Onsager-Machlup Theory for Nonequilibrium Steady States and Fluctuation Theorems
Tooru Taniguchi1
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.
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