1207.1026 (Matteo Smerlak)

Stochastic thermodynamics for inhomogeneous media    [PDF]

Matteo Smerlak

A unifying framework for the thermodynamics of fluctuating systems with Fokker-Planck dynamics has been developed by Seifert and others using the notion of stochastic entropy. Here we consider the extension of this formalism to the case of inhomogeneous media, where the diffusivity is state-dependent (multiplicative noise) and the usual fluctuation theorems can be violated. We introduce to this effect the concept of "relative stochastic entropy", and use it to generalize (i) the maximum-entropy principle for the Gibbs canonical ensemble, (ii) the second law of thermodynamics and (iii) Seifert's integral fluctuation theorems. Our "relative stochastic thermodynamics" can be used e.g. to describe the stochastic motion of colloidal particles dragged in viscous fluids with space-dependent viscosity and/or temperature.

View original: http://arxiv.org/abs/1207.1026