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Journal articles on the topic 'Entropy dynamics'

Author: Grafiati

Published: 22 February 2023

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1

McLachlan, A. D. "Entropy phase dynamics." Acta Crystallographica Section D Biological Crystallography 49, no. 1 (1993): 75–85. http://dx.doi.org/10.1107/s0907444992008102.

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2

Grmela, Miroslav, Michal Pavelka, Václav Klika, Bing-Yang Cao, and Nie Bendian. "Entropy and Entropy Production in Multiscale Dynamics." Journal of Non-Equilibrium Thermodynamics 44, no. 3 (2019): 217–33. http://dx.doi.org/10.1515/jnet-2018-0059.

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Abstract Heat conduction is investigated on three levels: equilibrium, Fourier, and Cattaneo. The Fourier level is either the point of departure for investigating the approach to equilibrium or the final stage in the investigation of the approach from the Cattaneo level. Both investigations bring to the Fourier level an entropy and a thermodynamics. In the absence of external and internal influences preventing the approach to equilibrium the entropy that arises in the latter investigation is the production of the classical entropy that arises in the former investigation. If the approach to equ

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3

Rosser, J. Barkley. "Econophysics and the Entropic Foundations of Economics." Entropy 23, no. 10 (2021): 1286. http://dx.doi.org/10.3390/e23101286.

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This paper examines relations between econophysics and the law of entropy as foundations of economic phenomena. Ontological entropy, where actual thermodynamic processes are involved in the flow of energy from the Sun through the biosphere and economy, is distinguished from metaphorical entropy, where similar mathematics used for modeling entropy is employed to model economic phenomena. Areas considered include general equilibrium theory, growth theory, business cycles, ecological economics, urban–regional economics, income and wealth distribution, and financial market dynamics. The power-law

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4

Piftankin, G., and D. Treschev. "Gibbs entropy and dynamics." Chaos: An Interdisciplinary Journal of Nonlinear Science 18, no. 2 (2008): 023116. http://dx.doi.org/10.1063/1.2907731.

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5

Biró, Tamás Sándor, Zoltán Néda, and András Telcs. "Entropic Divergence and Entropy Related to Nonlinear Master Equations." Entropy 21, no. 10 (2019): 993. http://dx.doi.org/10.3390/e21100993.

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We reverse engineer entropy formulas from entropic divergence, optimized to given classes of probability distribution function (PDF) evolution dynamical equation. For linear dynamics of the distribution function, the traditional Kullback–Leibler formula follows from using the logarithm function in the Csiszár’s f-divergence construction, while for nonlinear master equations more general formulas emerge. As applications, we review a local growth and global reset (LGGR) model for citation distributions, income distribution models and hadron number fluctuations in high energy collisions.

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6

Caticha, Ariel. "Entropic Dynamics: Quantum Mechanics from Entropy and Information Geometry." Annalen der Physik 531, no. 3 (2018): 1700408. http://dx.doi.org/10.1002/andp.201700408.

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7

HALDAR, SUDIP KUMAR, and BARNALI CHAKRABARTI. "DYNAMICAL FEATURES OF SHANNON INFORMATION ENTROPY OF BOSONIC CLOUD IN A TIGHT TRAP." International Journal of Modern Physics B 27, no. 13 (2013): 1350048. http://dx.doi.org/10.1142/s0217979213500483.

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We calculate Shannon information entropy of trapped interacting bosons in both the position and momentum spaces, Sr and Sk, respectively. The total entropy maintains the functional form S = a + b ln N for repulsive bosons. At the noninteracting limit the lower bound of entropic uncertainty relation is also satisfied whereas the diverging behavior of Sr and Sk at the critical point of collapse for attractive condensate accurately calculates the stability factor. Next we study the dynamics of Shannon information entropy with varying interparticle potential. We numerically solve the time-dependen

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8

Watanabe, Noboru. "On quantum dynamical entropy for open systems." International Journal of Quantum Information 14, no. 04 (2016): 1640005. http://dx.doi.org/10.1142/s0219749916400050.

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We review some notions for quantum dynamical entropies. The dynamical entropy of quantum systems is discussed and a numerical computation of the dynamical entropy is carried for the open system dynamics.

