Positivity of entropy production in the presence of a random thermostat

Journal of Statistical Physics

Volumn 86, Issue 5-6, 1997, Pages 935-951

  Ruelle, David ^a,b  

^a INSTITUT DES HAUTES ÉTUDES SCIENTIFIQUES   (France)

^b RUTGERS UNIVERSITY   (United States)

Author keywords

Entropy production; Nonequilibrium stationary state; Nonequilibrium statistical mechanics; Random dynamics; SRB state; Thermostat

Indexed keywords

EID: 0031092587     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02183609     Document Type: Article

References (20)

1. J. Bahnmüller, Pesin's entropy formula for random dynamical systems, preprint.
2. J. Bahnmüller and Th. Bogenschütz, A Margulis-Ruelle inequality for random dynamical systems, Arch. Math. 64:246-253 (1995).
3. Th. Bogenschütz, Entropy, pressure, and a variational principle for random dynamical systems, Random Comput. Dynam. 1:219-227 (1992).
4. N. I. Chernov, G. L. Eyink, J. L. Lebowitz, and Ya. G. Sinai, Steady-state electrical conduction in the periodic Lorentz gas, Commun. Math. Phys. 154:569-601 (1993).
5. G. Gallavotti and E. G. D. Cohen, Dynamical ensembles in nonequilibrium statistical mechanics, Phys. Rev. Lett. 74:2694-2697 (1995); dynamical ensembles in stationary states, J. Statist. Phys. 80:931-970 (1995).
6. G. Gallavotti and E. G. D. Cohen, Dynamical ensembles in nonequilibrium statistical mechanics, Phys. Rev. Lett. 74:2694-2697 (1995); dynamical ensembles in stationary states, J. Statist. Phys. 80:931-970 (1995).
7. J. Hoffmann-Jørgensen, The Theory of Analytic Spaces (Aarhus, 1970).
8. V. Jakšić and C.-A. Pillet. Return to equilibrium in classical mechanics (preprint).
9. Yu. Kifer, Ergodic Theory of Random Transformations (Birkhäuser, Boston, 1986).
10. Yu. Kifer, Random Perturbations of Dynamical Systems (Birkhäuser, Boston, 1988).
11. J. L. Lebowitz, Boltzmann's entropy and time's arrow, Phys. Today 46(9):32-38 (1993).
12. K. Ledrappier and J.-M. Strelcyn, A proof of the estimation from below in Pesin's entropy formula, Ergod. Theory Dynam. Syst. 2:203-219 (1982).
13. F. Ledrappier and L. S. Young, The metric entropy of diffeomorphisms: I. Characterization of measures satisfying Pesin's formula, II. Relations between entropy, exponents and dimension, Ann. Math. 122:509-539, 540-574 (1985).
14. F. Ledrappier and L. S. Young, Entropy formula for random transformations, Prob. Theory Related Fields 80:217-240 (1988).
15. Liu Pei-Dong, Entropy formula for random dynamical systems, preprint.
16. Liu Pei-Dong and Qian Min, Smooth Ergodic Theory of Random Dynamical Systems (Springer, Berlin, 1995).
17. V. A. Rohlin, On the fundamental ideas of measure theory, AMS Transl. (1) 10:1-52 (1962).
18. D. Ruelle, Ergodic theory of dynamical systems, Publ. Math. IHES 50:27-58 (1979).
19. D. Ruelle, An inequality for the entropy of differentiable maps, Bol. Soc. Bras. Mat. 9:83-87 (1978).
20. D. Ruelle, Positivity of entropy production in nonequilibrium statistical mechanics, J. Stat. Phys. 85:1-23 (1996).