Heat processes in non-equilibrium stochastic systems

TL;DR

This thesis develops a consistent framework for thermodynamic quantities in non-equilibrium stochastic systems, introducing a non-equilibrium heat capacity and analyzing its properties, including anomalous behaviors far from equilibrium.

Contribution

It provides a novel theoretical construction of thermodynamic quantities in non-equilibrium systems and extends the concept of heat capacity beyond equilibrium conditions.

Findings

Introduction of a non-equilibrium heat capacity with detailed properties

Identification of anomalous behaviors in far-from-equilibrium regimes

Enhanced description of effective dynamics in systems with multiple time scales

Abstract

This thesis is devoted to the theoretical study of slow thermodynamic processes in non-equilibrium stochastic systems. Its main result is a physically and mathematically consistent construction of relevant thermodynamic quantities in the quasistatic limit for a large class of non-equilibrium models. As an application of general methods a natural non-equilibrium generalization of heat capacity is introduced and its properties are analyzed in detail, including an anomalous far-from-equilibrium behavior. The developed methods are further applied to the related problem of time-scale separation where they enable to describe the effective dynamics of both slow and fast degrees of freedom in a more precise way.