Note on phase space contraction and entropy production in thermostatted hamiltonian systems

Chaos

Volumn 8, Issue 2, 1998, Pages 357-365

  Cohen, E G D ^a   Rondoni, L ^b  

^a ROCKEFELLER UNIVERSITY   (United States)

^b POLITECNICO DI TORINO   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000164823     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.166317     Document Type: Article

References (27)

1. D. Ruelle, "Positivity of entropy production in nonequilibrium statistical mechanics," J. Stat. Phys. 85, 1 (1996).
2. L. Rondoni and G. P. Morris, "Applications of periodic orbit theory to N-particle systems," J. Stat. Phys. 86, 991 (1997).
3. L. Rondoni and E. G. D. Cohen, "Orbital measures in nonequi ibrium statistical mechanics: the Onsager relations," archived in http:// xxx.lanl.gov/chao-dyn #9708019.
4. G. Gallavotti and D. Ruelle, "SRB states and nonequilibrium statistical mechanics," archived in mp_arc@math.utexas.edu, #96-645.
5. G. Gallavotti, "Chaotic hypothesis: Onsager reciprocity and fluctuation dissipation theorem," J. Stat. Phys. 84, 899 (1996).
6. G. Gallavotti, "Extension of Onsager's reciprocity to large fields and the chaotic hypothesis," Phys. Rev. Lett. 78, 4334 (1996).
7. D. Szasz, "Boltzmann's ergodic hypothesis, a conjecture for centuries?" Studia Sci. Math. Hungarica 31, 299 (1996).
8. K. F. Gauss, "Über ein neues allgemeines Grundgesetz der Mechanik," J. Reine Angew Math. IV, 232 (1829).
9. D. J. Evans and G. P. Morriss, Statistical Mechanics of Nonequilibrium Liquids (Academic, London, 1990).
10. 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).
11. G. P. Morriss and L. Rondoni, "Periodic orbit expansions for the Lorentz gas," J. Stat. Phys. 75, 553 (1994).
12. L. Rondoni and S. Stöcker (in preparation).
13. N. I. Chernov, G. L. Eyink, J. L. Lebowitz, and Ya. Sinai, "Steady state electric conductivity in the periodic Lorentz gas," Commun. Math. Phys. 154, 569 (1993).
14. J. Lloyd, M. Niemeyer, L. Rondoni, and G. P. Morriss, "The nonequilibrium Lorentz gas," Chaos 5, 536 (1995).
15. F. Bonetto, G. Gallavotti, and P. L. Garrido, "Chaotic principle: an experimental test," Physica D 105, 226 (1997).
16. P. Gaspard, "Hydrodynamic modes as singular eigenstates of the Liouvillian dynamics: Deterministic diffusion," Phys. Rev. E 53, 4399 (1996).
17. L. Casetti, M. Cerruti-Sola, M. Pettini, and E. G. D. Cohen, "The Fermi-Pasta-Ulam problem revisited," Phys. Rev. E 55, 6566 (1997).
18. S. Tasaki and P. Gaspard, J. Stat. Phys. 81, 935 (1995).
19. T. Tel, J. Vollmer, and W. Breymann, "Transient Chaos: the origin of transport in driven systems," Europhys. Lett. 35, 659 (1996); W. Breymann, T. Tel, and J. Vollmer, "Entropy production in open dynamics systems," Phys. Rev. Lett. 77, 2945 (1996).
20. T. Tel, J. Vollmer, and W. Breymann, "Transient Chaos: the origin of transport in driven systems," Europhys. Lett. 35, 659 (1996); W. Breymann, T. Tel, and J. Vollmer, "Entropy production in open dynamics systems," Phys. Rev. Lett. 77, 2945 (1996).
21. D. J. Evans and S. Sarman, "Equivalence of thermostatted nonlinear responses," Phys. Rev. E 48, 65 (1993); D. J. Evans, "The equivalence of Norton and Thevenin ensembles," Mol. Phys. 80, 221 (1993); G. Gallavotti, "Ergodicity, ensembles, irreversibility in Boltzmann and beyond," J. Stat. Phys. 78, 1571 (1995); G. Gallavotti and E. G. D. Cohen, "Dynamical ensembles in stationary states," ibid. 80, 931 (1995); L. Rondoni and G. P. Morriss, "Equivalence of 'nonequilibrium' ensembles for simple maps," Physica A 233, 767 (1996); G. Gallavotti, "Dynamical ensemble equivalence in fluid mechanics," archived in chao-dyn/ 9605006; G. Gallavotti, "New methods in nonequilibrium gases and fluids," archived in mp_arc 96-533.
