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Journal articles on the topic 'Entropy production rate'

Author: Grafiati

Published: 4 June 2021

Last updated: 18 February 2022

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1

Garbet, X., N. Dubuit, E. Asp, Y. Sarazin, C. Bourdelle, P. Ghendrih, and G. T. Hoang. "Turbulent fluxes and entropy production rate." Physics of Plasmas 12, no. 8 (August 2005): 082511. http://dx.doi.org/10.1063/1.1951667.

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2

TOMINAGA, Akira. "Local Entropy Production Rate of Thermoacoustic Phenomena." TEION KOGAKU (Journal of the Cryogenic Society of Japan) 39, no. 2 (2004): 54–59. http://dx.doi.org/10.2221/jcsj.39.54.

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3

Izquierdo-Kulich, Elena, Esther Alonso-Becerra, and José M. Nieto-Villar. "Entropy Production Rate for Avascular Tumor Growth." Journal of Modern Physics 02, no. 06 (2011): 615–20. http://dx.doi.org/10.4236/jmp.2011.226071.

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4

Xing Xiu-San. "On the formula for entropy production rate." Acta Physica Sinica 52, no. 12 (2003): 2970. http://dx.doi.org/10.7498/aps.52.2970.

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5

Beretta, Gian Paolo. "Maximum entropy production rate in quantum thermodynamics." Journal of Physics: Conference Series 237 (June 1, 2010): 012004. http://dx.doi.org/10.1088/1742-6596/237/1/012004.

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6

Wolpert, David H. "Minimal entropy production rate of interacting systems." New Journal of Physics 22, no. 11 (November 13, 2020): 113013. http://dx.doi.org/10.1088/1367-2630/abc5c6.

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7

Li, Shu-Nan, and Bing-Yang Cao. "On Entropic Framework Based on Standard and Fractional Phonon Boltzmann Transport Equations." Entropy 21, no. 2 (February 21, 2019): 204. http://dx.doi.org/10.3390/e21020204.

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Generalized expressions of the entropy and related concepts in non-Fourier heat conduction have attracted increasing attention in recent years. Based on standard and fractional phonon Boltzmann transport equations (BTEs), we study entropic functionals including entropy density, entropy flux and entropy production rate. Using the relaxation time approximation and power series expansion, macroscopic approximations are derived for these entropic concepts. For the standard BTE, our results can recover the entropic frameworks of classical irreversible thermodynamics (CIT) and extended irreversible thermodynamics (EIT) as if there exists a well-defined effective thermal conductivity. For the fractional BTEs corresponding to the generalized Cattaneo equation (GCE) class, the entropy flux and entropy production rate will deviate from the forms in CIT and EIT. In these cases, the entropy flux and entropy production rate will contain fractional-order operators, which reflect memory effects.

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8

Christen, Thomas. "Modeling Electric Discharges with Entropy Production Rate Principles." Entropy 11, no. 4 (December 8, 2009): 1042–54. http://dx.doi.org/10.3390/e11041042.

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9

Lin, Tong-ling, Ying-ru Zhao, and Jin-can Chen. "Expressions for Entropy Production Rate of Fuel Cells." Chinese Journal of Chemical Physics 21, no. 4 (August 2008): 361–66. http://dx.doi.org/10.1088/1674-0068/21/04/361-366.

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10

Zhang, Fuxi, and Min Qian. "Entropy production rate of the minimal diffusion process." Acta Mathematica Scientia 27, no. 1 (January 2007): 145–52. http://dx.doi.org/10.1016/s0252-9602(07)60013-7.

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11

Bandi, M. M., W. I. Goldburg, and J. R. Cressman. "Measurement of entropy production rate in compressible turbulence." Europhysics Letters (EPL) 76, no. 4 (November 2006): 595–601. http://dx.doi.org/10.1209/epl/i2006-10333-0.

