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Large Deviations of Lattice Hamiltonian Dynamics Coupled to Stochastic Thermostats

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Abstract

We discuss the Donsker-Varadhan theory of large deviations in the framework of Hamiltonian systems thermostated by a Gaussian stochastic coupling. We derive a general formula for the Donsker-Varadhan large deviation functional for dynamics which satisfy natural properties under time reversal. Next, we discuss the characterization of the stationary states as the solution of a variational principle and its relation to the minimum entropy production principle. Finally, we compute the large deviation functional of the current in the case of a harmonic chain thermostated by a Gaussian stochastic coupling.

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Authors and Affiliations

  1. Ecole Normale Supérieure, DMA, 45 rue d’Ulm, 75230, Paris Cedex 05, France

    Thierry Bodineau

  2. LPMA, Université Denis Diderot (P7), Boîte courrier 7012, 75251, Paris Cedex 05, France

    Raphaël Lefevere

Authors
  1. Thierry Bodineau
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  2. Raphaël Lefevere
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Correspondence to Thierry Bodineau.

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Bodineau, T., Lefevere, R. Large Deviations of Lattice Hamiltonian Dynamics Coupled to Stochastic Thermostats. J Stat Phys 133, 1–27 (2008). https://doi.org/10.1007/s10955-008-9601-4

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  • DOI: https://doi.org/10.1007/s10955-008-9601-4

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