Entropy production: From open volume-preserving to dissipative systems

Journal of Statistical Physics

Volumn 96, Issue 1-2, 1999, Pages 225-269

  Gilbert, T ^a   Dorfman, J R ^a  

^a University of Maryland   (United States)

Author keywords

Deterministic diffusion; Entropy production; Nonequilibrium stationary states; SRB measure; Thermostated systems

Indexed keywords

EID: 0033164036     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1004576517254     Document Type: Article

References (31)

1. 1. W. G. Hoover, Molecular Dynamics (Springer-Verlag, Heidelberg, 1986).
2. 2. D. J. Evans and G. P. Morriss, Statistical Mechanics of Non-Equilibrium Fluids (Academic Press, London, 1990).
3. 3. N. I. Chernov, G. L. Eyink, J. L. Lebowitz, and Ya. G. Sinai, Steady state electric conductivity in the periodic Lorentz gas, Comm. Math. Phys. 154:569 (1993).
4. 4. D. Ruelle, Positivity of entropy production in nonequilibrium statistical mechanics, J. Stat. Phys. 85:1 (1996).
5. 5. W. Breymann, T. Tél, and J. Vollmer, Entropy production for open dynamical systems, Phys. Rev. Lett. 77:2945 (1996).
6. 6. C. P. Dettmann and G. P. Morriss, Hamiltonian formulation of the Gaussian isokinetic thermostat, Phys. Rev. E 54:2495 (1996).
7. 7. B. L. Holian, W. G. Hoover, and H. A. Posch, Resolution of Loschmidt's paradox: The origin of irreversible behavior in reversible atomistic dynamics, Phys. Rev. Lett. 59:10 (1987).
8. 8. W. G. Hoover, Reversible mechanics and time's arrow, Phys. Rev. A 37:252 (1988).
9. 9. H. A. Posch and W. G. Hoover, Lyapunov instability of dense Lennard-Jones fluids, Phys. Rev. A 38:473 (1988).
10. 10. D. J. Evans, E. G. D. Cohen, and G. P. Morriss, Viscosity of a simple fluid from its maximal Lyapunov exponents, Phys. Rev. A 42:5990 (1990).
11. 11. D. J. Evans, E. G. D. Cohen, and G. P. Morriss, Probability of second law violations in shearing steady states, Phys. Rev. Lett. 71:2401 (1993).
12. 12. A. Baranyai, D. J. Evans, and E. G. D. Cohen, Field dependent conductivity and diffusion in a two-dimensional Lorentz gas, J. Stat. Phys. 70:1085 (1993).
13. 13. G. Gallavotti and E. G. D. Cohen, Dynamical ensembles in nonequilibrium statistical mechanics, J. Stat. Phys. 84:899 (1995); G. Gallavotti and E. G. D. Cohen, Dynamical ensembles in stationary states, Phys. Rev. Lett. 74:2694 (1995).
14. 13. G. Gallavotti and E. G. D. Cohen, Dynamical ensembles in nonequilibrium statistical mechanics, J. Stat. Phys. 84:899 (1995); G. Gallavotti and E. G. D. Cohen, Dynamical ensembles in stationary states, Phys. Rev. Lett. 74:2694 (1995).
15. 14. L. Rondoni, and G. P. Morriss, Stationary nonequilibrium ensembles for thermostated systems, Phys. Rev. E 53:2143 (1996).
16. 15. J. R. Dorfman and H. van Beijeren, Dynamical systems theory and transport coefficients: A survey with applications to Lorentz gases, Physica A 240:12 (1997).
17. 16. J. R. Dorfman, An Introduction to Chaos in Nonequilibrium Statistical Mechanics (Cambridge University Press, Cambridge, 1999).
18. 17. S. R. de Groot and P. Mazur, Non-Equilibriuin Thermodynamics (North-Holland, Amsterdam, 1962), reprinted in (Dover Publications, New York, 1984).
19. 18. T. Tél, J. Vollmer, and W. Breymann, Transient chaos: the origin of transport in driven systems, Europhys. Lett. 35:659 (1996); J. Vollmer, T. Tél, and W. Breymann, Equivalence of irreversible entropy production in driven systems: an elementary chaotic map approach, Phys. Rev. Lett. 79:2759 (1997).
20. 18. T. Tél, J. Vollmer, and W. Breymann, Transient chaos: the origin of transport in driven systems, Europhys. Lett. 35:659 (1996); J. Vollmer, T. Tél, and W. Breymann, Equivalence of irreversible entropy production in driven systems: an elementary chaotic map approach, Phys. Rev. Lett. 79:2759 (1997).
21. 19. P. Gaspard, Entropy production in open, volume preserving systems, J. Stat. Phys. 89:1215 (1997). P. Gaspard, Chaos, Scattering, and Statistical Mechanics (Cambridge University Press, Cambridge, 1998).
22. 19. P. Gaspard, Entropy production in open, volume preserving systems, J. Stat. Phys. 89:1215 (1997). P. Gaspard, Chaos, Scattering, and Statistical Mechanics (Cambridge University Press, Cambridge, 1998).
23. 20. S. Tasaki and P. Gaspard, Fick's law and fractality of nonequilibrium stationary states in a reversible multibaker map, J. Stat. Phys. 81:935 (1995).
24. 21. R. C. Tolman, The Principles of Statistical Mechanics (Oxford, London, 1938), reprinted in (Dover Publications, New York, 1979).
25. 22. P. and T. Ehrenfest, The Conceptual Foundations of the Statistical Approach in Mechanics (Cornell University Press, Ithaca, 1959).
26. 23. J. Vollmer, T. Tél, and W. Breymann, Entropy balance in the presence of drift and diffusive currents: an elementary map approach, Phys. Rev. E 58:1672 (1998); J. Vollmer, T. Tél, and W. Breymann, Entropy Balance, Time Reversibility, and Mass Transport in Dynamical Systems, Chaos 8:396 (1998).
27. 23. J. Vollmer, T. Tél, and W. Breymann, Entropy balance in the presence of drift and diffusive currents: an elementary map approach, Phys. Rev. E 58:1672 (1998); J. Vollmer, T. Tél, and W. Breymann, Entropy Balance, Time Reversibility, and Mass Transport in Dynamical Systems, Chaos 8:396 (1998).
28. 24. Ya. G. Sinaï, Topics in Ergodic Theory, Princeton Mathematical Series, 44 (Princeton University Press, 1994, Princeton N.J.).
29. 25. S. Tasaki, T. Gilbert, and J. R. Dorfman, An analytic construction of the SRB measures for Baker-type maps, Chaos 8:424 (1998).
30. 26. T. Gilbert, C. Ferguson, and J. R. Dorfman, Field driven thermostated system: A non-linear multi-baker map, Phys. Rev. E 59:364 (1999).
31. 27. G. P. Morriss, C. P. Dettmann, and L. Rondoni, Recent results for the thermostated Lorentz gas, Physica A 240:84 (1997).