The steady state fluctuation relation for the dissipation function

Journal of Statistical Physics

Volumn 128, Issue 6, 2007, Pages 1337-1363

  Searles, Debra J ^a   Rondoni, Lamberto ^b   Evans, Denis J ^c  

^a GRIFFITH UNIVERSITY   (Australia)

^b POLITECNICO DI TORINO   (Italy)

^c AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

Author keywords

Chaotic hypothesis; Correlation decay; Entropy production; Nonequilibrium phenomena; Time reversibility

Indexed keywords

EID: 34548555775     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-007-9372-3     Document Type: Article

References (57)

1. Evans, D.J., Searles, D.J.: The fluctuation theorem. Adv. Phys. 52, 1529-1585 (2002)
2. Searles, D.J., Evans, D.J.: Fluctuation relations for nonequilibrium systems. Aust. J. Chem. 57, 1119-1123 (2004)
3. Gallavotti, G.: Statistical Mechanics, a Short Treatise. Springer, Berlin (2000)
4. Bustamante, C., Liphardt, J., Ritort, F.: The nonequilibrium thermodynamics of small systems. Phys. Today 58, 43-48 (2005)
5. Evans, D.J., Searles, D.J., Rondoni, L.: Application of the Gallavotti-Cohen fluctuation relation to thermostatted steady states near equilibrium. Phys. Rev. E 71, 056120 (2005)
6. Evans, D.J., Cohen, E.G.D., Morriss, G.P.: Probability of second law violations in shearing steady states. Phys. Rev. Lett. 71, 2401-2404 (1993)
7. Parry, W.: Synchronisation of canonical measures for hyperbolic attractors. Commun. Math. Phys. 106, 267-275 (1986)
8. Vance, W.N.: Unstable periodic orbits and transport properties of nonequilibrium steady states. Phys. Rev. Lett. 69, 1356-1359 (1992)
9. Cvitanović, P., Artuso, R., Mainieri, R., Tanner, G., Vattay, G.: Chaos: Classical and Quantum, ChaosBook.org. Niels Bohr Institute, Copenhagen (2005)
10. Evans, D.J., Searles, D.J.: Equilibrium microstates which generate second law violating steady states. Phys. Rev. E 50, 1645-1648 (1994)
11. Evans, D.J., Searles, D.J.: Steady sates, invariant measures and response theory. Phys. Rev. E 52, 5839-5848 (1995)
12. Searles, D.J., Ayton, G., Evans, D.J.: Generalised fluctuation formula. AIP Conf. Ser. 519, 271-280 (2000)
13. Searles, D.J., Evans, D.J.: Ensemble dependence of the transient fluctuation theorem. J. Chem. Phys. 113, 3503-3509 (2000)
14. Searles, D.J., Evans, D.J.: Fluctuation theorem for heat flow. Int. J. Thermophys. 22, 123-124 (2001)
15. Williams, S.R., Searles, D.J., Evans, D.J.: Independence of the transient fluctuation theorem to thermostatting. Phys. Rev. E 70, 066113 (2004)
16. Williams, S.R., Searles, D.J., Evans, D.J.: Numerical study of the steady state fluctuation relations far from equilibrium. J. Chem. Phys. 124, 194102/1-9 (2006)
17. Gallavotti, G., Cohen, E.G.D.: Dynamical ensembles in stationary states. J. Stat. Phys. 80, 931-970 (1995)
18. Gallavotti, G., Cohen, E.G.D.: Dynamical ensembles in nonequilibrium statistical mechanics. Phys. Rev. Lett. 74, 2694-2697 (1995)
19. Gallavotti, G.: Reversible Anosov diffeomorphisms and large deviations. Math. Phys. Electron. J. 1, 1-12 (1995)
20. Gallavotti, G.: Fluctuation theorem revisited. arXiv:cond-mat/0404699 (2004).
21. Searles, D.J., Evans, D.J.: The fluctuation theorem for stochastic systems. Phys. Rev. E 60, 159-164 (1999)
22. Kurchan, J.: Fluctuation theorem for stochastic dynamics. J. Phys. A 31, 3719-3729 (1998)
23. Lebowitz, J.L., Spohn, H.: A Gallavotti-Cohen-type symmetry in the large deviation functional for stochastic dynamics. J. Stat. Phys. 95, 333-365 (1999)
24. Maes, C.: The fluctuation theorem as a Gibbs property. J. Stat. Phys. 95, 367-392 (1999)
25. van Zon, R., Cohen, E.G.D.: Extension of the fluctuation theorem. Phys. Rev. Lett. 91, 110601 (2003)
26. van Zon, R., Cohen, E.G.D.: Extended heat-fluctuation theorems for a system with deterministic and stochastic forces. Phys. Rev. E 69, 056121 (2004)
27. Gallavotti, G.: Dynamical ensembles equivalence in fluid mechanics. Physica D 105, 163-184 (1997)
