Inferring nonequilibrium thermodynamics from tilted equilibrium using information-geometric Legendre transform

TL;DR

This paper introduces a method to infer nonequilibrium thermodynamic quantities, including entropy production, from limited measurements in relaxation processes using an information-geometric Legendre transform, applicable to classical stochastic systems.

Contribution

It develops a novel Legendre transform-based approach to estimate entropy production and related thermodynamic quantities from minimal observational data in nonstationary systems.

Findings

Exact minimum entropy production can be computed from limited data.

The method provides tight lower bounds on true entropy production.

It infers thermodynamic forces and relaxation constraints under certain conditions.

Abstract

Nonstationary thermodynamic quantities depend on the full details of nonstationary probability distributions, making them difficult to measure directly in experiments and numerics. We propose a method to infer thermodynamic quantities in relaxation processes by measuring only a few observables, using additional information obtained from measurements in tilted equilibrium, i.e., equilibrium with external fields applied. Our method is applicable to arbitrary classical stochastic systems, possibly underdamped, that relax to equilibrium. The method allows us to compute the exact value of the minimum entropy production (EP) compatible with the nonstationary observations, giving a tight lower bound on the true EP. Under a certain additional condition, it also allows the inference of the EP rate, thermodynamic forces, and a constraint on relaxation paths. Our method uses a Legendre transform of EP at the level of probability distributions, which we develop based on a similar Legendre transform in information geometry.