Information-fluctuation inequalities for collective response

TL;DR

This paper derives a universal inequality linking collective fluctuations in many-particle systems to hidden stochastic effects, providing insights into how global disorder influences collective responses.

Contribution

It introduces a new information-fluctuation inequality that bounds relative fluctuations using generalized mutual information, applicable to systems with hidden stochastic effects.

Findings

Derived a universal upper bound on relative fluctuations

Applied the inequality to Brownian gases with dynamical disorder

Provided insights into collective response mechanisms

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.