Nonequilibrium Work Relation in Macroscopic System

TL;DR

This paper derives a nonequilibrium work relation for macroscopic systems by connecting fluctuation theorems with the second law through a measure-valued process and thermodynamic limits, extending known equalities to metastable states.

Contribution

It introduces a novel formulation linking microscopic fluctuation theorems to macroscopic thermodynamics via a measure-valued process and establishes a new work relation for metastable states.

Findings

Re-derivation of the Jarzynski equality in the thermodynamic limit.

Establishment of a nonequilibrium work relation for metastable states.

Confirmation of the symmetry of the action functional leading to the second law.

Abstract

We reconsider a well-known relationship between the fluctuation theorem and the second law of thermodynamics by evaluating a probability measure-valued process. In order to establish a bridge between microscopic and macroscopic behaviors, we consider the thermodynamic limit of a stochastic dynamical system following the fundamental procedure often used in statistical mechanics. The thermodynamic path characterizing a macroscopic dynamical behavior can be formulated as an infimum of the action functional for the probability measure-valued process. In our formulation, the second law of thermodynamics can be derived by symmetry of the action functional, which is generated from the fluctuation theorem. We find that our formulation not only confirms that the ordinary Jarzynski equality in the thermodynamic limit can be rederived, but also enables us to establish a nontrivial nonequilibrium work relation for metastable states.