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9

Masyagin, Victor Fedorovich, Ruslan Viktorovich Zhalnin, Marina Eugenievna Ladonkina, Olga Nikolaevna Terekhina, and Vladimir Fedorovich Tishkin. "Application of the entropic slope limiter for solving gas dynamics equations using the implicit scheme of the discontinuous Galerkin method." Keldysh Institute Preprints, no. 7 (2021): 1–18. http://dx.doi.org/10.20948/prepr-2021-7.

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The paper presents the entropic slope limiter for solving gas dynamics equations using the implicit scheme of the discontinuous Galerkin method. It guarantees monotonicity of the numerical solution, non-negativity of pressure and entropy production for each finite element. The numerical method has been successfully verified using some well-known model gas-dynamic problems.

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Daguerre, L., G. Torroba, R. Medina, and M. Solís. "NON RELATIVISTIC QUANTUM FIELD THEORY: DYNAMICS AND IRREVERSIBILITY." Anales AFA 32, no. 4 (2022): 93–98. http://dx.doi.org/10.31527/analesafa.2021.32.4.93.

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We study aspects of quantum field theory at finite density using techniques and concepts from quantum information theory. We focus on massive Dirac fermions with chemical potential in 1+1 space-time dimensions. Using the entanglement entropy on an interval, we construct an entropic c-function that is finite. This c-function is not monotonous,and incorporates the long-range entanglement from the Fermi surface. Motivated by previous works on lattice models,we next compute the Renyi entropies numerically, and find Friedel-type oscillations. Next, we analyze the mutual in-formation as a measure of

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11

Lopes, António, and J. Tenreiro Machado. "Entropy Analysis of Soccer Dynamics." Entropy 21, no. 2 (2019): 187. http://dx.doi.org/10.3390/e21020187.

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This paper adopts the information and fractional calculus tools for studying the dynamics of a national soccer league. A soccer league season is treated as a complex system (CS) with a state observable at discrete time instants, that is, at the time of rounds. The CS state, consisting of the goals scored by the teams, is processed by means of different tools, namely entropy, mutual information and Jensen–Shannon divergence. The CS behavior is visualized in 3-D maps generated by multidimensional scaling. The points on the maps represent rounds and their relative positioning allows for a direct

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12

Seitz, William, and A. D. Kirwan. "Incomparability, entropy, and mixing dynamics." Physica A: Statistical Mechanics and its Applications 506 (September 2018): 880–87. http://dx.doi.org/10.1016/j.physa.2018.05.012.

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13

Alicki, R., and M. Fannes. "Quantum dynamics, measurement and entropy." Reports on Mathematical Physics 55, no. 1 (2005): 47–59. http://dx.doi.org/10.1016/s0034-4877(05)80003-5.

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14

VIALLET, C. M. "ALGEBRAIC DYNAMICS AND ALGEBRAIC ENTROPY." International Journal of Geometric Methods in Modern Physics 05, no. 08 (2008): 1373–91. http://dx.doi.org/10.1142/s0219887808003375.

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We give the definition of algebraic entropy, which is a global index of complexity for dynamical systems with a rational evolution. We explain its geometrical meaning, and different methods, heuristic or exact to calculate this entropy. This quantity is a very good integrability detector. It also has remarkable properties, which make it an interesting object of study by itself. It is in particular conjectured to be the logarithm of algebraic integer, with a limited range of values, still to be explored.

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15

Arbieto, A., and E. Rego. "Positive entropy through pointwise dynamics." Proceedings of the American Mathematical Society 148, no. 1 (2019): 263–71. http://dx.doi.org/10.1090/proc/14682.

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16

Prigogine, I. "Dissipative structures, dynamics and entropy." International Journal of Quantum Chemistry 9, S9 (2009): 443–56. http://dx.doi.org/10.1002/qua.560090854.

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17

Simpson, Stephen G. "Symbolic Dynamics: Entropy = Dimension = Complexity." Theory of Computing Systems 56, no. 3 (2014): 527–43. http://dx.doi.org/10.1007/s00224-014-9546-8.

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18

Ignaccolo, Massimiliano, Mirek Latka, Wojciech Jernajczyk, Paolo Grigolini, and Bruce J. West. "The dynamics of EEG entropy." Journal of Biological Physics 36, no. 2 (2009): 185–96. http://dx.doi.org/10.1007/s10867-009-9171-y.