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12

Qian, Min, and Fuxi Zhang. "Entropy Production Rate of the Coupled Diffusion Process." Journal of Theoretical Probability 24, no. 3 (March 23, 2011): 729–45. http://dx.doi.org/10.1007/s10959-011-0352-9.

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13

Kleidon, A. "Entropy production by evapotranspiration and its geographic variation." Soil and Water Research 3, Special Issue No. 1 (June 30, 2008): S89—S94. http://dx.doi.org/10.17221/1192-swr.

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The hydrologic cycle is a system far from thermodynamic equilibrium that is characterized by its rate of entropy production in the climatological mean steady state. Over land, the hydrologic cycle is strongly affected by the presence of terrestrial vegetation. In order to investigate the role of the biota in the hydrologic cycle, it is critical to investigate the consequences of biotic effects from this thermodynamic perspective. Here I quantify entropy production by evapotranspiration with a climate system model of intermediate complexity and estimate its sensitivity to vegetation cover. For present-day conditions, the global mean entropy production of evaporation is 8.4 mW/m<sup>2</sup>/K, which is about 1/3 of the estimated entropy production of the whole hydrologic cycle. On average, ocean surfaces generally produce more than twice as much entropy as land surfaces. On land, high rates of entropy production of up to 16 mW/m<sup>2</sup>/K are found in regions of high evapotranspiration, although relative humidity of the atmospheric boundary layer is also an important factor. With an additional model simulation of a “Desert” simulation, where the effects of vegetation on land surface functioning is removed, I estimate the sensitivity of these entropy production rates to the presence of vegetation. Land averaged evapotranspiration decreases from 2.4 to 1.4 mm/d, while entropy production is reduced comparatively less from 4.2 to 3.1 mW/m<sup>2</sup>/K. This is related to the reduction in relative humidity of the atmospheric boundary layer as a compensatory effect, and points out the importance of a more complete treatment of entropy production calculations to investigate the role of biotic effects on Earth system functioning.

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14

Gibbins, Goodwin, and Joanna D. Haigh. "Entropy Production Rates of the Climate." Journal of the Atmospheric Sciences 77, no. 10 (October 1, 2020): 3551–66. http://dx.doi.org/10.1175/jas-d-19-0294.1.

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AbstractThere is ongoing interest in the global entropy production rate as a climate diagnostic and predictor, but progress has been limited by ambiguities in its definition; different conceptual boundaries of the climate system give rise to different internal production rates. Three viable options are described, estimated, and investigated here, two—the material and the total radiative (here “planetary”) entropy production rates—that are well established and a third that has only recently been considered but appears very promising. This new option is labeled the “transfer” entropy production rate and includes all irreversible processes that transfer heat within the climate, radiative, and material, but not those involved in the exchange of radiation with space. Estimates in three model climates put the material rate in the range 27–48 mW m−2 K−1, the transfer rate at 67–76 mW m−2 K−1, and the planetary rate at 1279–1312 mW m−2 K−1. The climate relevance of each rate is probed by calculating their responses to climate changes in a simple radiative–convective model. An increased greenhouse effect causes a significant increase in the material and transfer entropy production rates but has no direct impact on the planetary rate. When the same surface temperature increase is forced by changing the albedo instead, the material and transfer entropy production rates increase less dramatically and the planetary rate also registers an increase. This is pertinent to solar radiation management as it demonstrates the difficulty of reversing greenhouse gas–mediated climate changes by albedo alterations. It is argued that the transfer perspective has particular significance in the climate system and warrants increased prominence.

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15

Månsson, Bengt Å. G. "Entropy Production in Oscillating Chemical Systems." Zeitschrift für Naturforschung A 40, no. 9 (September 1, 1985): 877–84. http://dx.doi.org/10.1515/zna-1985-0903.

