Abstract
According to thermodynamics the irreversible entropy production of diffusive relaxation processes diverges at the boundary to the vacuum, i.e., to a state of vanishing particle density. By means of a multibaker map we point out that this divergence is not present in the spatially discrete dynamics, which brings forth the evolution equations of irreversible thermodynamics in the continuum limit. In addition, we show that the irreversible entropy production of relaxation towards a nonempty steady state is proportional to the decay rate of the thermodynamic system subjected to absorbing boundary conditions. This generalizes results of the escape rate formalism.
Similar content being viewed by others
REFERENCES
P. Gaspard and G. Nicolis, Phys. Rev. Lett. 65:1693 (1990).
J. R. Dorfman and P. Gaspard, Phys. Rev. E 51:28 (1995).
W. Breymann, T. Tél, and J. Vollmer, Phys. Rev. Lett. 77:2945 (1996).
P. Gaspard, Chaos, Scattering and Statistical Mechanics (Cambridge University Press, Cambridge, 1999).
J. W. Haus and K. W. Kehr, Phys. Rep. 150:263 (1987).
P. Brémaund, Markov Chains: Gibbs Fields, Monte Carlo Simulation, and Queues, Vol. 31, Texts in Applied Mathematics (Springer, New York, 1999).
T. Tél, in Directions in Chaos: Experimental Study and Characterization of Chaos, H. Bai-lin, ed. (World Scientific, Singapore, 1990), Vol. 3, pp. 149–211.
E. Ott and T. Tél, Chaos 3:417 (1993).
T. Tél, in StatPhys 19, H. Bai-lin, ed. (World Scientific, Singapore, 1996), pp. 346–62.
P. Gaspard, Phys. Rev. E 53:4379 (1996).
D. J. Evans and G. P. Morriss, Statistical Mechanics of Nonequilibrium Liquids (Academic Press, London, 1990).
N. I. Chernov, G. L. Eyink, J. L. Lebowitz, and Y. G. Sinai, Phys. Rev. Lett. 70:2209 (1993).
J. Vollmer, T. Tél, and W. Breymann, Phys. Rev. E 58:1672 (1998).
W. Breymann, T. Tél, and J. Vollmer, Chaos 8:396 (1998).
T. Tél and J. Vollmer, in Hard Ball Systems and the Lorentz Gas, D. Szász, ed. (Springer, Berlin, 2000), Vol. 101, Encyclopædia of Mathematical Sciences, pp. 367–420.
J. Vollmer, Physics Reports (2002), Habilitation Thesis, University Essen.
J. Vollmer, T. Tél, and W. Breymann, Phys. Rev. Lett. 79:2759 (1997).
P. Gaspard, J. Stat. Phys. 68:673 (1992).
S. Tasaki and P. Gaspard, J. Stat. Phys. 81:935 (1995).
T. Tél, J. Vollmer, and W. Breymann, Europhys. Lett. 35:659 (1996); to be published.
P. Gaspard, J. Stat. Phys. 88:1215 (1997).
P. Gaspard, Phys. A 240:54 (1997).
T. Gilbert and J. R. Dorfman, J. Stat. Phys. 96:225 (1999).
S. Tasaki and P. Gaspard, Theoretical Chemistry Accounts 102:385 (1999).
E. Hopf, Ergodentheorie (Springer, Berlin, 1937).
L. Mátyás, T. Tél, and J. Vollmer, Phys. Rev. E 62:349 (2000), also available at arXiv:chao-dyn/9912034.
F. Reif, Fundamentals of Statistical and Thermal Physics (McGraw-Hill, New York, 1965).
P. Gaspard and J. R. Dorfman, Phys. Rev. E 52:3525 (1995).
Z. Kaufmann, H. Lustfeld, A. Németh, and P. Szépfalusy, Phys. Rev. Lett. 78:4031 (1997).
Z. Kaufmann, Phys. Rev. E 59:6552 (1999).
J. Liggett, Fluid Mechanics (McGraw-Hill, New-York, 1994).
T. Gilbert, J. R. Dorfman, and P. Gaspard, Phys. Rev. Lett. 85:1606 (2000).
T. Gilbert, J. R. Dorfman, and P. Gaspard, Nonlinearity 14:239 (2001).
P. Gaspard, I. Claus, T. Gilbert, and J. R. Dorfman, Phys. Rev. Lett. 86:1506 (2001).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Vollmer, J., Mátyás, L. & Tél, T. Escape-Rate Formalism, Decay to Steady States, and Divergences in the Entropy-Production Rate. Journal of Statistical Physics 109, 875–893 (2002). https://doi.org/10.1023/A:1020483103158
Issue Date:
DOI: https://doi.org/10.1023/A:1020483103158