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The Steady State Fluctuation Relation for the Dissipation Function

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Abstract

We give a proof of transient fluctuation relations for the entropy production (dissipation function) in nonequilibrium systems, which is valid for most time reversible dynamics. We then consider the conditions under which a transient fluctuation relation yields a steady state fluctuation relation for driven nonequilibrium systems whose transients relax, producing a unique nonequilibrium steady state. Although the necessary and sufficient conditions for the production of a unique nonequilibrium steady state are unknown, if such a steady state exists, the generation of the steady state fluctuation relation from the transient relation is shown to be very general. It is essentially a consequence of time reversibility and of a form of decay of correlations in the dissipation, which is needed also for, e.g., the existence of transport coefficients. Because of this generality the resulting steady state fluctuation relation has the same degree of robustness as do equilibrium thermodynamic equalities. The steady state fluctuation relation for the dissipation stands in contrast with the one for the phase space compression factor, whose convergence is problematic, for systems close to equilibrium. We examine some model dynamics that have been considered previously, and show how they are described in the context of this work.

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Authors and Affiliations

  1. Nanoscale Science and Technology Centre and School of Biomolecular and Physical Sciences, Griffith University, Brisbane, Qld, 4111, Australia

    Debra J. Searles

  2. Dipartimento di Matematica and CNISM, Politenico di Torino, Corso Duca degli Abruzzi 24, 10129, Torino, Italy

    Lamberto Rondoni

  3. Research School of Chemistry, Australian National University, Canberra, ACT, 0200, Australia

    Denis J. Evans

Authors
  1. Debra J. Searles
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  2. Lamberto Rondoni
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  3. Denis J. Evans
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Correspondence to Debra J. Searles.

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Searles, D.J., Rondoni, L. & Evans, D.J. The Steady State Fluctuation Relation for the Dissipation Function. J Stat Phys 128, 1337–1363 (2007). https://doi.org/10.1007/s10955-007-9372-3

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  • DOI: https://doi.org/10.1007/s10955-007-9372-3

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