Information-fluctuation inequalities for collective response

Abstract

Hidden stochastic effects acting uniformly on a many-particle system can generate strong correlations and macroscopic relative fluctuations that persist at large system sizes, even when the particles themselves remain causally independent. Here we derive a universal upper bound on relative fluctuations for a large class of observables, formulated in terms of a generalized mutual information between observable states and the hidden variable. This information-fluctuation inequality provides general insights into the principles governing collective response induced by global disorder. We demonstrate the result with applications to non-interacting Brownian gases exposed to various types of dynamical disorder.