Is it possible to experimentally verify the fluctuation relation? A review of theoretical motivations and numerical evidence

Journal of Statistical Mechanics: Theory and Experiment

Volumn , Issue 2, 2007, Pages

  Zamponi, Francesco ^a  

^a CEA SACLAY   (France)

Author keywords

Stationary states (theory); Transport processes heat transfer (experiment); Transport processes heat transfer (theory)

Indexed keywords

EID: 42749105071     PISSN: 17425468     EISSN: 17425468     Source Type: Journal    
DOI: 10.1088/1742-5468/2007/02/P02008     Document Type: Article

References (79)

1. Evans D J, Cohen E G D and Morriss G 1993 Probability of second law violations in shearing steady flows Phys. Rev. Lett. 70 2401
2. Ciliberto S and Laroche C 1998 An experimental test of the Gallavotti-Cohen fluctuation theorem J. Physique IV 8 Pr6-215
3. Ciliberto S, Garnier N, Hernandez S, Lacpatia C, Pinton J F and Ruiz Chavarria G 2004 Experimental test of the Gallavotti-Cohen fluctuation theorem in turbulent flows Physica A 340 240
4. Bandi M M, Cressman J R Jr and Goldburg W I 2006 Test of the fluctuation relation in compressible turbulence on a free surface Preprint nlin.CD/0607037
5. Shang X-D, Tong P and Xia K-Q 2005 Test of steady-state fluctuation theorem in turbulent Rayleigh-Bénard convection Phys. Rev. E 72 015301
6. Goldburg W I, Goldschmidt Y Y and Kellay H 2001 Fluctuation and dissipation in liquid-crystal electroconvection Phys. Rev. Lett. 87 245502
7. Garnier N and Ciliberto S 2005 Nonequilibrium fluctuations in a resistor Phys. Rev. Lett. 71 060101
8. Feitosa K and Menon N 2004 A fluidized granular medium as an instance of the fluctuation theorem Phys. Rev. Lett. 92 164301
9. Eckmann J-P and Ruelle D 1985 Ergodic theory of chaos and strange attractors Rev. Mod. Phys. 57 617
10. Cvitanović P 2006 Chaos: classical and quantum online at http://chaosbook.dk
11. Sinai Y G 1968 Markov partitions and C-diffeomorphisms Funct. Anal. Appl. 2 64
12. Sinai Y G 1968 Construction of Markov partitions Funct. Anal. Appl. 2 70
13. Bowen R and Ruelle D 1975 The ergodic theory of axiom A flows Inventiones Math. 29 181
14. Ruelle D 1976 A measure associated with axiom A attractors Am. J. Math. 98 619
15. Sinai Y G 1977 Lectures in Ergodic Theory (Lecture Notes in Mathematics) (Princeton, NJ: Princeton University Press)
16. Ruelle D 1978 Thermodynamic Formalism (Reading, MA: Addison Wesley)
17. Gallavotti G and Cohen E G D 1995 Dynamical ensembles in nonequilibrium statistical mechanics Phys. Rev. Lett. 74 2694
18. Gallavotti G and Cohen E G D 1995 Dynamical ensembles in stationary states J. Stat. Phys. 80 931
19. Gallavotti G 1995 Reversible Anosov diffeomorphisms and large deviations Math. Phys. Electron. J. 1 1
20. Ruelle D 1995 Turbulence, Strange Attractors and Chaos (New York: World Scientific)
21. Ruelle D 1999 Smooth dynamics and new theoretical ideas in non-equilibrium statistical mechanics J. Stat. Phys. 95 393
22. Gallavotti G 2000 Statistical Mechanics. A Short Treatise (Berlin: Springer)
23. Gallavotti G 2002 Foundations of Fluid Dynamics (Berlin: Springer)
24. Gallavotti G, Bonetto F and Gentile G 2004 Aspects of the Ergodic, Qualitative and Statistical Theory of Motion (Berlin: Springer)
25. Ruelle D 2004 Conversations on nonequilibriun physics with an extraterrestrial Phys. Today (May) 48
