Thermodynamic entropic uncertainty relation

TL;DR

This paper establishes a new thermodynamic uncertainty relation linking Shannon entropy of observables, symmetry entropy, and entropy production, with implications for stochastic thermodynamics and decision-making models.

Contribution

It introduces a novel uncertainty relation involving Shannon entropy and symmetry entropy, providing a quantitative link between observable uncertainty and entropy production.

Findings

Sum of entropy production and symmetry entropy ≥ ln 2

Sum of entropy production and Shannon entropy ≥ ln 2

Application to diffusion decision model shows trade-off between accuracy and entropy production

Abstract

Thermodynamic uncertainty relations reveal a fundamental trade-off between the precision of a trajectory observable and entropy production, where the uncertainty of the observable is quantified by its variance. In information theory, Shannon entropy is a common measure of uncertainty. However, a clear quantitative relationship between the Shannon entropy of an observable and the entropy production in stochastic thermodynamics remains to be established. In this Letter, we show that an uncertainty relation can be formulated in terms of the Shannon entropy of an observable and the entropy production. We introduce symmetry entropy, an entropy measure that quantifies the symmetry of the observable distribution, and demonstrate that a greater asymmetry in the observable distribution requires higher entropy production. Specifically, we establish that the sum of the entropy production and the symmetry entropy cannot be less than $\ln 2$. As a corollary, we also prove that the sum of the entropy production and the Shannon entropy of the observable is no less than $\ln 2$. As an application, we demonstrate our relation in the diffusion decision model, revealing a fundamental trade-off between decision accuracy and entropy production in stochastic decision-making processes.