Dynamical ensembles in nonequilibrium statistical mechanics and their representations

Chaos

Volumn 8, Issue 2, 1998, Pages 374-383

  Rondoni, Lamberto ^a   Stöcker, Sabine ^a  

^a POLITECNICO DI TORINO   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039835378     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.166319     Document Type: Article

References (31)

1. D. J. Searles, D. J. Evans, and D. J. Isbister, "The number dependence of the maximum Lyapunov exponent," Physica A 240, 96 (1997).
2. D. Szasz, "Boltzmann's ergodic hypothesis, a conjecture for centuries?," Stud. Sci. Math. Hung. 31, 299 (1996).
3. J. P. Eckmann and D. Ruelle, "Ergodic theory of chaos and strange attractors," Rev. Mod. Phys. 57, 617 (1985).
4. G. P. Morriss, "The information dimension of the nonequilibrium distribution function," Phys. Lett. A 122, 236 (1987); G. P. Morriss, "The Lyapunov dimension of two-body planar Couette flow," Phys. Rev. A 37, 2118-2124 (1988); 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).
5. G. P. Morriss, "The information dimension of the nonequilibrium distribution function," Phys. Lett. A 122, 236 (1987); G. P. Morriss, "The Lyapunov dimension of two-body planar Couette flow," Phys. Rev. A 37, 2118-2124 (1988); 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).
6. G. P. Morriss, "The information dimension of the nonequilibrium distribution function," Phys. Lett. A 122, 236 (1987); G. P. Morriss, "The Lyapunov dimension of two-body planar Couette flow," Phys. Rev. A 37, 2118-2124 (1988); 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).
7. G. Gallavotti and E. G. D. Cohen, "Dynamical ensembles in stationary states," J. Stat. Phys. 80, 931 (1995).
8. C. Grebogi, E. Ott, and J. A. Yorke, "Unstable periodic orbits and the dimension of multifractal chaotic attractors," Phys. Rev. A 37(5), 1711 (1988).
9. D. Ruelle, Elements of Differentiable Dynamics and Bifurcation Theory (Academic, New York, 1989).
10. Ya. G. Sinai, in Dynamical systems II (Springer-Verlag, Berlin, 1989).
11. R. Bowen, "Markov partitions for axiom A diffeomorphisms," Am. J. Math. 92, 725 (1970); On Axiom A Diffeomorphisms, CBMS Regional Conference Series in Mathematics (American Mathematical Society, Providence, 1978), Vol. 35.
12. R. Bowen, "Markov partitions for axiom A diffeomorphisms," Am. J. Math. 92, 725 (1970); On Axiom A Diffeomorphisms, CBMS Regional Conference Series in Mathematics (American Mathematical Society, Providence, 1978), Vol. 35.
13. W. Parry, "Synchronisation of canonical measures for hyperbolic attractors," Commun. Math. Phys. 106, 267 (1986).
14. R. Artuso, E. Aurell, and P. Cvitanovic, "Recycling of strange sets: I. Cycle expansions," Nonlinearity 3, 325 (1990); "Recycling of strange sets: II. Applications," Nonlinearity 3, 361 (1990).
15. R. Artuso, E. Aurell, and P. Cvitanovic, "Recycling of strange sets: I. Cycle expansions," Nonlinearity 3, 325 (1990); "Recycling of strange sets: II. Applications," Nonlinearity 3, 361 (1990).
16. D. J. Evans, E. G. D. Cohen, and G. P. Morriss, "Probability of second law violations in shearing steady flows," Phys. Rev. Lett. 71, 2401 (1993).
17. G. Gallavotti, "Extension of Onsagers reciprocity to large fields and the chaotic hypothesis," Phys. Rev. Lett. 789, 434 (1996); G. Gallavotti and D. Ruelle, "SRB states and non equilibrium statistical mechanics," archived in mp_arc@math.utexas.edu, #96-645, 1996.
18. G. Gallavotti, "Extension of Onsagers reciprocity to large fields and the chaotic hypothesis," Phys. Rev. Lett. 789, 434 (1996); G. Gallavotti and D. Ruelle, "SRB states and non equilibrium statistical mechanics," archived in mp_arc@math.utexas.edu, #96-645, 1996.
19. T. Yamada and K. Kawasaki, Prog. Theor. Phys. 38, 1031 (1967).
20. D. J. Evans and D. J. Searles, "Steady states, invariant measures, and response theory," Phys. Rev. E 52, 5839 (1995).
21. E. Ott and T. Tel, "Chaotic scattering: An introduction," Chaos 3, 417 (1993).
22. T. Tel, "On the organization of transient chaos - application to irregular scattering," J. Phys. A 22, L691 (1989).
23. P. Gaspard and J. R. Dorfman, "Chaotic scattering theory, thermodynamic formalism, and transport coefficients," Phys. Rev. E 52, 3525 (1995).
24. Z. Kovacs (private communication).
25. G. P. Morriss and L. Rondoni, "Equivalence of 'nonequilibrium' ensembles for simple maps," Physica A 233, 767 (1996).
26. G. P. Morriss and L. Rondoni, "Periodic orbit expansions for the Lorentz gas," J. Stat. Phys. 75, 553 (1994).
27. C. P. Dettmann and G. P. Morriss, "Stability ordering of cycle expansions," Phys. Rev. Lett. 78, 4201 (1997).
28. D. Ruelle, "Positivity of entropy production in nonequilibrium statistical mechanics," J. Stat. Phys. 85, 1 (1996).
29. L. Rondoni and G. P. Morriss, "Applications of periodic orbit theory to N-particle systems," J. Stat. Phys. 86, 991 (1997).
30. L. Rondoni and E. G. D. Cohen, "Orbital measures in non-equilibrium statistical mechanics: the Onsager relations," archived in chao-dyn/ 9708019.
31. E. G. D. Cohen and L. Rondoni, "Note on phase space contraction and entropy production in thermostatted Hamiltonian systems," Chaos 8, 357 (1998).