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Onsager-Machlup Theory for Nonequilibrium Steady States and Fluctuation Theorems

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Abstract

A generalization of the Onsager-Machlup theory from equilibrium to nonequilibrium steady states and its connection with recent fluctuation theorems are discussed for a dragged particle restricted by a harmonic potential in a heat reservoir. Using a functional integral approach, the probability functional for a path is expressed in terms of a Lagrangian function from which an entropy production rate and dissipation functions are introduced, and nonequilibrium thermodynamic relations like the energy conservation law and the second law of thermodynamics are derived. Using this Lagrangian function we establish two nonequilibrium detailed balance relations, which not only lead to a fluctuation theorem for work but also to one related to energy loss by friction. In addition, we carried out the functional integral for heat explicitly, leading to the extended fluctuation theorem for heat. We also present a simple argument for this extended fluctuation theorem in the long time limit.

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Authors and Affiliations

  1. The Rockefeller University, 1230 York Avenue, New York, NY, 10021, USA

    Tooru Taniguchi & E. G. D. Cohen

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  1. Tooru Taniguchi
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  2. E. G. D. Cohen
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Correspondence to Tooru Taniguchi.

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PACS numbers: 05.70.Ln, 05.40.-a, 05.10.Gg.

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Taniguchi, T., Cohen, E.G.D. Onsager-Machlup Theory for Nonequilibrium Steady States and Fluctuation Theorems. J Stat Phys 126, 1–41 (2007). https://doi.org/10.1007/s10955-006-9252-2

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  • DOI: https://doi.org/10.1007/s10955-006-9252-2

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