Some aspects of non-equilibrium thermodynamics for small stochastic systems - part I

Abstract: We rise the question to what extent some well-known concepts of equilibrium thermodynamics allow for a meaningful generalization beyond thermal equilibrium. Restricting ourselves to the framework of stochastic systems with a small number of degrees of freedom, we will discuss the following topics: the structure of non-equilibrium states, Lyapunov functionals for the relaxation to steady non-equilibria, and (non-)quasistatic processes out of equilibrium. Remarkable simplifications are found in a close-to-equilibrium regime. (Some technical details are left to Part II of the talk that will be given by J. Pešek.)