Bridging Freidlin-Wentzell large deviations theory and stochastic thermodynamics

TL;DR

This paper connects Freidlin-Wentzell large deviations theory with stochastic thermodynamics for overdamped Langevin systems, deriving a series expansion of the quasipotential and relating escape rates to entropy production.

Contribution

It introduces a novel link between large deviations and thermodynamics, including a series expansion of the quasipotential and bounds on escape rates based on entropy production.

Findings

Derived a series expansion of the quasipotential around the free energy.

Identified conditions for linear response far from equilibrium.

Bounded escape rates by entropy production of trajectories.

Abstract

For overdamped Langevin systems subjected to weak thermal noise and nonconservative forces, we establish a connection between Freidlin-Wentzell large deviations theory and stochastic thermodynamics. First, we derive a series expansion of the quasipotential around the detailed-balance solution, i.e. the system's free energy, and identify the condition for the linear response regime to hold even far from equilibrium. Second, we prove that the escape rate from dissipative fixed points of the macroscopic dynamics is bounded by the entropy production of trajectories that relax into, and escape from the attractors. These results provide the foundation to study the nonequilibrium thermodynamics of dissipative metastable states.