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19

Kausch, Sherry L., Brynne Sullivan, Michael C. Spaeder, and Jessica Keim-Malpass. "Individual illness dynamics: An analysis of children with sepsis admitted to the pediatric intensive care unit." PLOS Digital Health 1, no. 3 (2022): e0000019. http://dx.doi.org/10.1371/journal.pdig.0000019.

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Illness dynamics and patterns of recovery may be essential features in understanding the critical illness course. We propose a method to characterize individual illness dynamics in patients who experienced sepsis in the pediatric intensive care unit. We defined illness states based on illness severity scores generated from a multi-variable prediction model. For each patient, we calculated transition probabilities to characterize movement among illness states. We calculated the Shannon entropy of the transition probabilities. Using the entropy parameter, we determined phenotypes of illness dyna

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20

Wu, Zhe, Guang Yang, Qiang Zhang, Shengyue Tan, and Shuyong Hou. "Information Dynamic Correlation of Vibration in Nonlinear Systems." Entropy 22, no. 1 (2019): 56. http://dx.doi.org/10.3390/e22010056.

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In previous studies, information dynamics methods such as Von Neumann entropy and Rényi entropy played an important role in many fields, covering both macroscopic and microscopic studies. They have a solid theoretical foundation, but there are few reports in the field of mechanical nonlinear systems. So, can we apply Von Neumann entropy and Rényi entropy to study and analyze the dynamic behavior of macroscopic nonlinear systems? In view of the current lack of suitable methods to characterize the dynamics behavior of mechanical systems from the perspective of nonlinear system correlation, we pr

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21

Gopal, Sharan, and Srikanth Ravulapalli. "Dynamics of real projective transformations." Applied General Topology 19, no. 2 (2018): 239. http://dx.doi.org/10.4995/agt.2018.7962.

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<div data-canvas-width="358.1721365118214">The dynamics of a projective transformation on a real projective space are studied in this paper. The two main aspects of these transformations that are studied here are the topological entropy and the zeta function. Topological entropy is an inherent property of a dynamical system whereas the zeta function is a useful tool for the study of periodic points. We find the zeta function for a general projective transformation but entropy only for certain transformations on the real projective line.</div>

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22

Janečka, Adam, and Michal Pavelka. "Gradient Dynamics and Entropy Production Maximization." Journal of Non-Equilibrium Thermodynamics 43, no. 1 (2018): 1–19. http://dx.doi.org/10.1515/jnet-2017-0005.

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AbstractWe 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 potent

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23

Chen, Kuo, and Murugappan Muthukumar. "Entropic barrier of topologically immobilized DNA in hydrogels." Proceedings of the National Academy of Sciences 118, no. 28 (2021): e2106380118. http://dx.doi.org/10.1073/pnas.2106380118.

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The single most intrinsic property of nonrigid polymer chains is their ability to adopt enormous numbers of chain conformations, resulting in huge conformational entropy. When such macromolecules move in media with restrictive spatial constraints, their trajectories are subjected to reductions in their conformational entropy. The corresponding free energy landscapes are interrupted by entropic barriers separating consecutive spatial domains which function as entropic traps where macromolecules can adopt their conformations more favorably. Movement of macromolecules by negotiating a sequence of

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24

MATESANZ, DAVID, and GUILLERMO J. ORTEGA. "A (ECONOPHYSICS) NOTE ON VOLATILITY IN EXCHANGE RATE TIME SERIES." International Journal of Modern Physics C 19, no. 07 (2008): 1095–103. http://dx.doi.org/10.1142/s0129183108012789.

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We propose a volatility and uncertainty country ranking based on the entropic analysis of the real exchange rate dynamics. We show that this ranking is highly correlated with the volatility in the gross domestic product after events of currency crises. By comparing entropy with variance ranking we demonstrate that entropy measures better volatility effects of crises.

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25

Campos, Juan, Andrea Corli, and Luisa Malaguti. "Saturated Fronts in Crowds Dynamics." Advanced Nonlinear Studies 21, no. 2 (2021): 303–26. http://dx.doi.org/10.1515/ans-2021-2118.

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Abstract We consider a degenerate scalar parabolic equation, in one spatial dimension, of flux-saturated type. The equation also contains a convective term. We study the existence and regularity of traveling-wave solutions; in particular we show that they can be discontinuous. Uniqueness is recovered by requiring an entropy condition, and entropic solutions turn out to be the vanishing-diffusion limits of traveling-wave solutions to the equation with an additional non-degenerate diffusion. Applications to crowds dynamics, which motivated the present research, are also provided.

