Bounds for Fisher information and its production under flow

TL;DR

This paper establishes new bounds on Fisher information and its production in nonequilibrium systems, revealing fundamental limits and relationships influenced by flux and the arrow of time.

Contribution

It introduces a nontrivial lower bound for Fisher information with flux and a novel upper bound on its production, advancing understanding of information dynamics in nonequilibrium processes.

Findings

Derived a lower bound for Fisher information with flux vector.

Established an upper bound on the rate of information production.

Linked information measures to the arrow of time in nonequilibrium systems.

Abstract

We prove that two well-known measures of information are interrelated in interesting and useful ways when applied to nonequilibrium circumstances. A nontrivial form of the lower bound for the Fisher information measure is derived in presence of a flux vector, which satisfies the continuity equation. We also establish a novel upper bound on the time derivative (production) in terms of the arrow of time and derive a lower bound by the logarithmic Sobolev inequality. These serve as the revealing dynamics of the information content and its limitations pertaining to nonequilibrium processes.