only nicely illustrate the 'feed-back' of methods developed for quantum dynamical systems to the classical theory, but it could also be proved directly by 'algebraic' methods and could thus further simplify the original proof of the variational principle (at least 'in principle'). 23 refs. (Author)

Combinatorial Image Entropy

DEFF Research Database (Denmark)

Yuri, Shtarkov; Justesen, Jørn

1997-01-01

The concept of entropy for an image on a discrete two dimensional grid is introduced. This concept is used as an information theoretic bound on the coding rate for the image. It is proved that this quantity exists as a limit for arbitrary sets satisfying certain conditions.......The concept of entropy for an image on a discrete two dimensional grid is introduced. This concept is used as an information theoretic bound on the coding rate for the image. It is proved that this quantity exists as a limit for arbitrary sets satisfying certain conditions....

Multiscale sample entropy and cross-sample entropy based on symbolic representation and similarity of stock markets

Science.gov (United States)

Wu, Yue; Shang, Pengjian; Li, Yilong

2018-03-01

A modified multiscale sample entropy measure based on symbolic representation and similarity (MSEBSS) is proposed in this paper to research the complexity of stock markets. The modified algorithm reduces the probability of inducing undefined entropies and is confirmed to be robust to strong noise. Considering the validity and accuracy, MSEBSS is more reliable than Multiscale entropy (MSE) for time series mingled with much noise like financial time series. We apply MSEBSS to financial markets and results show American stock markets have the lowest complexity compared with European and Asian markets. There are exceptions to the regularity that stock markets show a decreasing complexity over the time scale, indicating a periodicity at certain scales. Based on MSEBSS, we introduce the modified multiscale cross-sample entropy measure based on symbolic representation and similarity (MCSEBSS) to consider the degree of the asynchrony between distinct time series. Stock markets from the same area have higher synchrony than those from different areas. And for stock markets having relative high synchrony, the entropy values will decrease with the increasing scale factor. While for stock markets having high asynchrony, the entropy values will not decrease with the increasing scale factor sometimes they tend to increase. So both MSEBSS and MCSEBSS are able to distinguish stock markets of different areas, and they are more helpful if used together for studying other features of financial time series.

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.

Thermoeconomic diagnosis and entropy generation paradox

DEFF Research Database (Denmark)

Sigthorsson, Oskar; Ommen, Torben Schmidt; Elmegaard, Brian

2017-01-01

In the entropy generation paradox, the entropy generation number, as a function of heat exchanger effectiveness, counter-intuitively approaches zero in two limits symmetrically from a single maximum. In thermoeconomic diagnosis, namely in the characteristic curve method, the exergy destruction...... to the entropy generation paradox, as a decreased heat exchanger effectiveness (as in the case of an operation anomaly in the component) can counter-intuitively result in decreased exergy destruction rate of the component. Therefore, along with an improper selection of independent variables, the heat exchanger...... increases in case of an operation anomaly in a component. The normalised exergy destruction rate as the dependent variable therefore resolves the relation of the characteristic curve method with the entropy generation paradox....

Black brane entropy and hydrodynamics

NARCIS (Netherlands)

Booth, I.; Heller, M.P.; Spaliński, M.

2010-01-01

A generalization of entropy to near-equilibrium phenomena is provided by the notion of a hydrodynamic entropy current. Recent advances in holography have lead to the formulation of fluid-gravity duality, a remarkable connection between the hydrodynamics of certain strongly coupled media and dynamics

Black brane entropy and hydrodynamics

NARCIS (Netherlands)

Booth, I.; Heller, M.P.; Spaliński, M.

