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Journal of Statistical Physics

, Volume 149, Issue 5, pp 773–802 | Cite as

Thermodynamic Transformations of Nonequilibrium States

  • Lorenzo Bertini
  • Davide Gabrielli
  • Giovanni Jona-Lasinio
  • Claudio Landim
Article

Abstract

We consider a macroscopic system in contact with boundary reservoirs and/or under the action of an external field. We discuss the case in which the external forcing depends explicitly on time and drives the system from a nonequilibrium state to another one. In this case the amount of energy dissipated along the transformation becomes infinite when an unbounded time window is considered. Following the general proposal by Oono and Paniconi and using results of the macroscopic fluctuation theory, we give a natural definition of a renormalized work. We then discuss its thermodynamic relevance by showing that it satisfies a Clausius inequality and that quasi static transformations minimize the renormalized work. In addition, we connect the renormalized work to the quasi potential describing the fluctuations in the stationary nonequilibrium ensemble. The latter result provides a characterization of the quasi potential that does not involve rare fluctuations.

Keywords

Nonequilibrium stationary states Thermodynamic transformations Clausius inequality Large fluctuations Relative entropy 

Notes

Acknowledgements

We are grateful to J. Lebowitz for his insistence on a thermodynamic characterization of the quasi potential. We acknowledge stimulating discussions with T. Komatsu, N. Nakagawa, S. Sasa, and H. Tasaki. We also thank F. Flandoli for useful comments on hydrodynamic equations with time dependent boundary conditions. We thank a referee for several comments and questions which have led to an improvement of our paper.

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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • Lorenzo Bertini
    • 1
  • Davide Gabrielli
    • 2
  • Giovanni Jona-Lasinio
    • 3
  • Claudio Landim
    • 4
    • 5
  1. 1.Dipartimento di MatematicaUniversità di Roma ‘La Sapienza’RomeItaly
  2. 2.Dipartimento di MatematicaUniversità dell’AquilaCoppitoItaly
  3. 3.Dipartimento di Fisica and INFNUniversità di Roma La SapienzaRomeItaly
  4. 4.IMPARio de JaneiroBrazil
  5. 5.CNRS UMR 6085Université de RouenSaint-Étienne-du-RouvrayFrance

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