Information-Geometric Signatures of Nonconservative Driving

TL;DR

This paper introduces an information-geometric method using Kullback-Leibler divergence and Fisher information to identify nonconservative driving in Markov processes, providing bounds on entropy production.

Contribution

It presents a novel geometric signature for nonconservative driving and derives a lower bound on entropy production based on the relaxation gap, applicable to Markov jump and Fokker-Planck dynamics.

Findings

The acceleration of KL divergence relates to Fisher information near equilibrium in detailed balance systems.

The relaxation gap quantifies deviations from detailed balance and bounds entropy production.

The bounds are especially tight for networks with simple cyclic topologies.

Abstract

We propose an information-geometric signature of nonconservative driving that detects violations of detailed balance using the Kullback--Leibler divergence and the Fisher information. For Markov jump processes satisfying detailed balance, we show that, near equilibrium, the acceleration of the Kullback--Leibler divergence relative to the equilibrium state is given by twice the Fisher information with respect to time. In contrast, for relaxation toward a nonequilibrium steady state, this relation is generally violated even near the steady state. We refer to the resulting discrepancy as the relaxation gap and derive a lower bound on the steady-state entropy production rate in terms of this gap. We demonstrate that this bound is particularly tight for networks with simple cyclic topologies. Finally, we show that analogous relations and bounds hold for Fokker--Planck dynamics.