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Abstract The entropy production in oscillating homogenous chemical systems is investigated by analyzing the difference between the average entropy production rate in a stable periodic oscillatory mode and in the corresponding unstable stationary state. A general analytical expression for this difference in the neighborhood of a Hopf bifurcation is derived. The entropy production in two typical models of chemical systems with unstable stationary states and stable periodic oscillations is investigated, using fixed concentrations as control parameters. The models exemplify both positive and negative entropy production rate differences. One of the investigated models has four free concentrations, the other three. The rate expressions are given by second order mass action kinetics with reverse reactions taken into account. The flows of reactants and products are controlled so that only the free concentrations vary, and the entropy of mixing associated with these flows is discussed.

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16

Christen, Thomas. "Modelling diffusion in nonuniform solids using entropy production rate." Journal of Physics D: Applied Physics 40, no. 18 (August 30, 2007): 5723–26. http://dx.doi.org/10.1088/0022-3727/40/18/032.

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17

Mehrafarin, M. "Fluctuations and the quantization of the entropy production rate." Journal of Physics A: Mathematical and General 27, no. 17 (September 7, 1994): 5847–55. http://dx.doi.org/10.1088/0305-4470/27/17/017.

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18

Garbet, X., J. Abiteboul, E. Trier, Ö. Gürcan, Y. Sarazin, A. Smolyakov, S. Allfrey, et al. "Entropy production rate in tokamaks with nonaxisymmetric magnetic fields." Physics of Plasmas 17, no. 7 (July 2010): 072505. http://dx.doi.org/10.1063/1.3454365.

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19

Hase, M. O., and M. J. de Oliveira. "Irreversible spherical model and its stationary entropy production rate." Journal of Physics A: Mathematical and Theoretical 45, no. 16 (April 4, 2012): 165003. http://dx.doi.org/10.1088/1751-8113/45/16/165003.

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20

Gu, Wei Li, and Yuan Quan Liu. "Analysis on the Flow Process of Hot Oil in the Organic Heat Transfer Material Heater Based on Finite Time Thermodynamics." Advanced Materials Research 250-253 (May 2011): 2979–83. http://dx.doi.org/10.4028/www.scientific.net/amr.250-253.2979.

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Analyses the flow process of hot oil in the organic heat transfer material heater based on finite time thermodynamics for the first time, obtains the entropy production rate which includes entropy production rate of dissipation effect and entropy production rate of potential difference, analyses the influence of flow pattern, physical parameters, structure and operation of the organic heat transfer material heater on the entropy production rate of dissipation effect, illustrates the influence of related parameters including Renold number, velocity, viscosity and pipe diameter on the entropy production rate of dissipation effect, and points out the type of hot oil must be considered to decrease the entropy production rate of dissipation effect and the velocity must be control under the premise of avoiding overheat.

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21

Županović, Paško, Milan Brumen, Marko Jagodič, and Davor Juretić. "Bacterial chemotaxis and entropy production." Philosophical Transactions of the Royal Society B: Biological Sciences 365, no. 1545 (May 12, 2010): 1397–403. http://dx.doi.org/10.1098/rstb.2009.0307.

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Entropy production is calculated for bacterial chemotaxis in the case of a migrating band of bacteria in a capillary tube. It is found that the speed of the migrating band is a decreasing function of the starting concentration of the metabolizable attractant. The experimentally found dependence of speed on the starting concentration of galactose, glucose and oxygen is fitted with power-law functions. It is found that the corresponding exponents lie within the theoretically predicted interval. The effect of the reproduction of bacteria on band speed is considered, too. The acceleration of the band is predicted due to the reproduction rate of bacteria. The relationship between chemotaxis, the maximum entropy production principle and the formation of self-organizing structure is discussed.

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22

Borghesi, Giulio, and Josette Bellan. "Irreversible entropy production rate in high-pressure turbulent reactive flows." Proceedings of the Combustion Institute 35, no. 2 (2015): 1537–47. http://dx.doi.org/10.1016/j.proci.2014.05.016.