26. Gallavotti G 1995 Ergodicity, ensembles, irreversibility in Boltzmann and beyond J. Stat. Phys. 78 1571
27. Gallavotti G 2006 Entropy, nonequilibrium, chaos and infinitesimals Preprint cond-mat/0606477
28. Ruelle D 1996 Positivity of entropy production in nonequilibrium statistical mechanics J. Stat. Phys. 85 1
29. Gallavotti G 1996 Extension of Onsager's reciprocity to large fields and the chaotic hypothesis Phys. Rev. Lett. 77 4334
30. Gallavotti G 1996 Chaotic hypothesis: Onsager reciprocity and fluctuation-dissipation theorem J. Stat. Phys. 84 899
31. Evans D J and Searles D J 1994 Equilibrium microstates which generate second law violating steady states Phys. Rev. E 50 1645
32. Evans D J and Searles D J 2002 The fluctuation theorem Adv. Phys. 51 1529
33. Cohen E G D and Gallavotti G 1999 Note on two theorems in nonequilibrium statistical mechanics J. Stat. Phys. 96 1343
34. Gentile G 1998 A large deviation theorem for Anosov flows Forum Math. 10 89
35. Kurchan J 1998 Fluctuation theorem for stochastic dynamics J. Phys. A: Math. Gen. 31 3719
36. Puglisi A, Rondoni L and Vulpiani A 2006 Relevance of initial and final conditions for the fluctuation relation in Markov processes J. Stat. Mech. P08010
37. Lebowitz J and Spohn H 1999 A Gallavotti-Cohen type symmetry in large deviation functional for stochastic dynamics J. Stat. Phys. 95 333
38. Maes C 1999 The fluctuation theorem as a Gibbs property J. Stat. Phys. 95 367
39. Crooks G E 1999 Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences Phys. Rev. E 60 2721
40. Bertini L, De Sole A, Gabrielli D, Jona-Lasinio G and Landim C 2001 Fluctuations in stationary nonequilibrium states of irreversible processes Phys. Rev. Lett. 87 040601
41. Bertini L, De Sole A, Gabrielli D, Jona-Lasinio G and Landim C 2005 Current fluctuations in stochastic lattice gases Phys. Rev. Lett. 94 030601
42. Derrida B, Lebowitz J L and Speer E R 2002 Exact free energy functional for a driven diffusive open stationary nonequilibrium system Phys. Rev. Lett. 89 030601
43. Depken M 2002 On the Gallavotti-Cohen symmetry for stochastic systems Preprint cond-mat/0209284
44. Bonetto F and Gallavotti G 1997 Reversibility, coarse graining and the chaoticity principle Commun. Math. Phys. 189 263
45. Gallavotti G 1999 New methods in nonequilibrium gases and fluids Open Syst. Inf. Dyn. 6 101
46. Zamponi F, Bonetto F, Cugliandolo L F and Kurchan J 2005 A fluctuation theorem for non-equilibrium relaxational systems driven by external forces J. Stat. Mech. P09013
47. Gallavotti G 2006 Microscopic chaos and macroscopic entropy in fluids J. Stat. Mech. P10011
48. Zamponi F, Ruocco G and Angelani L 2004 Fluctuations of entropy production in the isokinetic ensemble J. Stat. Phys. 115 1655
49. Giuliani A, Zamponi F and Gallavotti G 2005 Fluctuation relation beyond linear response theory J. Stat. Phys. 119 909
50. Kubo R 1957 Statistical-mechanical theory of irreversible processes. I. general theory and simple applications to magnetic and conduction problems J. Phys. Soc. Japan 12 570
51. Evans D J and Morriss G P 1990 Statistical Mechanics of Nonequilibrium Fluids (New York: Academic)
52. de Groot S and Mazur P 1984 Non Equilibrium Thermodynamics (New York: Dover)
53. Bonetto F, Gallavotti G and Garrido P 1997 Chaotic principle: an experimental test Physica D 105 226
