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Onsager-Machlup Theory for Nonequilibrium Steady States and Fluctuation Theorems

Tooru TaniguchiContact Information and E. G. D. Cohen1

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

Received: 26 July 2006  Accepted: 26 October 2006  Published online: 22 December 2006

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.

Keywords  nonequilibrium Onsager-Machlup theory - functional integration - fluctuation theorems - nonequilibrium steady state thermodynamics - nonequilibrium detailed balance - inertial effects

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

Contact Information Tooru Taniguchi
Email: ttaniguchi@rockefeller.edu
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  1. Monnai, Takaaki (2010) Quantum work-fluctuation theorem: Exact case study for a perturbed oscillator. Physical Review E 81(1)
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  2. Öttinger, Hans Christian (2010) Nonequilibrium Thermodynamics of the First and Second Kind: Averages and Fluctuations. Journal of Statistical Physics
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  3. Baule, A (2010) A path integral approach to random motion with nonlinear friction. Journal of Physics A Mathematical and Theoretical 43(2)
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  9. Deza, Roberto R. (2009) Fluctuation theorems from non-equilibrium Onsager-Machlup theory for a Brownian particle in a time-dependent harmonic potential. Central European Journal of Physics
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  10. Baule, A. (2008) Invariant Quantities in Shear Flow. Physical Review Letters 101(24)
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