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23

Garbet, X., J. Abiteboul, Y. Sarazin, A. Smolyakov, S. Allfrey, V. Grandgirard, P. Ghendrih, G. Latu, and A. Strugarek. "Entropy production rate in tokamak plasmas with helical magnetic perturbations." Journal of Physics: Conference Series 260 (November 1, 2010): 012010. http://dx.doi.org/10.1088/1742-6596/260/1/012010.

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24

Itto, Yuichi. "Entropy production rate of diffusivity fluctuations under diffusing diffusivity equation." Journal of Physics: Conference Series 1391 (November 2019): 012054. http://dx.doi.org/10.1088/1742-6596/1391/1/012054.

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25

Qian, Min, Xuejuan Zhang, R. J. Wilson, and Jianfeng Feng. "Efficiency of Brownian motors in terms of entropy production rate." EPL (Europhysics Letters) 84, no. 1 (October 2008): 10014. http://dx.doi.org/10.1209/0295-5075/84/10014.

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26

Wang, Feng-Yu, Jie Xiong, and Lihu Xu. "Asymptotics of Sample Entropy Production Rate for Stochastic Differential Equations." Journal of Statistical Physics 163, no. 5 (April 7, 2016): 1211–34. http://dx.doi.org/10.1007/s10955-016-1513-0.

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27

Bensah, Yaw D., and JA Sekhar. "Morphological assessment with the maximum entropy production rate (MEPR) postulate." Current Opinion in Chemical Engineering 3 (February 2014): 91–98. http://dx.doi.org/10.1016/j.coche.2013.11.005.

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28

Li, Yuting I., and Michael E. Cates. "Steady state entropy production rate for scalar Langevin field theories." Journal of Statistical Mechanics: Theory and Experiment 2021, no. 1 (January 20, 2021): 013211. http://dx.doi.org/10.1088/1742-5468/abd311.

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29

Lindgren, Kristian, and Bengt Å. G. Månsson. "Entropy Production in a Chaotic Chemical System." Zeitschrift für Naturforschung A 41, no. 9 (September 1, 1986): 1111–17. http://dx.doi.org/10.1515/zna-1986-0904.

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The average rate of entropy production in a homogenous chemical system is investigated in oscillating periodic and chaotic modes as well as in coexisting stationary states. The simulations are based on an abstract model of a chemical reaction system with three freely varying concentrations. Five concentrations are assumed to be kept constant by suitable flows across the boundary. A fixed concentration is used as a control parameter. Second order mass action kinetics with reverse reaction is used. An unexpected result is that periodic modes in some windows in the chaotic interval have higher average rate of entropy production than the surrounding chaotic modes. A chaotic mode coexists with a stable stationary state with smaller entropy production. A unique (unstable) stationary state produces more entropy than the corresponding oscillating mode.

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30

Hou, Hucan, Yongxue Zhang, and Zhenlin Li. "A numerically research on energy loss evaluation in a centrifugal pump system based on local entropy production method." Thermal Science 21, no. 3 (2017): 1287–99. http://dx.doi.org/10.2298/tsci150702143h.

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Inspired by wide application of the second law of thermodynamics to flow and heat transfer devices, local entropy production analysis method was creatively introduced into energy assessment system of centrifugal water pump. Based on Reynolds stress turbulent model and energy equation model, the steady numerical simulation of the whole flow passage of one IS centrifugal pump was carried out. The local entropy production terms were calculated by user defined functions, mainly including wall entropy production, turbulent entropy production, and viscous entropy production. The numerical results indicated that the irreversible energy loss calculated by the local entropy production method agreed well with that calculated by the traditional method but with some deviations which were probably caused by high rotatability and high curvature of impeller and volute. The wall entropy production and turbulent entropy production took up large part of the whole entropy production about 48.61% and 47.91%, respectively, which indicated that wall friction and turbulent fluctuation were the major factors in affecting irreversible energy loss. Meanwhile, the entropy production rate distribution was discussed and compared with turbulent kinetic energy dissipation rate distribution, it showed that turbulent entropy production rate increased sharply at the near wall regions and both distributed more uniformly. The blade region in leading edge near suction side, trailing edge and volute tongue were the main regions to generate irreversible exergy loss. This research broadens a completely new view in evaluating energy loss and further optimizes pump using entropy production minimization.