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26

Abo-Kahla, D. A. M., and M. Abdel-Aty. "Information entropy of multi-qubit Rabi system." International Journal of Quantum Information 13, no. 06 (2015): 1550042. http://dx.doi.org/10.1142/s0219749915500422.

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We consider quantum information entropy phenomenon for multi-qubit Rabi system. By introducing different measurements schemes, we establish the relation between information entropy approach and Von Neumann entropy. It is shown that the information entropy is more sensitive to the time development than the Von Neumann entropy. Furthermore, the suggested protocol exhibits excellent scaling of relevant characteristics, with respect to population dynamics, such that more accurate dynamical results may be obtained using information entropy due to variation of the frequency detuning and the coupling

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27

Sefiedgar, Akram Sadat. "How can rainbow gravity affect gravitational force?" International Journal of Modern Physics D 25, no. 14 (2016): 1650101. http://dx.doi.org/10.1142/s0218271816501017.

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According to Verlinde’s recent proposal, the gravity is originally an entropic force. In this paper, we obtain the corrections to the entropy-area law of black holes within rainbow gravity. The corrected entropy-area law leads to the modifications of the number of bits [Formula: see text]. Inspired by Verlinde’s argument on the entropic force, and using the modified number of bits, we can investigate the effects of rainbow gravity on the modified Newtonian dynamics, Newton’s law of gravitation, and Einstein’s general relativity in entropic force approach.

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28

EBELING, WERNER, JAN FREUND, and KATJA RATEITSCHAK. "ENTROPY AND EXTENDED MEMORY IN DISCRETE CHAOTIC DYNAMICS." International Journal of Bifurcation and Chaos 06, no. 04 (1996): 611–25. http://dx.doi.org/10.1142/s0218127496000308.

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We investigate simple one-dimensional maps which allow for exact solutions of their related statistical properties. In addition to the originally refined dynamical description a coarsegrained level of description based on certain partitions of the phase space is selected. The deterministic micropscopic dynamics is shifted to a stochastic symbolic dynamics. The higher order entropies are studied for the logistic map, the tent map, and the shark fin map. Markov sources of any prescribed order are constructed explicitly. In a special case, long memory tails are observed. Systems of this type may

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29

YAMANAKA, Y., and K. NAKAMURA. "ENTROPY LAW FROM INHOMOGENEOUS THERMOFIELD DYNAMICS." Modern Physics Letters A 09, no. 31 (1994): 2879–91. http://dx.doi.org/10.1142/s0217732394002720.

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In the framework of thermofield dynamics for spatially inhomogeneous time-dependent nonequilibrium situations, we derive the kinetic equation, which is different from the Boltzmann equation due to quantum effects. It is shown that this kinetic equation leads to the entropy law. An expression for the entropy flow is found.

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30

Vopson, Melvin M., and S. Lepadatu. "Second law of information dynamics." AIP Advances 12, no. 7 (2022): 075310. http://dx.doi.org/10.1063/5.0100358.

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One of the most powerful laws in physics is the second law of thermodynamics, which states that the entropy of any system remains constant or increases over time. In fact, the second law is applicable to the evolution of the entire universe and Clausius stated, “The entropy of the universe tends to a maximum.” Here, we examine the time evolution of information systems, defined as physical systems containing information states within Shannon’s information theory framework. Our observations allow the introduction of the second law of information dynamics (infodynamics). Using two different infor

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31

HOCHMAN, MICHAEL. "On notions of determinism in topological dynamics." Ergodic Theory and Dynamical Systems 32, no. 1 (2011): 119–40. http://dx.doi.org/10.1017/s0143385710000738.

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AbstractWe examine the relations between topological entropy, invertibility, and prediction in topological dynamics. We show that topological determinism in the sense of Kamińsky, Siemaszko, and Szymański imposes no restriction on invariant measures except zero entropy. Also, we develop a new method for relating topological determinism and zero entropy, and apply it to obtain a multidimensional analog of this theory. We examine prediction in symbolic dynamics and show that while the condition that each past admits a unique future only occurs in finite systems, the condition that each past has

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32

Busiello, D. M., J. Hidalgo, and A. Maritan. "Entropy production for coarse-grained dynamics." New Journal of Physics 21, no. 7 (2019): 073004. http://dx.doi.org/10.1088/1367-2630/ab29c0.

