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Reversibility in Infinite Hamiltonian Systems with Conservative Noise

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Abstract:

The set of stationary measures of an infinite Hamiltonian system with noise is investigated. The model consists of particles moving in with bounded velocities and subject to a noise that does not violate the classical laws of conservation, see [OVY]. Following [LO] we assume that the noise has also a finite radius of interaction, and prove that translation invariant stationary states of finite specific entropy are reversible with respect to the stochastic component of the evolution. Therefore the results of [LO] imply that such invariant measures are superpositions of Gibbs states.

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Authors and Affiliations

  1. Department of Probability and Statistics, Eötvös Lor´nd University of Sciences, H-1088 Budapest, Múzeum krt. 6-8, Hungary. E-mail: jofri@cs.elte.hu, , , , , , HU

    József Fritz

  2. II Universitá di Roma “Tor Vergata,” Dipartimento di Matematica, 00133 Roma, Italy.¶E-mail: liverani@mat.utovrm.it, , , , , , IT

    Carlangelo Liverani

  3. Université de Cergy–Pontoise, Département de Mathématiques, 2 avenue Adolphe Chauvin, Pontoise 95302 Cergy--Pontoise Cedex, France and Centre de Mathématiques Appliquées, Ecole Polytechnique, 91128 Palaiseau Cedex, France. E-mail: olla@paris.polytechnique.fr, , , , , , FR

    Stefano Olla

Authors
  1. József Fritz
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  2. Carlangelo Liverani
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  3. Stefano Olla
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Received: 26 September 1996 / Accepted: 3 January 1997

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Fritz, J., Liverani, C. & Olla, S. Reversibility in Infinite Hamiltonian Systems with Conservative Noise . Comm Math Phys 189, 481–496 (1997). https://doi.org/10.1007/s002200050212

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  • DOI: https://doi.org/10.1007/s002200050212

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