54. Bonetto F, Chernov N I and Lebowitz J L 1998 (Global and local) fluctuations of phase space contraction in deterministic stationary non-equilibrium Chaos 8 823
55. Rondoni L and Morriss G P 2003 Large fluctuations and axiom-C structures in deterministically thermostatted systems Open Syst. Inf. Dyn. 10 105
56. Biferale L, Pierotti D and Vulpiani A 1998 Time-reversible dynamical systems for turbulence J. Phys. A: Math. Gen. 31 21
57. Rondoni L and Segre E 1999 Fluctuations in two-dimensional reversibly damped turbulence Nonlinearity 12 1471
58. Gallavotti G, Rondoni L and Segre E 2004 Lyapunov spectra and nonequilibrium ensembles equivalence in 2d fluid Physica D 187 358
59. Giardin C, Kurchan J and Peliti L 2006 Direct evaluation of large-deviation functions Phys. Rev. Lett. 96 120603
60. Evans D J, Searles D J and Rondoni L 2005 Application of the Gallavotti-Cohen fluctuation relation to thermostated steady states near equilibrium Phys. Rev. E 71 056120
61. Farago J 2002 Injected power fluctuations in Langevin equation J. Stat. Phys. 107 781
62. Van Zon R and Cohen E G D 2003 Extension of the fluctuation theorem Phys. Rev. Lett. 91 110601
63. Bonetto F, Gallavotti G, Giuliani A and Zamponi F 2006 Chaotic hypothesis, fluctuation theorem and singularities J. Stat. Phys. 123 39
64. Van Zon R and Cohen E G D 2004 Extended heat-fluctuation theorems for a system with deterministic and stochastic forces Phys. Rev. E 69 056121
65. Visco P, Puglisi A, Barrat A, Trizac E and van Wijland F 2006 Fluctuations of power injection in randomly driven granular gases J. Stat. Phys. 125 529
66. Visco P 2006 Work fluctuations for a brownian particle between two thermostats J. Stat. Mech. P06006
67. Gilbert T 2006 Fluctuation theorem applied to the Nosé-Hoover thermostated Lorentz gas Phys. Rev. E 73 035102
68. Kurchan J 2006 The Gallavotti-Cohen theorem and the zero-noise limit at press [cond-mat/0612397]
69. Gallavotti G 1997 Dynamical ensembles equivalence in fluid mechanics Physica D 105 163
70. Aumatre S, Fauve S, McNamara S and Poggi P 2001 Power injected in dissipative systems and the fluctuation theorem Eur. Phys. J. B 19 449
71. Ruelle D 2000 A remark on the equivalence of isokinetic and isoenergetic thermostats in the thermodynamic limit J. Stat. Phys. 100 757
72. Puglisi A, Visco P, Barrat A, Trizac E and van Wijland F 2005 Fluctuations of internal energy flow in a vibrated granular gas Phys. Rev. Lett. 95 110202
73. Visco P, Puglisi A, Barrat A, Trizac E and van Wijland F 2005 Injected power and entropy flow in a heated granular gas Europhys. Lett. 72 55
74. Bonetto F, Gallavotti G, Giuliani A and Zamponi F 2006 Fluctuations relation and external thermostats: an application to granular materials J. Stat. Mech. P05009
75. Aumaitre S, Alastuey A and Fauve S 2006 A quasi-elastic limit for vibrated granular gases in preparation [cond-mat/0612108]
76. Gallavotti G and Ruelle D 1997 SRB states and nonequilibrium statistical mechanics close to equilibrium Commun. Math. Phys. 190 279
77. Gallavotti G 2000 Nonequilibrium in statistical and fluid mechanics: ensembles and their equivalence. Entropy driven intermittency J. Math. Phys. 41 4061
78. Gallavotti G 1999 A local fluctuation theorem Physica A 263 39
79. Gallavotti G and Perroni F 1999 An experimental test of the local fluctuation theorem in chains of weakly interacting Anosov systems Preprint nlin.CD/9909007