Effective Dynamics of Open Systems in Non-Equilibrium Statistical Mechanics

Abstract

This dissertation investigates effective dynamics of models for open systems, of classical and quantum nature, arising in non-equilibrium statistical mechanics. The evolution of the system's position degree of freedom in these models is described by a stochastic integro-differential equation, whose damping and noise coefficients are dependent on the system's position. The equation is driven by a colored noise process which is quasi-Markov. We study the behavior of the system in the limit as the characteristic time scales tend to zero. In particular, we derive a stochastic differential equation (SDE) describing the system's position in the considered limit. We find that the limiting SDE contains additional drift terms, the so-called noise-induced drifts, in both classical and quantum case. We discuss the implications of these correction drift terms in the context of concrete physical systems.