Journal of Statistical Physics

, Volume 123, Issue 2, pp 237–276 | Cite as

Non Equilibrium Current Fluctuations in Stochastic Lattice Gases

  • L. Bertini
  • A. De Sole
  • D. Gabrielli
  • G. Jona-Lasinio
  • C. Landim


We study current fluctuations in lattice gases in the macroscopic limit extending the dynamic approach for density fluctuations developed in previous articles. More precisely, we establish a large deviation principle for a space-time fluctuation j of the empirical current with a rate functional I(j). We then estimate the probability of a fluctuation of the average current over a large time interval; this probability can be obtained by solving a variational problem for the functional I. We discuss several possible scenarios, interpreted as dynamical phase transitions, for this variational problem. They actually occur in specific models. We finally discuss the time reversal properties of I and derive a fluctuation relationship akin to the Gallavotti-Cohen theorem for the entropy production.

Key words

Stationary non equilibrium states Stochastic lattice gases Current fluctuations Gallavotti-Cohen symmetry 


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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • L. Bertini
    • 1
  • A. De Sole
    • 2
    • 3
  • D. Gabrielli
    • 4
  • G. Jona-Lasinio
    • 5
  • C. Landim
    • 6
    • 7
  1. 1.Dipartimento di MatematicaUniversità di Roma La SapienzaRomaItaly
  2. 2.INDAMUniversità di Roma La SapienzaRomaItaly
  3. 3.Department of MathematicsHarvard UniversityCambridgeUSA
  4. 4.Dipartimento di MatematicaUniversità dell'AquilaCoppitoItaly
  5. 5.Dipartimento di Fisica and INFNUniversità di Roma “La Sapienza”RomaItaly
  6. 6.IMPARio de JaneiroBrasil
  7. 7.CNRS UMR 6085Université de RouenMont-Saint-Aignan CedexFrance

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