2011-01-01

A generalization of entropy to near-equilibrium phenomena is provided by the notion of a hydrodynamic entropy current. Recent advances in holography have lead to the formulation of fluid-gravity duality, a remarkable connection between the hydrodynamics of certain strongly coupled media and dynamics

Exploration and Development of High Entropy Alloys for Structural Applications

Directory of Open Access Journals (Sweden)

Daniel B. Miracle

2014-01-01

Full Text Available We develop a strategy to design and evaluate high-entropy alloys (HEAs for structural use in the transportation and energy industries. We give HEA goal properties for low (≤150 °C, medium (≤450 °C and high (≥1,100 °C use temperatures. A systematic design approach uses palettes of elements chosen to meet target properties of each HEA family and gives methods to build HEAs from these palettes. We show that intermetallic phases are consistent with HEA definitions, and the strategy developed here includes both single-phase, solid solution HEAs and HEAs with intentional addition of a 2nd phase for particulate hardening. A thermodynamic estimate of the effectiveness of configurational entropy to suppress or delay compound formation is given. A 3-stage approach is given to systematically screen and evaluate a vast number of HEAs by integrating high-throughput computations and experiments. CALPHAD methods are used to predict phase equilibria, and high-throughput experiments on materials libraries with controlled composition and microstructure gradients are suggested. Much of this evaluation can be done now, but key components (materials libraries with microstructure gradients and high-throughput tensile testing are currently missing. Suggestions for future HEA efforts are given.

Absolutely relative or relatively absolute: violations of value invariance in human decision making.

Science.gov (United States)

Teodorescu, Andrei R; Moran, Rani; Usher, Marius

2016-02-01

Making decisions based on relative rather than absolute information processing is tied to choice optimality via the accumulation of evidence differences and to canonical neural processing via accumulation of evidence ratios. These theoretical frameworks predict invariance of decision latencies to absolute intensities that maintain differences and ratios, respectively. While information about the absolute values of the choice alternatives is not necessary for choosing the best alternative, it may nevertheless hold valuable information about the context of the decision. To test the sensitivity of human decision making to absolute values, we manipulated the intensities of brightness stimuli pairs while preserving either their differences or their ratios. Although asked to choose the brighter alternative relative to the other, participants responded faster to higher absolute values. Thus, our results provide empirical evidence for human sensitivity to task irrelevant absolute values indicating a hard-wired mechanism that precedes executive control. Computational investigations of several modelling architectures reveal two alternative accounts for this phenomenon, which combine absolute and relative processing. One account involves accumulation of differences with activation dependent processing noise and the other emerges from accumulation of absolute values subject to the temporal dynamics of lateral inhibition. The potential adaptive role of such choice mechanisms is discussed.

On variational definition of quantum entropy

International Nuclear Information System (INIS)

Belavkin, Roman V.

2015-01-01

Entropy of distribution P can be defined in at least three different ways: 1) as the expectation of the Kullback-Leibler (KL) divergence of P from elementary δ-measures (in this case, it is interpreted as expected surprise); 2) as a negative KL-divergence of some reference measure ν from the probability measure P; 3) as the supremum of Shannon’s mutual information taken over all channels such that P is the output probability, in which case it is dual of some transportation problem. In classical (i.e. commutative) probability, all three definitions lead to the same quantity, providing only different interpretations of entropy. In non-commutative (i.e. quantum) probability, however, these definitions are not equivalent. In particular, the third definition, where the supremum is taken over all entanglements of two quantum systems with P being the output state, leads to the quantity that can be twice the von Neumann entropy. It was proposed originally by V. Belavkin and Ohya [1] and called the proper quantum entropy, because it allows one to define quantum conditional entropy that is always non-negative. Here we extend these ideas to define also quantum counterpart of proper cross-entropy and cross-information. We also show inequality for the values of classical and quantum information

Progress in Preparation and Research of High Entropy Alloys

Directory of Open Access Journals (Sweden)

CHEN Yong-xing

2017-11-01

Full Text Available The current high entropy alloys' studies are most in block, powder, coating, film and other areas. There are few studies of high entropy alloys in other areas and they are lack of unified classification. According to the current high entropy alloys' research situation, The paper has focused on the classification on all kinds of high entropy alloys having been researched, introduced the selecting principle of elements, summarized the preparation methods, reviewed the research institutions, research methods and research contents of high entropy alloys, prospected the application prospect of high entropy alloys, put forward a series of scientific problems of high entropy alloys, including less research on mechanism, incomplete performance research, unsystematic thermal stability study, preparation process parameters to be optimized, lightweight high entropy alloys' design, the expansion on the research field, etc, and the solutions have been given. Those have certain guiding significance for the expansion of the application of high entropy alloys subjects in the future research direction.