22. D. J. Evans and S. Sarman, "Equivalence of thermostatted nonlinear responses," Phys. Rev. E 48, 65 (1993); D. J. Evans, "The equivalence of Norton and Thevenin ensembles," Mol. Phys. 80, 221 (1993); G. Gallavotti, "Ergodicity, ensembles, irreversibility in Boltzmann and beyond," J. Stat. Phys. 78, 1571 (1995); G. Gallavotti and E. G. D. Cohen, "Dynamical ensembles in stationary states," ibid. 80, 931 (1995); L. Rondoni and G. P. Morriss, "Equivalence of 'nonequilibrium' ensembles for simple maps," Physica A 233, 767 (1996); G. Gallavotti, "Dynamical ensemble equivalence in fluid mechanics," archived in chao-dyn/ 9605006; G. Gallavotti, "New methods in nonequilibrium gases and fluids," archived in mp_arc 96-533.
23. D. J. Evans and S. Sarman, "Equivalence of thermostatted nonlinear responses," Phys. Rev. E 48, 65 (1993); D. J. Evans, "The equivalence of Norton and Thevenin ensembles," Mol. Phys. 80, 221 (1993); G. Gallavotti, "Ergodicity, ensembles, irreversibility in Boltzmann and beyond," J. Stat. Phys. 78, 1571 (1995); G. Gallavotti and E. G. D. Cohen, "Dynamical ensembles in stationary states," ibid. 80, 931 (1995); L. Rondoni and G. P. Morriss, "Equivalence of 'nonequilibrium' ensembles for simple maps," Physica A 233, 767 (1996); G. Gallavotti, "Dynamical ensemble equivalence in fluid mechanics," archived in chao-dyn/ 9605006; G. Gallavotti, "New methods in nonequilibrium gases and fluids," archived in mp_arc 96-533.
24. D. J. Evans and S. Sarman, "Equivalence of thermostatted nonlinear responses," Phys. Rev. E 48, 65 (1993); D. J. Evans, "The equivalence of Norton and Thevenin ensembles," Mol. Phys. 80, 221 (1993); G. Gallavotti, "Ergodicity, ensembles, irreversibility in Boltzmann and beyond," J. Stat. Phys. 78, 1571 (1995); G. Gallavotti and E. G. D. Cohen, "Dynamical ensembles in stationary states," ibid. 80, 931 (1995); L. Rondoni and G. P. Morriss, "Equivalence of 'nonequilibrium' ensembles for simple maps," Physica A 233, 767 (1996); G. Gallavotti, "Dynamical ensemble equivalence in fluid mechanics," archived in chao-dyn/ 9605006; G. Gallavotti, "New methods in nonequilibrium gases and fluids," archived in mp_arc 96-533.
25. D. J. Evans and S. Sarman, "Equivalence of thermostatted nonlinear responses," Phys. Rev. E 48, 65 (1993); D. J. Evans, "The equivalence of Norton and Thevenin ensembles," Mol. Phys. 80, 221 (1993); G. Gallavotti, "Ergodicity, ensembles, irreversibility in Boltzmann and beyond," J. Stat. Phys. 78, 1571 (1995); G. Gallavotti and E. G. D. Cohen, "Dynamical ensembles in stationary states," ibid. 80, 931 (1995); L. Rondoni and G. P. Morriss, "Equivalence of 'nonequilibrium' ensembles for simple maps," Physica A 233, 767 (1996); G. Gallavotti, "Dynamical ensemble equivalence in fluid mechanics," archived in chao-dyn/ 9605006; G. Gallavotti, "New methods in nonequilibrium gases and fluids," archived in mp_arc 96-533.
26. D. J. Evans and S. Sarman, "Equivalence of thermostatted nonlinear responses," Phys. Rev. E 48, 65 (1993); D. J. Evans, "The equivalence of Norton and Thevenin ensembles," Mol. Phys. 80, 221 (1993); G. Gallavotti, "Ergodicity, ensembles, irreversibility in Boltzmann and beyond," J. Stat. Phys. 78, 1571 (1995); G. Gallavotti and E. G. D. Cohen, "Dynamical ensembles in stationary states," ibid. 80, 931 (1995); L. Rondoni and G. P. Morriss, "Equivalence of 'nonequilibrium' ensembles for simple maps," Physica A 233, 767 (1996); G. Gallavotti, "Dynamical ensemble equivalence in fluid mechanics," archived in chao-dyn/ 9605006; G. Gallavotti, "New methods in nonequilibrium gases and fluids," archived in mp_arc 96-533.
27. D. J. Evans and S. Sarman, "Equivalence of thermostatted nonlinear responses," Phys. Rev. E 48, 65 (1993); D. J. Evans, "The equivalence of Norton and Thevenin ensembles," Mol. Phys. 80, 221 (1993); G. Gallavotti, "Ergodicity, ensembles, irreversibility in Boltzmann and beyond," J. Stat. Phys. 78, 1571 (1995); G. Gallavotti and E. G. D. Cohen, "Dynamical ensembles in stationary states," ibid. 80, 931 (1995); L. Rondoni and G. P. Morriss, "Equivalence of 'nonequilibrium' ensembles for simple maps," Physica A 233, 767 (1996); G. Gallavotti, "Dynamical ensemble equivalence in fluid mechanics," archived in chao-dyn/ 9605006; G. Gallavotti, "New methods in nonequilibrium gases and fluids," archived in mp_arc 96-533.