Abstract
We discuss the entropy of nonequilibrium steady states. We analyze the so-called spontaneous production of entropy in certain reversible deterministic nonequilibrium system, and its link with the collapse of such systems towards an attractor that is of lower dimension than the dimension of phase space. This means that in the steady state limit, the Gibbs entropy diverges to negative infinity. We argue that if the Gibbs entropy is expanded in a series involving 1, 2,... body terms, the divergence of the Gibbs entropy is manifest only in terms involving integrals whose dimension is higher than, approximately, the Kaplan–Yorke dimension of the steady state attractor. All the low order terms are finite and sum in the weak field limit to the local equilibrium entropy of linear irreversible thermodynamics.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
D. J. Evans and G. P. Morriss, Statistical Mechanics of Nonequilibrium Liquids (Academic Press, New York 1990); also, http://rsc.anu.edu.au/'evans/evansmorrissbook.htm.
S. Sarman, D. J. Evans, and P. T. Cummings, Physics Reports, M. J. Klein, ed. (Elsevier, 1998), 305(1-2):1.
G. Gallavotti, Physica D 105:163 (1997).
J. Vollmer, T. Tel, and W. Breymann, Phys. Rev. Lett. 79:2759 (1997).
L. Rondoni and E. Segre, Nonlinearity 12:1471 (1999).
G. M. Wang, E. M. Sevick, E. Mittag, D. J. Searles, and D. J. Evans, Experimental demonstration of violations of the second law of thermodynamics, Phys. Rev. Lett. (submitted).
S. Ciliberto and C. Laroche, J. Physique IV 8(6):215 (1998).
G. Ayton, D. J. Evans, and D. J. Searles, J. Chem. Phys. 115:2033 (2001).
D. J. Evans and D. J. Searles, Phys. Rev. E 50:1645 (1994).
J. W. Gibbs, Elementary Principles in Statistical Mechanics (Yale University Press, Boston, 1902).
B. D. Butler, G. Ayton, O. G. Jepps, and D. J. Evans, J. Chem. Phys. 109:6519–6522 (1998).
J. L. Kaplan and J. A. Yorke, Comm. Math. Phys. 67:93 (1979).
D. J. Evans, E. G. D. Cohen, D. J. Searles, and F. Bonetto, J. Stat. Phys. 101:17 (2000).
S. R. de Groot and P. Mazur, Non-Equilibrium Thermodynamics (Dover Pub., New York, 1984).
B. Moran and W. G. Hoover, J. Stat. Phys. 48:709 (1987).
J. Lloyd et al., Chaos 5(3):536 (1995).
E. G. D. Cohen and L. Rondoni, Chaos 8(2):357 (1998).
C. P. Dettmann and G. P. Morriss, Phys. Rev. E 54:4782 (1996).
Ch. Dellago et al., Phys. Rev. E 52(5):4817 (1995).
G. P. Morriss, C. P. Dettmann, and L. Rondoni, Physica A 240:84 (1997).
H. S. Green, The Molecular Theory of Fluids (North-Holland, Amsterdam, 1952); see also, H. J. Raveché, J. Chem. Phys. 55:2242 (1971).
A. Baranyai and D. J. Evans, Phys. Rev. A 40:3817 (1989).
A. Baranyai and D. J. Evans, Phys. Rev. A 42:849 (1990).
P. Gaspard, J. Stat. Phys. 88:1215 (1997). J. Vollmer, T. Tell, and W. Breymann, Phys. Rev. E 58:1672 (1998). J. Vollmer and W. Breymann, Phys. Rev. Lett. 79:2759 (1997). W. Breymann and J. Vollmer, Chaos 8:396 (1998).
T. Gilbert and J. R. Dorfman, J. Stat. Phys. 96:225 (1999).
L. Rondoni and E. G. D. Cohen, Nonlinearity 13:1905 (2000).
S. Goldstein, J. L. Lebowitz, and Ya. Sinai, Chaos 8(2):393 (1998).
D. J. Evans, E. G. D. Cohen, and G. P. Morriss, Phys. Rev. Lett. 71:2401–2404 (1993); Erratum, 71:3616 (1993).
G. Gallavotti and E. G. D. Cohen, Phys. Rev. Lett. 74:2694 (1995).
D. J. Searles and D. J. Evans, J. Chem. Phys. 113:3503–3509 (2000).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Evans, D.J., Rondoni, L. Comments on the Entropy of Nonequilibrium Steady States. Journal of Statistical Physics 109, 895–920 (2002). https://doi.org/10.1023/A:1020435219996
Issue Date:
DOI: https://doi.org/10.1023/A:1020435219996