Entropy and information causality in general probabilistic theories

International Nuclear Information System (INIS)

Barnum, Howard; Leifer, Matthew; Spekkens, Robert; Barrett, Jonathan; Clark, Lisa Orloff; Stepanik, Nicholas; Wilce, Alex; Wilke, Robin

2010-01-01

We investigate the concept of entropy in probabilistic theories more general than quantum mechanics, with particular reference to the notion of information causality (IC) recently proposed by Pawlowski et al (2009 arXiv:0905.2292). We consider two entropic quantities, which we term measurement and mixing entropy. In the context of classical and quantum theory, these coincide, being given by the Shannon and von Neumann entropies, respectively; in general, however, they are very different. In particular, while measurement entropy is easily seen to be concave, mixing entropy need not be. In fact, as we show, mixing entropy is not concave whenever the state space is a non-simplicial polytope. Thus, the condition that measurement and mixing entropies coincide is a strong constraint on possible theories. We call theories with this property monoentropic. Measurement entropy is subadditive, but not in general strongly subadditive. Equivalently, if we define the mutual information between two systems A and B by the usual formula I(A: B)=H(A)+H(B)-H(AB), where H denotes the measurement entropy and AB is a non-signaling composite of A and B, then it can happen that I(A:BC)< I(A:B). This is relevant to IC in the sense of Pawlowski et al: we show that any monoentropic non-signaling theory in which measurement entropy is strongly subadditive, and also satisfies a version of the Holevo bound, is informationally causal, and on the other hand we observe that Popescu-Rohrlich boxes, which violate IC, also violate strong subadditivity. We also explore the interplay between measurement and mixing entropy and various natural conditions on theories that arise in quantum axiomatics.

Permutation Entropy: New Ideas and Challenges

Directory of Open Access Journals (Sweden)

Karsten Keller

2017-03-01

Full Text Available Over recent years, some new variants of Permutation entropy have been introduced and applied to EEG analysis, including a conditional variant and variants using some additional metric information or being based on entropies that are different from the Shannon entropy. In some situations, it is not completely clear what kind of information the new measures and their algorithmic implementations provide. We discuss the new developments and illustrate them for EEG data.

High Entropy Random Selection Protocols

NARCIS (Netherlands)

H. Buhrman (Harry); M. Christandl (Matthias); M. Koucky (Michal); Z. Lotker (Zvi); B. Patt-Shamir; M. Charikar; K. Jansen; O. Reingold; J. Rolim

2007-01-01

textabstractIn this paper, we construct protocols for two parties that do not trust each other, to generate random variables with high Shannon entropy. We improve known bounds for the trade off between the number of rounds, length of communication and the entropy of the outcome.

Renyi entropy and conformal defects

Energy Technology Data Exchange (ETDEWEB)

Bianchi, Lorenzo [Humboldt-Univ. Berlin (Germany). Inst. fuer Physik; Hamburg Univ. (Germany). II. Inst. fuer Theoretische Physik; Meineri, Marco [Scuola Normale Superiore, Pisa (Italy); Perimeter Institute for Theoretical Physics, Waterloo, ON (Canada); Istituto Nazionale di Fisica Nucleare, Pisa (Italy); Myers, Robert C. [Perimeter Institute for Theoretical Physics, Waterloo, ON (Canada); Smolkin, Michael [California Univ., Berkely, CA (United States). Center for Theoretical Physics and Department of Physics

2016-04-18

We propose a field theoretic framework for calculating the dependence of Renyi entropies on the shape of the entangling surface in a conformal field theory. Our approach rests on regarding the corresponding twist operator as a conformal defect and in particular, we define the displacement operator which implements small local deformations of the entangling surface. We identify a simple constraint between the coefficient defining the two-point function of the displacement operator and the conformal weight of the twist operator, which consolidates a number of distinct conjectures on the shape dependence of the Renyi entropy. As an example, using this approach, we examine a conjecture regarding the universal coefficient associated with a conical singularity in the entangling surface for CFTs in any number of spacetime dimensions. We also provide a general formula for the second order variation of the Renyi entropy arising from small deformations of a spherical entangling surface, extending Mezei's results for the entanglement entropy.