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31

Li, Shu-Nan, and Bing-Yang Cao. "Fractional-order heat conduction models from generalized Boltzmann transport equation." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 378, no. 2172 (May 11, 2020): 20190280. http://dx.doi.org/10.1098/rsta.2019.0280.

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The relationship between fractional-order heat conduction models and Boltzmann transport equations (BTEs) lacks a detailed investigation. In this paper, the continuity, constitutive and governing equations of heat conduction are derived based on fractional-order phonon BTEs. The underlying microscopic regimes of the generalized Cattaneo equation are thereafter presented. The effective thermal conductivity κ eff converges in the subdiffusive regime and diverges in the superdiffusive regime. A connection between the divergence and mean-square displacement 〈|Δ x | 2 〉 ∼ t γ is established, namely, κ eff ∼ t γ −1 , which coincides with the linear response theory. Entropic concepts, including the entropy density, entropy flux and entropy production rate, are studied likewise. Two non-trivial behaviours are observed, including the fractional-order expression of entropy flux and initial effects on the entropy production rate. In contrast with the continuous time random walk model, the results involve the non-classical continuity equations and entropic concepts. This article is part of the theme issue ‘Advanced materials modelling via fractional calculus: challenges and perspectives’.

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32

Cocconi, Luca, Rosalba Garcia-Millan, Zigan Zhen, Bianca Buturca, and Gunnar Pruessner. "Entropy Production in Exactly Solvable Systems." Entropy 22, no. 11 (November 3, 2020): 1252. http://dx.doi.org/10.3390/e22111252.

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The rate of entropy production by a stochastic process quantifies how far it is from thermodynamic equilibrium. Equivalently, entropy production captures the degree to which global detailed balance and time-reversal symmetry are broken. Despite abundant references to entropy production in the literature and its many applications in the study of non-equilibrium stochastic particle systems, a comprehensive list of typical examples illustrating the fundamentals of entropy production is lacking. Here, we present a brief, self-contained review of entropy production and calculate it from first principles in a catalogue of exactly solvable setups, encompassing both discrete- and continuous-state Markov processes, as well as single- and multiple-particle systems. The examples covered in this work provide a stepping stone for further studies on entropy production of more complex systems, such as many-particle active matter, as well as a benchmark for the development of alternative mathematical formalisms.

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33

Meysman, Filip J. R., and Stijn Bruers. "Ecosystem functioning and maximum entropy production: a quantitative test of hypotheses." Philosophical Transactions of the Royal Society B: Biological Sciences 365, no. 1545 (May 12, 2010): 1405–16. http://dx.doi.org/10.1098/rstb.2009.0300.

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The idea that entropy production puts a constraint on ecosystem functioning is quite popular in ecological thermodynamics. Yet, until now, such claims have received little quantitative verification. Here, we examine three ‘entropy production’ hypotheses that have been forwarded in the past. The first states that increased entropy production serves as a fingerprint of living systems. The other two hypotheses invoke stronger constraints. The state selection hypothesis states that when a system can attain multiple steady states, the stable state will show the highest entropy production rate. The gradient response principle requires that when the thermodynamic gradient increases, the system's new stable state should always be accompanied by a higher entropy production rate. We test these three hypotheses by applying them to a set of conventional food web models. Each time, we calculate the entropy production rate associated with the stable state of the ecosystem. This analysis shows that the first hypothesis holds for all the food webs tested: the living state shows always an increased entropy production over the abiotic state. In contrast, the state selection and gradient response hypotheses break down when the food web incorporates more than one trophic level, indicating that they are not generally valid.