28. Rondoni, L., Segre, E.: Fluctuations in two-dimensional reversibly damped turbulence. Nonlinearity 12, 1471-1487 (1999)
29. Gallavotti, G., Rondoni, L., Segre, E.: Lyapunov spectra and nonequilibrium ensembles equivalence in 2D fluid mechanics. Physica D 187, 338-357 (2004)
30. Gallavotti, G.: A local fluctuation theorem. Physica A 263, 39-50 (1999)
31. Rondoni, L., Tèl, T., Vollmer, J.: Fluctuation theorems for entropy production in open systems. Phys. Rev. E 61, R4679-R4682 (2000)
32. Ayton, G., Evans, D.J., Searles, D.J.: A local fluctuation theorem. J. Chem. Phys. 115, 2033-2037 (2001)
33. Zamponi, F., Ruocco, G., Angelani, L.: Fluctuations of entropy production in the isokinetic ensemble. J. Stat. Phys. 115, 1655-1668 (2004)
34. Giuliani, A., Zamponi, F., Gallavotti, G.: Fluctuation relation beyond linear response theory. J. Stat. Phys. 119, 909-944 (2005). Note that the fluctuation relation that is validated in these papers is the Ω-FR
35. Dolowschiak, M., Kovacs, Z.: Fluctuation formula in the Nosé-Hoover thermostated Lorentz gas. Phys. Rev. E 71, 025202 (2005)
36. Wang, G.M., Sevick, E.M., Mittag, E., Searles, D.J., Evans, D.J.: Experimental demonstration of violations of the second law of thermodynamics for small systems and short time scales. Phys. Rev. Lett. 89, 050601 (2002)
37. Garnier, N., Ciliberto, S.: Nonequilibrium fluctuations in a resistor. Phys. Rev. E 71, 060101 (2005)
38. Wang, G.M., Reid, J.C., Carberry, D.M., Williams, D.R.M., Sevick, E.M., Evans, D.J.: Experimental study of the fluctuation theorem in a nonequilibrium steady state. Phys. Rev. E 71, 046142 (2005)
39. Puglisi, A., Rondoni, L., Vulpiani, A.: Relevance of initial and final conditions for the fluctuation relation in Markov processes. J. Stat. Mech. 8, P08010 (2006)
40. Cohen, E.G.D., Gallavotti, G.: Note on two theorems in nonequilibrium statistical mechanics. J. Stat. Phys. 96, 1343-1349 (1999)
41. Evans, D.J., Morriss, G.P.: Statistical Mechanics of Nonequilibrium Liquids. Academic, London (1990)
42. Liem, S.Y., Brown, D., Clarke, J.H.R.: Investigation of the homogeneous-shear nonequilibrium-molecular-dynamics method. Phys. Rev. A 45, 3706-3713 (1992)
43. de Groot, S.R., Mazur, P.: Non-Equilibrium Thermodynamics. Dover, New York (1984)
44. Ruelle, D.: Smooth dynamics and new theoretical ideas in nonequilibrium statistical mechanics. J. Stat. Phys. 95, 393-468 (1999)
45. Khinchin, A.I.: Mathematical Foundations of Statistical Mechanics. Dover, New York (1949)
46. Jarzynski, C.: Nonequilibrium equality for free energy differences. Phys. Rev. Lett. 78, 2690-2693 (1997)
47. Crooks, G.E.: Path ensemble averages in systems driven far from equilibrium. Phys. Rev. E 61, 2361-2366 (2000)
48. Bonetto, F., Gallavotti, G.: Reversibility, coarse graining and the chaoticity principle. Commun. Math. Phys. 189, 263 (1997)
49. Bonetto, F., Gallavotti, G., Garrido, P.L.: Chaotic principle: an experimental test. Physica D 105, 226-252 (1997)
50. Bonetto, F., Gallavotti, G., Giuliani, A., Zamponi, F.: Chaotic hypothesis, fluctuation theorem and singularities. J. Stat. Phys. 123, 39-54 (2006)
51. Ruelle, D.: Conversations on nonequilibrium physics with an extraterrestrial. Phys. Today 57(5), 48-53 (2004)
52. Rondoni, L.: Deterministic thermostats and fluctuation relations. In: Garbaczewski, P., Olkiewicz, R. (eds.) Dynamics of Dissipation. Springer, Berlin (2002)
53. Evans, D.J., Morriss, G.: Nonlinear response theory for steady planar Couette flow. Phys. Rev. A 30, 1528-1530 (1984)
54. Evans, D.J., Searles, D.J., Rondoni, L.: in preparation
55. Giberti, C., Rondoni, L., Vernia, C.: Coexistence of chaotic and non-chaotic states in the two-dimensional Gauss-Navier-Stokes dynamics. Physica D 187, 358-369 (2004)
56. Gilbert, T.: Fluctuation theorem applied to the Nosé-Hoover thermostatted Lorentz gas. Phys. Rev. E 73, 035102 (2006)
57. Evans, D.J., Searles, D.J.: Nonlinear response theory and the fluctuation theorem. J. Chem. Phys. (2007, submitted), http://arxiv.org/abs/cond-mat/ 0612105