Renyi entropy and conformal defects

International Nuclear Information System (INIS)

Bianchi, Lorenzo; Myers, Robert C.; Smolkin, Michael

2016-01-01

We propose a field theoretic framework for calculating the dependence of Renyi entropies on the shape of the entangling surface in a conformal field theory. Our approach rests on regarding the corresponding twist operator as a conformal defect and in particular, we define the displacement operator which implements small local deformations of the entangling surface. We identify a simple constraint between the coefficient defining the two-point function of the displacement operator and the conformal weight of the twist operator, which consolidates a number of distinct conjectures on the shape dependence of the Renyi entropy. As an example, using this approach, we examine a conjecture regarding the universal coefficient associated with a conical singularity in the entangling surface for CFTs in any number of spacetime dimensions. We also provide a general formula for the second order variation of the Renyi entropy arising from small deformations of a spherical entangling surface, extending Mezei's results for the entanglement entropy.

Microstructure and Mechanical Behavior of High-Entropy Alloys

Science.gov (United States)

Licavoli, Joseph J.; Gao, Michael C.; Sears, John S.; Jablonski, Paul D.; Hawk, Jeffrey A.

2015-10-01

High-entropy alloys (HEAs) have generated interest in recent years due to their unique positioning within the alloy world. By incorporating a number of elements in high proportion, usually of equal atomic percent, they have high configurational entropy, and thus, they hold the promise of interesting and useful properties such as enhanced strength and alloy stability. The present study investigates the mechanical behavior, fracture characteristics, and microstructure of two single-phase FCC HEAs CoCrFeNi and CoCrFeNiMn with some detailed attention given to melting, homogenization, and thermo-mechanical processing. Ingots approaching 8 kg in mass were made by vacuum induction melting to avoid the extrinsic factors inherent to small-scale laboratory button samples. A computationally based homogenization heat treatment was given to both alloys in order to eliminate any solidification segregation. The alloys were then fabricated in the usual way (forging, followed by hot rolling) with typical thermo-mechanical processing parameters employed. Transmission electron microscopy was subsequently used to assess the single-phase nature of the alloys prior to mechanical testing. Tensile specimens (ASTM E8) were prepared with tensile mechanical properties obtained from room temperature through 800 °C. Material from the gage section of selected tensile specimens was extracted to document room and elevated temperature deformation within the HEAs. Fracture surfaces were also examined to note fracture failure modes. The tensile behavior and selected tensile properties were compared with results in the literature for similar alloys.

Information and Entropy

Science.gov (United States)

Caticha, Ariel

2007-11-01

What is information? Is it physical? We argue that in a Bayesian theory the notion of information must be defined in terms of its effects on the beliefs of rational agents. Information is whatever constrains rational beliefs and therefore it is the force that induces us to change our minds. This problem of updating from a prior to a posterior probability distribution is tackled through an eliminative induction process that singles out the logarithmic relative entropy as the unique tool for inference. The resulting method of Maximum relative Entropy (ME), which is designed for updating from arbitrary priors given information in the form of arbitrary constraints, includes as special cases both MaxEnt (which allows arbitrary constraints) and Bayes' rule (which allows arbitrary priors). Thus, ME unifies the two themes of these workshops—the Maximum Entropy and the Bayesian methods—into a single general inference scheme that allows us to handle problems that lie beyond the reach of either of the two methods separately. I conclude with a couple of simple illustrative examples.

