Long range correlations and phase transitions in non-equilibrium diffusive systems

Journal of Statistical Physics

Volumn 133, Issue 6, 2008, Pages 1013-1031

  Bodineau, T ^a   Derrida, B ^a   Lecomte, V ^b   Van Wijland, F ^c  

^a ECOLE NORMALE SUPÉRIEURE   (France)

^b UNIVERSITY OF GENEVA   (Switzerland)

^c UNIVERSITÉ PARIS DIDEROT   (France)

Author keywords

Diffusive dynamics; Fluctuations; Non equilibrium; Phase transition

Indexed keywords

EID: 57849126625     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-008-9647-3     Document Type: Article

References (32)

1. H. Spohn 1983 Long range correlations for stochastic lattice gases in a non-equilibrium steady state J. Phys. A 16 4275 4291
2. R. Schmitz E.G.D. Cohen 1985 Fluctuations in a fluid under a stationary heat-flux. 1. General theory J. Stat. Phys. 39 285 316
3. J.R. Dorfman T.R. Kirkpatrick J.V. Sengers 1994 Generic long-range correlations in molecular fluids Annu. Rev. Phys. Chem. 45 213 239
4. J.M. Ortiz de Zarate J.V. Sengers 2004 On the physical origin of long-ranged fluctuations in fluids in thermal nonequilibrium states J. Stat. Phys. 115 1341 1359
5. B. Derrida C. Enaud C. Landim S. Olla 2005 Fluctuations in the weakly asymmetric exclusion process with open boundary conditions J. Stat. Phys. 118 795 811
6. Bertini, L., De Sole, A., Gabrielli, D., Jona-Lasinio, G., Landim, C.: On the long range correlations of thermodynamic systems out of equilibrium. cond-mat arXiv:0705.2996 (2007)
7. B. Derrida J.L. Lebowitz E.R. Speer 2007 Entropy of open lattice systems J. Stat. Phys. 126 1083 1108
8. Derrida, B.: Non-equilibrium steady states: fluctuations and large deviations of the density and of the current. J. Stat. Mech. P07023 (2007)
9. M.R. Evans 2000 Phase transitions in one-dimensional nonequilibrium systems Braz. J. Phys. 30 42 57
10. Y. Kafri E. Levine D. Mukamel G.M. Schütz J. Torok 2002 Criterion for phase separation in one-dimensional driven systems Phys. Rev. Lett. 89 035702
11. A. Parmeggiani T. Franosch E. Frey 2003 Phase coexistence in driven one-dimensional transport Phys. Rev. Lett. 90 086601
12. M.R. Evans Y. Kafri H.M. Koduvely D. Mukamel 1998 Phase separation and coarsening in one-dimensional driven diffusive systems Phys. Rev. E 58 2764 2778
13. M.R. Evans Y. Kafri H.M. Koduvely D. Mukamel 1998 Phase separation in one-dimensional driven diffusive systems: Local dynamics leading to long-range Hamiltonians Phys. Rev. Lett. 80 425 429
14. M. Clincy B. Derrida M.R. Evans 2003 Phase transitions in the ABC model Phys. Rev. E 67 066115
15. G. Fayolle C. Furtlehner 2004 Dynamical windings of random walks and exclusion models. Part I: Thermodynamic limit in Z(2) J. Stat. Phys. 114 229 260
16. T. Bodineau B. Derrida 2005 Distribution of current in nonequilibrium diffusive systems and phase transitions Phys. Rev. E 72 066110
17. T. Bodineau B. Derrida 2004 Current fluctuations in non-equilibrium diffusive systems: an additivity principle Phys. Rev. Lett. 92 180601
18. G. Fayolle C. Furtlehner 2007 Stochastic dynamics of discrete curves and multi-type exclusion processes J. Stat. Phys. 127 1049 1094
19. C. Appert-Rolland B. Derrida V. Lecomte F. van Wijland 2008 Universal cumulants of the current in diffusive systems on a ring Phys. Rev. E 78 021122
20. G.M. Schütz 2003 Critical phenomena universal dynamics in one-dimensional driven diffusive systems with two species of particles J. Phys. A: Math. Gen. 36 R339 R379
21. L. Bertini A. De Sole D. Gabrielli G. Jona-Lasinio C. Landim 2001 Fluctuations in stationary non equilibrium states of irreversible processes Phys. Rev. Lett. 87 040601
22. L. Bertini A. De Sole D. Gabrielli G. Jona-Lasinio C. Landim 2002 Macroscopic fluctuation theory for stationary non equilibrium states J. Stat. Phys. 107 635 675
23. L. Bertini A. De Sole D. Gabrielli G. Jona-Lasinio C. Landim 2003 Large deviations for the boundary driven symmetric simple exclusion process Math. Phys. Anal. Geom. 6 231 267
24. L. Bertini A. De Sole D. Gabrielli G. Jona-Lasinio C. Landim 2004 Minimum dissipation principle in stationary non equilibrium states J. Stat. Phys. 116 831 841
25. Bertini, L., De Sole, A., Gabrielli, D., Jona Lasinio, G., Landim, C.: Stochastic interacting particle systems out of equilibrium, J. Stat. Mech. P07014 (2007)
26. Freidlin, M., Wentzell, A.: Random Perturbations of Dynamical Systems. Springer, New York (1998)
27. L. Bertini D. Gabrielli J. Lebowitz 2005 Large deviations for a stochastic model of heat flow J. Stat. Phys. 121 5-6 843 885
28. T. Bodineau B. Derrida 2007 Cumulants and large deviations of the current in non-equilibrium steady states C. R. Phys. 8 540 555
29. L. Bertini A. De Sole D. Gabrielli G. Jona-Lasinio C. Landim 2006 Non equilibrium current fluctuations in stochastic lattice gases J. Stat. Phys. 123 237 276
30. Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II. Nonequilibrium Statistical Mechanics. Springer Series in Solid-State Sciences, vol. 31. Springer, New York (1998)
31. Spohn, H.: Large Scale Dynamics of Interacting Particles. Springer, Berlin (1991)
32. C. Kipnis S. Olla S. Varadhan 1989 Hydrodynamics and large deviations for simple exclusion processes Commun. Pure Appl. Math. 42 115 137