Abstract
Given a thermodynamic process which carries a system from one equilibrium state to another, we construct a quantity whose average, over an ensemble of microscopic realizations of the process, depends only on these end states, even if at intermediate times the system is out of equilibrium. This result (1) can be used to express the entropy difference between two equilibrium states in terms of an irreversible process connecting them, (2) leads to two statistical statements of the Clausius–Duhem inequality, and (3) can be generalized to situations in which the system begins and/or ends in nonequilibrium states.
REFERENCES
J. W. Gibbs, Elementary Principles in Statistical Mechanics (New York, 1902, Charles Scribner's Sons), Chapter XIII.
G. Crooks, “The Entropy Production Fluctuation Theorem and the Nonequilibrium Work Relation for Free Energy Differences, ” cond-mat/9901352, available from the Los Alamos preprint archives (http://xxx.lanl.gov).
D. J. Evans, E. G. D. Cohen, and G. P. Morriss, Phys. Rev. Lett. 71:2401 (1993).
G. Gallavotti and E. G. D. Cohen, J. Stat. Phys. 80:931 (1995); Phys. Rev. Lett. 74:2694 (1995).
L. D. Landau and E. M. Lifshitz, Statistical Physics, 3rd ed., Part 1, Chapter XII (Pergamon Press, Oxford, 1980).
C. Jarzynski, Phys. Rev. Lett. 78:2690 (1997); C. Jarzynski, Phys. Rev. E 56:5018 (1997); G. E. Crooks, J. Stat. Phys. 90:1481 (1998); C. Jarzynski, Acta Phys. Pol. B 29:1609 (1998); R. M. Neal, “Annealed Importance Sampling, ” Technical Report No. 9805 (revised), Dept. of Statistics, Toronto (1998).
D. J. Evans and D. J. Searles, Phys. Rev. E 50:1645 (1994).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Jarzynski, C. Microscopic Analysis of Clausius–Duhem Processes. Journal of Statistical Physics 96, 415–427 (1999). https://doi.org/10.1023/A:1004541004050
Issue Date:
DOI: https://doi.org/10.1023/A:1004541004050