ENTROPIES AND FLUX-SPLITTINGS FOR THE ISENTROPIC EULER EQUATIONS

Institute of Scientific and Technical Information of China (English)

无

2001-01-01

The authors establish the existence of a large class of mathematical entropies (the so-called weak entropies) associated with the Euler equations for an isentropic, compressible fluid governed by a general pressure law. A mild assumption on the behavior of the pressure law near the vacuum is solely required. The analysis is based on an asymptotic expansion of the fundamental solution (called here the entropy kernel) of a highly singular Euler-Poisson-Darboux equation. The entropy kernel is only H lder continuous and its regularity is carefully investigated. Relying on a notion introduced earlier by the authors, it is also proven that, for the Euler equations, the set of entropy flux-splittings coincides with the set of entropies-entropy fluxes. These results imply the existence of a flux-splitting consistent with all of the entropy inequalities.

The pigeon's discrimination of visual entropy: a logarithmic function.

Science.gov (United States)

Young, Michael E; Wasserman, Edward A

2002-11-01

We taught 8 pigeons to discriminate 16-icon arrays that differed in their visual variability or "entropy" to see whether the relationship between entropy and discriminative behavior is linear (in which equivalent differences in entropy should produce equivalent changes in behavior) or logarithmic (in which higher entropy values should be less discriminable from one another than lower entropy values). Pigeons received a go/no-go task in which the lower entropy arrays were reinforced for one group and the higher entropy arrays were reinforced for a second group. The superior discrimination of the second group was predicted by a theoretical analysis in which excitatory and inhibitory stimulus generalization gradients fall along a logarithmic, but not a linear scale. Reanalysis of previously published data also yielded results consistent with a logarithmic relationship between entropy and discriminative behavior.

The Conditional Entropy Power Inequality for Bosonic Quantum Systems

DEFF Research Database (Denmark)

de Palma, Giacomo; Trevisan, Dario

2018-01-01

We prove the conditional Entropy Power Inequality for Gaussian quantum systems. This fundamental inequality determines the minimum quantum conditional von Neumann entropy of the output of the beam-splitter or of the squeezing among all the input states where the two inputs are conditionally...... independent given the memory and have given quantum conditional entropies. We also prove that, for any couple of values of the quantum conditional entropies of the two inputs, the minimum of the quantum conditional entropy of the output given by the conditional Entropy Power Inequality is asymptotically...... achieved by a suitable sequence of quantum Gaussian input states. Our proof of the conditional Entropy Power Inequality is based on a new Stam inequality for the quantum conditional Fisher information and on the determination of the universal asymptotic behaviour of the quantum conditional entropy under...

Time-dependent entropy evolution in microscopic and macroscopic electromagnetic relaxation

International Nuclear Information System (INIS)

Baker-Jarvis, James

2005-01-01

This paper is a study of entropy and its evolution in the time and frequency domains upon application of electromagnetic fields to materials. An understanding of entropy and its evolution in electromagnetic interactions bridges the boundaries between electromagnetism and thermodynamics. The approach used here is a Liouville-based statistical-mechanical theory. I show that the microscopic entropy is reversible and the macroscopic entropy satisfies an H theorem. The spectral entropy development can be very useful for studying the frequency response of materials. Using a projection-operator based nonequilibrium entropy, different equations are derived for the entropy and entropy production and are applied to the polarization, magnetization, and macroscopic fields. I begin by proving an exact H theorem for the entropy, progress to application of time-dependent entropy in electromagnetics, and then apply the theory to relevant applications in electromagnetics. The paper concludes with a discussion of the relationship of the frequency-domain form of the entropy to the permittivity, permeability, and impedance

Minimal entropy approximation for cellular automata

International Nuclear Information System (INIS)

Fukś, Henryk

2014-01-01

We present a method for the construction of approximate orbits of measures under the action of cellular automata which is complementary to the local structure theory. The local structure theory is based on the idea of Bayesian extension, that is, construction of a probability measure consistent with given block probabilities and maximizing entropy. If instead of maximizing entropy one minimizes it, one can develop another method for the construction of approximate orbits, at the heart of which is the iteration of finite-dimensional maps, called minimal entropy maps. We present numerical evidence that the minimal entropy approximation sometimes outperforms the local structure theory in characterizing the properties of cellular automata. The density response curve for elementary CA rule 26 is used to illustrate this claim. (paper)