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33

Goharshenasanesfahani, S., and S. Smadici. "Magnetic entropy dynamics in ultrafast demagnetization." Journal of Physics: Condensed Matter 33, no. 3 (2020): 035802. http://dx.doi.org/10.1088/1361-648x/abbc31.

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34

Chiara, Gabriele De, Simone Montangero, Pasquale Calabrese, and Rosario Fazio. "Entanglement entropy dynamics of Heisenberg chains." Journal of Statistical Mechanics: Theory and Experiment 2006, no. 03 (2006): P03001. http://dx.doi.org/10.1088/1742-5468/2006/03/p03001.

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35

SARRIS, C. M., and ARACELI N. PROTO. "INFORMATION ENTROPY AND NONLINEAR SEMIQUANTUM DYNAMICS." International Journal of Bifurcation and Chaos 19, no. 10 (2009): 3473–84. http://dx.doi.org/10.1142/s0218127409024918.

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We describe how, departing from the Shannon entropy, it is possible to deal with semiquantum time-independent nonlinear Hamiltonians. The interplay between the quantal and classical degrees of freedom can be easily seen, and the set of differential equations that govern the temporal evolution of the quantal mean values and the classical variables is obtained. We find invariants of motion and, particularly, we describe under which conditions, the uncertainty principle remains as an invariant of motion too. Through the analysis of these invariants, it is possible to follow the transition of the

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36

Minh, David D. L., Donald Hamelberg, and J. Andrew McCammon. "Accelerated entropy estimates with accelerated dynamics." Journal of Chemical Physics 127, no. 15 (2007): 154105. http://dx.doi.org/10.1063/1.2794754.

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37

Ohya, M., and Y. Fujii. "Entropy change in linear-response dynamics." Il Nuovo Cimento B Series 11 91, no. 1 (1986): 25–30. http://dx.doi.org/10.1007/bf02722219.

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38

Garbaczewski, Piotr. "Differential Entropy and Dynamics of Uncertainty." Journal of Statistical Physics 123, no. 2 (2006): 315–55. http://dx.doi.org/10.1007/s10955-006-9058-2.

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39

URADE, Masayoshi, and Toshihiro IWAKI. "C134 Molecular Dynamics Study on Entropy." Proceedings of the Thermal Engineering Conference 2005 (2005): 115–16. http://dx.doi.org/10.1299/jsmeted.2005.115.

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40

Sobezyk, K., and J. Trȩbicki. "Maximum entropy principle in stochastic dynamics." Probabilistic Engineering Mechanics 5, no. 3 (1990): 102–10. http://dx.doi.org/10.1016/0266-8920(90)90001-z.

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41

Encarnação, Sara, Marcos Gaudiano, Francisco Santos, José Tenedório, and Jorge Pacheco. "Urban Dynamics, Fractals and Generalized Entropy." Entropy 15, no. 12 (2013): 2679–97. http://dx.doi.org/10.3390/e15072679.

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42

Birn, J., M. Hesse, K. Schindler, and S. Zaharia. "Role of entropy in magnetotail dynamics." Journal of Geophysical Research: Space Physics 114, A9 (2009): n/a. http://dx.doi.org/10.1029/2008ja014015.

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43

Vecchi, Italo. "Entropy compactification in Lagrangean gas dynamics." Mathematical Methods in the Applied Sciences 14, no. 3 (1991): 207–16. http://dx.doi.org/10.1002/mma.1670140305.

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44

XIE, JIAN-SHENG. "A new entropy formula of Ledrappier–Young type for linear toral dynamics." Ergodic Theory and Dynamical Systems 34, no. 3 (2012): 1037–54. http://dx.doi.org/10.1017/etds.2012.151.

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AbstractA detailed Ledrappier–Young theory is presented for linear toral dynamics. First, a proof is given for a simplified definition for local entropies which holds in more general settings besides the current linear dynamics. Then it is shown that the transverse dimensions can be defined directly via the Smale structure of the linear dynamical system. A new entropy formula of Ledrappier–Young type is obtained. The conjecture of Ledrappier and Xie [Vanishing transverse entropy in smooth ergodic theory. Ergod. Th. & Dynam. Sys. 31(4) (2011), 1229–1235] is also discussed for such linear dy

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Li, Yuxing, Bingzhao Tang, Bo Geng, and Shangbin Jiao. "Fractional Order Fuzzy Dispersion Entropy and Its Application in Bearing Fault Diagnosis." Fractal and Fractional 6, no. 10 (2022): 544. http://dx.doi.org/10.3390/fractalfract6100544.