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34

Ge, Hao, Da-Quan Jiang, and Min Qian. "Reversibility and entropy production of inhomogeneous Markov chains." Journal of Applied Probability 43, no. 04 (December 2006): 1028–43. http://dx.doi.org/10.1017/s0021900200002400.

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In this paper we introduce the concepts of instantaneous reversibility and instantaneous entropy production rate for inhomogeneous Markov chains with denumerable state spaces. The following statements are proved to be equivalent: the inhomogeneous Markov chain is instantaneously reversible; it is in detailed balance; its entropy production rate vanishes. In particular, for a time-periodic birth-death chain, which can be regarded as a simple version of a physical model (Brownian motors), we prove that its rotation number is 0 when it is instantaneously reversible or periodically reversible. Hence, in our model of Markov chains, the directed transport phenomenon of Brownian motors can occur only in nonequilibrium and irreversible systems.

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35

Ge, Hao, Da-Quan Jiang, and Min Qian. "Reversibility and entropy production of inhomogeneous Markov chains." Journal of Applied Probability 43, no. 4 (December 2006): 1028–43. http://dx.doi.org/10.1239/jap/1165505205.

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In this paper we introduce the concepts of instantaneous reversibility and instantaneous entropy production rate for inhomogeneous Markov chains with denumerable state spaces. The following statements are proved to be equivalent: the inhomogeneous Markov chain is instantaneously reversible; it is in detailed balance; its entropy production rate vanishes. In particular, for a time-periodic birth-death chain, which can be regarded as a simple version of a physical model (Brownian motors), we prove that its rotation number is 0 when it is instantaneously reversible or periodically reversible. Hence, in our model of Markov chains, the directed transport phenomenon of Brownian motors can occur only in nonequilibrium and irreversible systems.

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36

Luchko, Yuri. "Entropy Production Rate of a One-Dimensional Alpha-Fractional Diffusion Process." Axioms 5, no. 1 (February 5, 2016): 6. http://dx.doi.org/10.3390/axioms5010006.

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37

de Koeijer, Gelein M., Signe Kjelstrup, Peter Salamon, Gino Siragusa, Markus Schaller, and Karl Heinz Hoffmann. "Comparison of Entropy Production Rate Minimization Methods for Binary Diabatic Distillation." Industrial & Engineering Chemistry Research 41, no. 23 (November 2002): 5826–34. http://dx.doi.org/10.1021/ie010872p.

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38

Jaramillo, J. D. Vasquez, and J. Fransson. "Charge Transport and Entropy Production Rate in Magnetically Active Molecular Dimer." Journal of Physical Chemistry C 121, no. 49 (November 30, 2017): 27357–68. http://dx.doi.org/10.1021/acs.jpcc.7b10350.

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39

Dixit, Purushottam D. "Entropy production rate as a criterion for inconsistency in decision theory." Journal of Statistical Mechanics: Theory and Experiment 2018, no. 5 (May 25, 2018): 053408. http://dx.doi.org/10.1088/1742-5468/aac137.

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40

Monteoliva, Diana, and Juan Pablo Paz. "Decoherence and the Rate of Entropy Production in Chaotic Quantum Systems." Physical Review Letters 85, no. 16 (October 16, 2000): 3373–76. http://dx.doi.org/10.1103/physrevlett.85.3373.

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41

Ross, John, and Marcel O. Vlad. "Exact Solutions for the Entropy Production Rate of Several Irreversible Processes." Journal of Physical Chemistry A 109, no. 46 (November 2005): 10607–12. http://dx.doi.org/10.1021/jp054432d.

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42

Nieto-Villar, J. M., R. Quintana, and J. Rieumont. "Entropy Production Rate as a Lyapunov Function in Chemical Systems: Proof." Physica Scripta 68, no. 3 (January 1, 2003): 163–65. http://dx.doi.org/10.1238/physica.regular.068a00163.

