Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-24T14:05:32.841Z Has data issue: false hasContentIssue false
  • English
  • Français

A fluctuation theorem in a random environment

Published online by Cambridge University Press:  01 February 2008

F. BONETTO ,
G. GALLAVOTTI  and
G. GENTILE
F. BONETTO
Affiliation:
School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, USA (email: [email protected])
G. GALLAVOTTI
Affiliation:
Dipartimento di Fisica, INFN, Università di Roma ‘La Sapienza’, P.le A. Moro 2, I 00185 Roma, Italy (email: [email protected])
G. GENTILE
Affiliation:
Dipartimento di Matematica, Università di Roma Tre, Roma, I-00146, Italy (email: [email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

A simple class of chaotic systems in a random environment is considered and their shadowing properties are studied. As an example of application, the fluctuation theorem is extended under the assumption of reversibility.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 28 , Issue 1 , February 2008 , pp. 21 - 47
Copyright
Copyright © Cambridge University Press 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Bonetto, F., Falco, P. and Giuliani, A.. Analyticity of the SRB measure of a lattice of coupled Anosov diffeomorphisms of the torus. J. Math. Phys. 45 (2004), 3282–3309.CrossRefGoogle Scholar
[2]Ruelle, D.. Positivity of entropy production in the presence of a random thermostat. J. Statist. Phys. 86 (1997), 935–951.CrossRefGoogle Scholar
[3]Bricmont, J. and Kupiainen, A.. Coupled analytic maps. Nonlinearity 8 (1995), 379–396.CrossRefGoogle Scholar
[4]Jiang, M. and Mazel, A. E.. Uniqueness and exponential decay of correlations for some two-dimensional spin lattice systems. J. Statist. Phys. 82 (1996), 797–821.CrossRefGoogle Scholar
[5]Jiang, M. and Pesin, Ya. B.. Equilibrium measures for coupled map lattices: existence, uniqueness and finite-dimensional approximations. Comm. Math. Phys. 193 (1998), 675–711.CrossRefGoogle Scholar
[6]Bricmont, J. and Kupiainen, A.. High temperature expansions and dynamical systems. Commun. Math. Phys. 178 (1996), 703–732.CrossRefGoogle Scholar
[7]Bricmont, J. and Kupiainen, A.. Infinite-dimensional SRB measures. Physica D 103 (1997), 18–33.Google Scholar
[8]Gallavotti, G., Bonetto, F. and Gentile, G.. Aspects of the Ergodic, Qualitative and Statistical Theory of Motion. Springer, Berlin, 2004.CrossRefGoogle Scholar
[9]Gallavotti, G. and Cohen, E.. Dynamical ensembles in nonequilibrium statistical mechanics. Phys. Rev. Lett. 74 (1995), 2694–2697.CrossRefGoogle ScholarPubMed
[10]Gallavotti, G. and Cohen, E.. Dynamical ensembles in stationary states. J. Statist. Phys. 80 (1995), 931–970.Google Scholar
[11]Gallavotti, G.. Reversible Anosov diffeomorphisms and large deviations. Math. Phys. Electron. J. 1 (1995), 1–12.Google Scholar
[12]Kurchan, J.. Fluctuation theorem for stochastic dynamics. J. Phys. A: Math. Gen. 31 (1998), 3719–3729.CrossRefGoogle Scholar
[13]Lebowitz, J. and Spohn, H.. A Gallavotti–Cohen-type symmetry in the large deviation functional for stochastic dynamics. J. Statist. Phys. 95 (1999), 333–365.CrossRefGoogle Scholar
[14]Maes, C.. The fluctuation theorem as a Gibbs property. J. Statist. Phys. 95 (1999), 367–392.CrossRefGoogle Scholar
[15]Bonetto, F., Kupiainen, A. and Lebowitz, J.. Absolute continuity of projected SRB measures of coupled Arnold cat map lattices. Ergod. Th. & Dynam. Sys. 25 (2005), 59–88.CrossRefGoogle Scholar
[16]Liu, P.-D.. Dynamics of random transformations: smooth ergodic theory. Ergod. Th. & Dynam. Sys. 21 (2001), 1279–1319.Google Scholar