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Fuzzy dispersion entropy (FuzzDE) is a very recently proposed non-linear dynamical indicator, which combines the advantages of both dispersion entropy (DE) and fuzzy entropy (FuzzEn) to detect dynamic changes in a time series. However, FuzzDE only reflects the information of the original signal and is not very sensitive to dynamic changes. To address these drawbacks, we introduce fractional order calculation on the basis of FuzzDE, propose FuzzDEα, and use it as a feature for the signal analysis and fault diagnosis of bearings. In addition, we also introduce other fractional order entropies, i

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46

Beretta, Gian Paolo. "Modeling Non-Equilibrium Dynamics of a Discrete Probability Distribution: General Rate Equation for Maximal Entropy Generation in a Maximum-Entropy Landscape with Time-Dependent Constraints." Entropy 10, no. 3 (2008): 160–82. http://dx.doi.org/10.3390/entropy-e10030160.

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47

Bod’ová, Katarína, Enikő Szép, and Nicholas H. Barton. "Dynamic maximum entropy provides accurate approximation of structured population dynamics." PLOS Computational Biology 17, no. 12 (2021): e1009661. http://dx.doi.org/10.1371/journal.pcbi.1009661.

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Realistic models of biological processes typically involve interacting components on multiple scales, driven by changing environment and inherent stochasticity. Such models are often analytically and numerically intractable. We revisit a dynamic maximum entropy method that combines a static maximum entropy with a quasi-stationary approximation. This allows us to reduce stochastic non-equilibrium dynamics expressed by the Fokker-Planck equation to a simpler low-dimensional deterministic dynamics, without the need to track microscopic details. Although the method has been previously applied to a

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48

Liu, Yan, Kai Ma, Hao He, and Kuan Gao. "Obtaining Information about Operation of Centrifugal Compressor from Pressure by Combining EEMD and IMFE." Entropy 22, no. 4 (2020): 424. http://dx.doi.org/10.3390/e22040424.

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Based on entropy characteristics, some complex nonlinear dynamics of the dynamic pressure at the outlet of a centrifugal compressor are analyzed, as the centrifugal compressor operates in a stable and unstable state. First, the 800-kW centrifugal compressor is tested to gather the time sequence of dynamic pressure at the outlet by controlling the opening of the anti-surge valve at the outlet, and both the stable and unstable states are tested. Then, multi-scale fuzzy entropy and an improved method are introduced to analyze the gathered time sequence of dynamic pressure. Furthermore, the decomp

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49

Sen, Monoj Kumar, Alendu Baura, and Bidhan Chandra Bag. "Study of Thermodynamically Inspired Quantities for Both Thermal and External Colored Non-Gaussian Noises Driven Dynamical System." International Journal of Stochastic Analysis 2011 (July 10, 2011): 1–25. http://dx.doi.org/10.1155/2011/721352.

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We have studied dynamics of both internal and external noises-driven dynamical system in terms of information entropy at both nonstationary and stationary states. Here a unified description of entropy flux and entropy production is considered. Based on the Fokker-Planck description of stochastic processes and the entropy balance equation we have calculated time dependence of the information entropy production and entropy flux in presence and absence of nonequilibrium constraint (NEC). In the presence of NEC we have observed extremum behavior in the variation of entropy production as function o

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50

Grmela, M., V. Klika, and M. Pavelka. "Gradient and GENERIC time evolution towards reduced dynamics." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 378, no. 2170 (2020): 20190472. http://dx.doi.org/10.1098/rsta.2019.0472.

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Reduction of a mesoscopic dynamical theory to equilibrium thermodynamics brings to the latter theory the fundamental thermodynamic relation (i.e. entropy as a function of the thermodynamic state variables). The reduction is made by following the mesoscopic time evolution to its conclusion, i.e. to fixed points at which the time evolution ceases to continue. The approach to fixed points is driven by entropy, that, if evaluated at the fixed points, becomes the thermodynamic entropy. Since the fixed points are parametrized by the thermodynamic state variables (by constants of motion), the thermod

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