Abstract
A new approach to stochastic thermodynamics is developed, in which the local equilibrium hypothesis is extended to incorporate the effect of fluctuations. A fluctuating entropy in the form of a random functional of the fluctuating state variables is introduced, whose balance equation allows to identify the stochastic entropy flux and stochastic entropy production. The statistical properties of these quantities are analyzed and illustrated on representative examples.
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References
S.R. de Groot, P. Mazur, Non-equilibrium Thermodynamics (Dover Publications, 2011)
P. Glansdorff, I. Prigogine, Thermodynamic Theory of Structure, Stability and Fluctuations (John Wiley & Sons, 1971)
F. Schlögl, Z. Phys. B 20, 177 (1975)
F. Schlögl, Z. Phys. 248, 446 (1971)
L. Jiu-Li, C. Van den Broeck, G. Nicolis, Z. Phys. B - Condensed Matter 56, 165 (1984)
C.Y. Mou, L. Jiu-li, G. Nicolis, J. Chem. Phys. 84, 7011 (1986)
M. Esposito, U. Harbola, S. Mukamel, Rev. Mod. Phys. 81, 1665 (2009)
H. Ge, Phys. Rev. E 80, 021137 (2009)
M. Santillán, H. Qian, Phys. Rev. E 83, 041130 (2011)
C. Van den Broeck, Proceedings of the International School “Enrico Fermi” 184, 155 (2013)
U. Seifert, Rep. Prog. Phys. 75, 126001 (2014)
L.D. Landau, E.M. Lifshitz, Fluid Mechanics (Pergamon Press, 1987)
C.W. Gardiner, Stochastic Methods, 4th ed., Springer Series in Synergetics 13 (2009)
D.T. Gillespie, Markov Processes: An Introduction for Physical Scientists (Academic Press, 1991)
N.G. van Kampen, Stochastic Processes in Physics and Chemistry, 3rd edn. (North-Holland, 2007)
H. Touchette, Phys. Rep. 478, 1 (2009)
G. Gallavotti, E.G.D. Cohen, Phys. Rev. Lett. 74, 2694 (1995)
P. Gaspard, J. Chem. Phys. 120, 8898 (2004)
R. Kubo, Rep. Prog. Phys. 29, 255 (1966)
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De Decker, Y., Garcia Cantú Ros, A. & Nicolis, G. Extended local equilibrium approach to stochastic thermodynamics. Eur. Phys. J. Spec. Top. 224, 947–968 (2015). https://doi.org/10.1140/epjst/e2015-02438-3
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DOI: https://doi.org/10.1140/epjst/e2015-02438-3