Entropy and Entanglement of the Electromagnetically Induced Transparency System

Institute of Scientific and Technical Information of China (English)

LIU Xiao-Juan; FANG Mao-Fa; ZHOU Qing-Ping

2004-01-01

@@ We study the entropy and the entanglement of an electromagnetically induced transparency system. The quantum entanglement between the atom and the two quantized laser fields is discussed by using quantum reduced entropy and that between the two quantized laser fields by using quantum relative entropy. We also examine whether influences of EIT on entropy and quantum entanglement of the system considered occur or not. Our results show that the minimum value of the atomic reduced entropy may be regarded as an entropy criterion on the electromagnetically induced transparency occurring.

On thermodynamic limits of entropy densities

NARCIS (Netherlands)

Moriya, H; Van Enter, A

We give some sufficient conditions which guarantee that the entropy density in the thermodynamic limit is equal to the thermodynamic limit of the entropy densities of finite-volume (local) Gibbs states.

Properties of Risk Measures of Generalized Entropy in Portfolio Selection

Directory of Open Access Journals (Sweden)

Rongxi Zhou

2017-12-01

Full Text Available This paper systematically investigates the properties of six kinds of entropy-based risk measures: Information Entropy and Cumulative Residual Entropy in the probability space, Fuzzy Entropy, Credibility Entropy and Sine Entropy in the fuzzy space, and Hybrid Entropy in the hybridized uncertainty of both fuzziness and randomness. We discover that none of the risk measures satisfy all six of the following properties, which various scholars have associated with effective risk measures: Monotonicity, Translation Invariance, Sub-additivity, Positive Homogeneity, Consistency and Convexity. Measures based on Fuzzy Entropy, Credibility Entropy, and Sine Entropy all exhibit the same properties: Sub-additivity, Positive Homogeneity, Consistency, and Convexity. These measures based on Information Entropy and Hybrid Entropy, meanwhile, only exhibit Sub-additivity and Consistency. Cumulative Residual Entropy satisfies just Sub-additivity, Positive Homogeneity, and Convexity. After identifying these properties, we develop seven portfolio models based on different risk measures and made empirical comparisons using samples from both the Shenzhen Stock Exchange of China and the New York Stock Exchange of America. The comparisons show that the Mean Fuzzy Entropy Model performs the best among the seven models with respect to both daily returns and relative cumulative returns. Overall, these results could provide an important reference for both constructing effective risk measures and rationally selecting the appropriate risk measure under different portfolio selection conditions.

Entropy Measurement for Biometric Verification Systems.

Science.gov (United States)

Lim, Meng-Hui; Yuen, Pong C

2016-05-01

Biometric verification systems are designed to accept multiple similar biometric measurements per user due to inherent intrauser variations in the biometric data. This is important to preserve reasonable acceptance rate of genuine queries and the overall feasibility of the recognition system. However, such acceptance of multiple similar measurements decreases the imposter's difficulty of obtaining a system-acceptable measurement, thus resulting in a degraded security level. This deteriorated security needs to be measurable to provide truthful security assurance to the users. Entropy is a standard measure of security. However, the entropy formula is applicable only when there is a single acceptable possibility. In this paper, we develop an entropy-measuring model for biometric systems that accepts multiple similar measurements per user. Based on the idea of guessing entropy, the proposed model quantifies biometric system security in terms of adversarial guessing effort for two practical attacks. Excellent agreement between analytic and experimental simulation-based measurement results on a synthetic and a benchmark face dataset justify the correctness of our model and thus the feasibility of the proposed entropy-measuring approach.

