Non-equilibrium Dynamics, Thermalization and Entropy Production

TL;DR

This paper explores the fundamental principles of non-equilibrium statistical mechanics, analyzing entropy production, the validity of existing formulas, and providing a new proof of the fluctuation theorem from a quantum perspective.

Contribution

It critically examines the standard entropy production formula and offers an alternative proof of the fluctuation theorem, linking quantum mechanics with non-equilibrium thermodynamics.

Findings

Standard entropy production formula is valid only with separated time scales.

Provides a new, simple proof of the fluctuation theorem.

Clarifies the quantum-mechanical basis of non-equilibrium concepts.

Abstract

This paper addresses fundamental aspects of statistical mechanics such as the motivation of a classical state space with spontaneous transitions, the meaning of non-equilibrium in the context of thermalization, and the justification of these concepts from the quantum-mechanical point of view. After an introductory part we focus on the problem of entropy production in non-equilibrium systems. In particular, the generally accepted formula for entropy production in the environment is analyzed from a critical perspective. It is shown that this formula is only valid in the limit of separated time scales of the system's and the environmental degrees of freedom. Finally, we present an alternative simple proof of the fluctuation theorem.