Counterexamples to the conjectured ordering between the waiting-time bound and the thermodynamic uncertainty bound on entropy production
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908751763603456 |
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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 |