On quantum Rényi entropies: A new generalization and some properties

International Nuclear Information System (INIS)

Müller-Lennert, Martin; Dupuis, Frédéric; Szehr, Oleg; Fehr, Serge; Tomamichel, Marco

2013-01-01

The Rényi entropies constitute a family of information measures that generalizes the well-known Shannon entropy, inheriting many of its properties. They appear in the form of unconditional and conditional entropies, relative entropies, or mutual information, and have found many applications in information theory and beyond. Various generalizations of Rényi entropies to the quantum setting have been proposed, most prominently Petz's quasi-entropies and Renner's conditional min-, max-, and collision entropy. However, these quantum extensions are incompatible and thus unsatisfactory. We propose a new quantum generalization of the family of Rényi entropies that contains the von Neumann entropy, min-entropy, collision entropy, and the max-entropy as special cases, thus encompassing most quantum entropies in use today. We show several natural properties for this definition, including data-processing inequalities, a duality relation, and an entropic uncertainty relation

Chain rules for smooth min-and max-entropies

DEFF Research Database (Denmark)

Vitanov, Alexande; Dupont-Dupuis, Fréderic; Tomamichel, Marco

2013-01-01

The chain rule for the Shannon and von Neumann en- tropy, which relates the total entropy of a system to the entropies of its parts, is of central importance to information theory. Here, we consider the chain rule for the more general smooth min- and max-entropies, used in one-shot in formation...... theory. For these en- tropy measures, the chain rule no longer holds as an equality. How- ever, the standard chain rule for the von Neum ann entropy is re- trieved asymptotically when evaluating the smooth entropies for many identical and independently distributed states....

A note on entanglement entropy and quantum geometry

International Nuclear Information System (INIS)

Bodendorfer, N

2014-01-01

It has been argued that the entropy computed in the isolated horizon framework of loop quantum gravity is closely related to the entanglement entropy of the gravitational field, and that the calculation performed is not restricted to horizons. We recall existing work on this issue and explain how recent work on generalizing these computations to arbitrary spacetime dimensions D+1⩾3 supports this point of view and makes the duality between entanglement entropy and the entropy computed from counting boundary states manifest. In a certain semiclassical regime in 3+1 dimensions, this entropy is given by the Bekenstein–Hawking formula. (paper)

A review of entropy generation in microchannels

Directory of Open Access Journals (Sweden)

Mohamed M Awad

2015-12-01

Full Text Available In this study, a critical review of thermodynamic optimum of microchannels based on entropy generation analysis is presented. Using entropy generation analysis as evaluation parameter of microchannels has been reported by many studies in the literature. In these studies, different working fluids such as nanofluids, air, water, engine oil, aniline, ethylene glycol, and non-Newtonian fluids have been used. For the case of nanofluids, “nanoparticles” has been used in various kinds such as Al2O3 and Cu, and “base fluid” has been used in various kinds such as water and ethylene glycol. Furthermore, studies on thermodynamic optimum of microchannels based on entropy generation analysis are summarized in a table. At the end, recommendations of future work for thermodynamic optimum of microchannels based on entropy generation analysis are given. As a result, this article can not only be used as the starting point for the researcher interested in entropy generation in microchannels, but it also includes recommendations for future studies on entropy generation in microchannels.

Trajectories entropy in dynamical graphs with memory

Directory of Open Access Journals (Sweden)

Francesco eCaravelli

2016-04-01

Full Text Available In this paper we investigate the application of non-local graph entropy to evolving and dynamical graphs. The measure is based upon the notion of Markov diffusion on a graph, and relies on the entropy applied to trajectories originating at a specific node. In particular, we study the model of reinforcement-decay graph dynamics, which leads to scale free graphs. We find that the node entropy characterizes the structure of the network in the two parameter phase-space describing the dynamical evolution of the weighted graph. We then apply an adapted version of the entropy measure to purely memristive circuits. We provide evidence that meanwhile in the case of DC voltage the entropy based on the forward probability is enough to characterize the graph properties, in the case of AC voltage generators one needs to consider both forward and backward based transition probabilities. We provide also evidence that the entropy highlights the self-organizing properties of memristive circuits, which re-organizes itself to satisfy the symmetries of the underlying graph.

