Information-Geometric Signatures of Nonconservative Driving

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.