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43

Kondepudi, Dilip, and Zachary Mundy. "Spontaneous Chiral Symmetry Breaking and Entropy Production in a Closed System." Symmetry 12, no. 5 (May 6, 2020): 769. http://dx.doi.org/10.3390/sym12050769.

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In this short article, we present a study of theoretical model of a photochemically driven, closed chemical system in which spontaneous chiral symmetry breaking occurs. By making all the steps in the reaction elementary reaction steps, we obtained the rate of entropy production in the system and studied its behavior below and above the transition point. Our results show that the transition is similar to a second-order phase transition with rate of entropy production taking the place of entropy and the radiation intensity taking the place of the critical parameter: the steady-state entropy production, when plotted against the incident radiation intensity, has a change in its slope at the critical point. Above the critical intensity, the slope decreases, showing that asymmetric states have lower entropy than the symmetric state.

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44

Skinner, Dominic J., and Jörn Dunkel. "Improved bounds on entropy production in living systems." Proceedings of the National Academy of Sciences 118, no. 18 (April 27, 2021): e2024300118. http://dx.doi.org/10.1073/pnas.2024300118.

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Living systems maintain or increase local order by working against the second law of thermodynamics. Thermodynamic consistency is restored as they consume free energy, thereby increasing the net entropy of their environment. Recently introduced estimators for the entropy production rate have provided major insights into the efficiency of important cellular processes. In experiments, however, many degrees of freedom typically remain hidden to the observer, and, in these cases, existing methods are not optimal. Here, by reformulating the problem within an optimization framework, we are able to infer improved bounds on the rate of entropy production from partial measurements of biological systems. Our approach yields provably optimal estimates given certain measurable transition statistics. In contrast to prevailing methods, the improved estimator reveals nonzero entropy production rates even when nonequilibrium processes appear time symmetric and therefore may pretend to obey detailed balance. We demonstrate the broad applicability of this framework by providing improved bounds on the energy consumption rates in a diverse range of biological systems including bacterial flagella motors, growing microtubules, and calcium oscillations within human embryonic kidney cells.

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45

Hoffmann, Karl, Kathrin Kulmus, Christopher Essex, and Janett Prehl. "Between Waves and Diffusion: Paradoxical Entropy Production in an Exceptional Regime." Entropy 20, no. 11 (November 16, 2018): 881. http://dx.doi.org/10.3390/e20110881.

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The entropy production rate is a well established measure for the extent of irreversibility in a process. For irreversible processes, one thus usually expects that the entropy production rate approaches zero in the reversible limit. Fractional diffusion equations provide a fascinating testbed for that intuition in that they build a bridge connecting the fully irreversible diffusion equation with the fully reversible wave equation by a one-parameter family of processes. The entropy production paradox describes the very non-intuitive increase of the entropy production rate as that bridge is passed from irreversible diffusion to reversible waves. This paradox has been established for time- and space-fractional diffusion equations on one-dimensional continuous space and for the Shannon, Tsallis and Renyi entropies. After a brief review of the known results, we generalize it to time-fractional diffusion on a finite chain of points described by a fractional master equation.

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46

Gibbins, Goodwin, and Joanna D. Haigh. "Comments on “Global and Regional Entropy Production by Radiation Estimated from Satellite Observations”." Journal of Climate 34, no. 9 (May 2021): 3721–28. http://dx.doi.org/10.1175/jcli-d-20-0685.1.