A gravitational entropy proposal

International Nuclear Information System (INIS)

Clifton, Timothy; Tavakol, Reza; Ellis, George F R

2013-01-01

We propose a thermodynamically motivated measure of gravitational entropy based on the Bel–Robinson tensor, which has a natural interpretation as the effective super-energy–momentum tensor of free gravitational fields. The specific form of this measure differs depending on whether the gravitational field is Coulomb-like or wave-like, and reduces to the Bekenstein–Hawking value when integrated over the interior of a Schwarzschild black hole. For scalar perturbations of a Robertson–Walker geometry we find that the entropy goes like the Hubble weighted anisotropy of the gravitational field, and therefore increases as structure formation occurs. This is in keeping with our expectations for the behaviour of gravitational entropy in cosmology, and provides a thermodynamically motivated arrow of time for cosmological solutions of Einstein’s field equations. It is also in keeping with Penrose’s Weyl curvature hypothesis. (paper)

Entropy of isolated quantum systems after a quench.

Science.gov (United States)

Santos, Lea F; Polkovnikov, Anatoli; Rigol, Marcos

2011-07-22

A diagonal entropy, which depends only on the diagonal elements of the system's density matrix in the energy representation, has been recently introduced as the proper definition of thermodynamic entropy in out-of-equilibrium quantum systems. We study this quantity after an interaction quench in lattice hard-core bosons and spinless fermions, and after a local chemical potential quench in a system of hard-core bosons in a superlattice potential. The former systems have a chaotic regime, where the diagonal entropy becomes equivalent to the equilibrium microcanonical entropy, coinciding with the onset of thermalization. The latter system is integrable. We show that its diagonal entropy is additive and different from the entropy of a generalized Gibbs ensemble, which has been introduced to account for the effects of conserved quantities at integrability.

ECG contamination of EEG signals: effect on entropy.

Science.gov (United States)

Chakrabarti, Dhritiman; Bansal, Sonia

2016-02-01

Entropy™ is a proprietary algorithm which uses spectral entropy analysis of electroencephalographic (EEG) signals to produce indices which are used as a measure of depth of hypnosis. We describe a report of electrocardiographic (ECG) contamination of EEG signals leading to fluctuating erroneous Entropy values. An explanation is provided for mechanism behind this observation by describing the spread of ECG signals in head and neck and its influence on EEG/Entropy by correlating the observation with the published Entropy algorithm. While the Entropy algorithm has been well conceived, there are still instances in which it can produce erroneous values. Such erroneous values and their cause may be identified by close scrutiny of the EEG waveform if Entropy values seem out of sync with that expected at given anaesthetic levels.

Entropy of orthogonal polynomials with Freud weights and information entropies of the harmonic oscillator potential

Science.gov (United States)

Van Assche, W.; Yáñez, R. J.; Dehesa, J. S.

1995-08-01

The information entropy of the harmonic oscillator potential V(x)=1/2λx2 in both position and momentum spaces can be expressed in terms of the so-called ``entropy of Hermite polynomials,'' i.e., the quantity Sn(H):= -∫-∞+∞H2n(x)log H2n(x) e-x2dx. These polynomials are instances of the polynomials orthogonal with respect to the Freud weights w(x)=exp(-||x||m), m≳0. Here, a very precise and general result of the entropy of Freud polynomials recently established by Aptekarev et al. [J. Math. Phys. 35, 4423-4428 (1994)], specialized to the Hermite kernel (case m=2), leads to an important refined asymptotic expression for the information entropies of very excited states (i.e., for large n) in both position and momentum spaces, to be denoted by Sρ and Sγ, respectively. Briefly, it is shown that, for large values of n, Sρ+1/2logλ≂log(π√2n/e)+o(1) and Sγ-1/2log λ≂log(π√2n/e)+o(1), so that Sρ+Sγ≂log(2π2n/e2)+o(1) in agreement with the generalized indetermination relation of Byalinicki-Birula and Mycielski [Commun. Math. Phys. 44, 129-132 (1975)]. Finally, the rate of convergence of these two information entropies is numerically analyzed. In addition, using a Rakhmanov result, we describe a totally new proof of the leading term of the entropy of Freud polynomials which, naturally, is just a weak version of the aforementioned general result.

Entropy and wigner functions