We discuss fluctuation relations in simple cases of non-equilibrium Langevin dynamics. In particular, we show that, close to non-equilibrium steady states with non-vanishing probability currents, some of these relations reduce to a modified version of the fluctuation-dissipation theorem. The latter may be interpreted as the equilibrium-like relation in the reference frame moving with the mean local velocity determined by the probability current.

http://webhome.weizmann.ac.il/home/fnfal/papers/JStat08.pdf

Fluctuation relations in simple examples of non-equilibrium steady states

This paper deals with some thermodynamical aspects of a class of models in non equilibrium quantum statistical mechanics (QSM) which are commonly used to describe the behaviour of infinite quantum systems perturbed by a time‐dependent periodic force We are interested to the thermodynamical properties of the set of non‐equilibrium steady states (NESS) of the perturbed system We extend the construction of the C‐Liouvillean originally introduce in [1] to our time‐dependent situation to define the C‐Liouvillean of Floquet KF The NESS are thus described by zero‐resonance eigenvectors of KF* We also give a time dependent version of the rate of entropy production [2] for the perturbed system based on the relative entropy as defined by Araki [3] in terms of the relative modular operator

Non‐equilibrium steady states

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Non‐equilibrium steady states