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AbstractA recent paper by Kato and Rose reports a negative correlation between the annual mean entropy production rate of the climate and the absorption of solar radiation in the CERES SYN1deg dataset, using the simplifying assumption that the system is steady in time. It is shown here, however, that when the nonsteady interannual storage of entropy is accounted for, the dataset instead implies a positive correlation; that is, global entropy production rates increase with solar absorption. Furthermore, this increase is consistent with the response demonstrated by an energy balance model and a radiative–convective model. To motivate this updated analysis, a detailed discussion of the conceptual relationship between entropy production, entropy storage, and entropy flows is provided. The storage-corrected estimate for the mean global rate of entropy production in the CERES dataset from all irreversible transfer processes is 81.9 mW m−2 K−1 and from only nonradiative processes is 55.2 mW m−2 K−1 (observations from March 2000 to February 2018).

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Danielewski, Marek. "Entropy Production and Stress–Deformation Effect on Interdiffusion." Defect and Diffusion Forum 323-325 (April 2012): 43–48. http://dx.doi.org/10.4028/www.scientific.net/ddf.323-325.43.

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A general, consistent with linear irreversible thermodynamics, theory of stress and elastic deformation during interdiffusion is shown. Special consideration is given to the entropy balance and its production rate during diffusion in Cu-Fe-Ni alloys. The entropy produced during diffusion does not depend on the reference frame and is always positive. The paper spans the gap between the Darken method, linear irreversible thermodynamics and treatments by Stephenson and Svoboda.

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Kostanovskiy, Alexandr V., and Margarita E. Kostanovskaya. "About definition of the local entropy rate of production in experiment of pulse electric heating." Izmeritel`naya Tekhnika, no. 3 (2020): 29–34. http://dx.doi.org/10.32446/0368-1025it.2020-3-29-34.

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Work is devoted to studying of a linear mode thermodynamic – a mode which is actively investigated now. One of the main concepts of a linear mode – local entropy rate of production. The purpose of given article consists in expansion of a circle of problems for which it is possible to calculate a local entropy rate of production, namely its definition, using the experimental “time-temperature” curves of heating/cooling. “Time-temperature” curves heating or cooling are widely used in non-stationary thermophysical experiments at studying properties of substances and materials: phase transitions of the first and second sort, a thermal capacity, thermal diffusivity. The quantitative substantiation of the formula for calculation of the local entropy rate of production in which it is used thermogram (change of temperature from time) which is received by a method of pulse electric heating is resulted. Initial time dependences of electric capacity and temperature are measured on the sample of niobium in a microsecond range simultaneously. Conformity of two dependences of the local entropy rate of production from time is shown: one is calculated under the known formula in which the brought electric capacity is used; another is calculated, using the thermogram.

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Lin, Zhi-Yuan, Wei Shen, Shan-He Su, and Jin-Can Chen. "The entropy production rate of double quantum-dot system with Coulomb coupling." Acta Physica Sinica 69, no. 13 (2020): 130501. http://dx.doi.org/10.7498/aps.69.20191879.

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Delali Bensah, Yaw, and J. A. Sekhar. "Solidification Morphology and Bifurcation Predictions with the Maximum Entropy Production Rate Model." Entropy 22, no. 1 (December 26, 2019): 40. http://dx.doi.org/10.3390/e22010040.

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The use of the principle of maximum entropy generation per unit volume is a new approach in materials science that has implications for understanding the morphological evolution during solid–liquid interface growth, including bifurcations with or without diffuseness. A review based on a pre-publication arXiv preprint is first presented. A detailed comparison with experimental observations indicates that the Maximum Entropy Production Rate-density model (MEPR) can correctly predict bifurcations for dilute alloys during solidification. The model predicts a critical diffuseness of the interface at which a plane-front or any other form of diffuse interface will become unstable. A further confidence test for the model is offered in this article by comparing the predicted liquid diffusion coefficients to those obtained experimentally. A comparison of the experimentally determined solute diffusion constant in dilute binary Pb–Sn alloys with those predicted by the various solidification instability models (1953–2011) is additionally discussed. A good predictability is noted for the MEPR model when the interface diffuseness is small. In comparison, the more traditional interface break-down models have low predictiveness.

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