Conjecture of an information-response inequality

TL;DR

This paper proposes a conjecture that mutual information bounds the invariant response in systems, proves this in the large information limit, and discusses implications for thermodynamics and estimation theory.

Contribution

It introduces a new inequality linking mutual information and invariant response, extending the fluctuation-response theorem to information-theoretic bounds.

Findings

Proven inequality in the large information limit

Application to thermodynamics of feedback control

Application to estimation theory

Abstract

The invariant response was defined from a formulation of the fluctuation-response theorem in the space of probability distributions. An inequality is here conjectured which sets the mutual information as an upper bound to the invariant response, and its large information limit is proven. Applications to the thermodynamics of feedback control and to estimation theory are discussed.