Françoise Cornu, Michel Bauer
Thermal contact in permanent regime is the archetype of non-equilibrium stationary states driven by constant non-equilibrium constraints enforced by reservoirs of exchanged conserved microscopic quantities. We consider a class of models with a finite number of possible configurations evolving under a master equation. If the microscopic deterministic dynamics which conserves energy is assumed to be ergodic, it is shown that the transition rates obey a modified detailed balance (MDB) which is generically expressed in terms of the microscopic exchange entropy variation. We investigate the generic statistical properties for measurable quantities which arise from the MDB constraint. For a finite-time evolution (transient regime) from an initial equilibrium state we derive a detailed fluctuation relation for the excess exchange entropy variation and an associated integral fluctuation relation. In the non-equilibrium stationary state (long-time regime), the proper mathematical definition of a large deviation function is introduced together with alternative definitions, and fluctuation relations are derived. The fluctuation relation for the exchange entropy variation is merely a particular case of the Lebowitz-Spohn fluctuation relation for the action functional [1]. The infinite time limit of any odd cumulant per unit time of an exchanged quantity is expressed in terms of a series involving higher even cumulants and powers of the thermodynamic force associated to the mean current ; every relation can be seen as a generalized Green-Kubo relation valid far from equilibrium. It entails a relation between the $n$th-order non-linear response coefficient of any odd cumulant per unit time in the vicinity of equilibrium and a finite number of lower-order non-linear response coefficients of even cumulants per unit time.
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http://arxiv.org/abs/1302.4538
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