Counterexamples to the conjectured ordering between the waiting-time bound and the thermodynamic uncertainty bound on entropy production

Fuente: arXiv
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Autore principale: Gu, Jie
Natura: Preprint
Pubblicazione: 2026
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author Gu, Jie
author_facet Gu, Jie
contents Two widely used model-free lower bounds on the steady-state entropy production rate of a continuous-time Markov jump process are the thermodynamic uncertainty relation (TUR) bound $σ_\text{TUR}$, derived from the mean and variance of a current, and the waiting-time distribution (WTD) bound $σ_\mathcal{L}$, derived from the irreversibility of partially observed transition sequences together with their waiting times. It has been conjectured that $σ_{\mathcal L}$ is always at least as tight as $σ_{\mathrm{TUR}}$ when both are constructed from the same partially observed link. Here we provide four-state counterexamples in a nonequilibrium steady state where $σ_{\mathcal L}<σ_{\mathrm{TUR}}$. This result shows that no universal ordering exists between these two inference bounds under partial observation.
format Preprint
id arxiv_https___arxiv_org_abs_2601_04039
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Counterexamples to the conjectured ordering between the waiting-time bound and the thermodynamic uncertainty bound on entropy production
Gu, Jie
Statistical Mechanics
Two widely used model-free lower bounds on the steady-state entropy production rate of a continuous-time Markov jump process are the thermodynamic uncertainty relation (TUR) bound $σ_\text{TUR}$, derived from the mean and variance of a current, and the waiting-time distribution (WTD) bound $σ_\mathcal{L}$, derived from the irreversibility of partially observed transition sequences together with their waiting times. It has been conjectured that $σ_{\mathcal L}$ is always at least as tight as $σ_{\mathrm{TUR}}$ when both are constructed from the same partially observed link. Here we provide four-state counterexamples in a nonequilibrium steady state where $σ_{\mathcal L}<σ_{\mathrm{TUR}}$. This result shows that no universal ordering exists between these two inference bounds under partial observation.
title Counterexamples to the conjectured ordering between the waiting-time bound and the thermodynamic uncertainty bound on entropy production
topic Statistical Mechanics
url https://arxiv.org/abs/2601.04039