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标题: "Exact First-Passage Time Response Theory from Steady-State Response"
原文链接: "https://arxiv.org/abs/2608.11202"
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## Condensed Matter > Statistical Mechanics

## Title:Exact First-Passage Time Response Theory from Steady-State Response

Authors:[Ruicheng Bao](https://arxiv.org/search/cond-mat?searchtype=author&query=Bao,+R), [Shiling Liang](https://arxiv.org/search/cond-mat?searchtype=author&query=Liang,+S)

[View PDF](https://arxiv.org/pdf/2608.11202) [HTML (experimental)](https://arxiv.org/html/2608.11202v1)

> Abstract:The mean first-passage time (MFPT) provides a universal temporal measure of transport, reaction, search, and switching processes in physical, chemical, and biological systems. Understanding how MFPTs respond to perturbations is therefore crucial for prediction and control, yet a systematic theory has been lacking. We establish a compact theoretical framework for linear and nonlinear MFPT response in continuous-time Markov processes. The key tool is an exact correspondence that maps the intrinsically transient response of MFPTs onto the steady-state response of an auxiliary system. This correspondence yields exact and universal response relations for MFPTs between arbitrary state pairs, expressed entirely in terms of unperturbed MFPTs and steady-state probabilities. We then obtain a factorized physical decomposition of the MFPT response into linear upstream, linear downstream, and nonlinear contributions. Further corollaries include response-curve inference rules, fundamental bounds on MFPT responses, analytical expressions for higher-order responses of MFPTs and steady-state probabilities, and multi-rate response formulas. Additionally, our result offers computational advantages in calculating both MFPTs and steady-state distributions. Finally, a biologically motivated folding network is analyzed, and a recently reported paradox on MFPT is clarified.

| Comments: |  |
| --- | --- |
| Subjects: | Statistical Mechanics (cond-mat.stat-mech); Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Mathematical Physics (math-ph); Biological Physics (physics.bio-ph) |
| Cite as: | [arXiv:2608.11202](https://arxiv.org/abs/2608.11202) \[cond-mat.stat-mech\] |
|  | (or [arXiv:2608.11202v1](https://arxiv.org/abs/2608.11202v1) \[cond-mat.stat-mech\] for this version) |
|  | [https://doi.org/10.48550/arXiv.2608.11202](https://doi.org/10.48550/arXiv.2608.11202) |

## Submission history

From: Ruicheng Bao \[[view email](https://arxiv.org/show-email/e298000b/2608.11202)\]  
**\[v1\]** Tue, 11 Aug 2026 17:59:01 UTC (166 KB)

[Which authors of this paper are endorsers?](https://arxiv.org/auth/show-endorsers/2608.11202) | Disable MathJax ([What is MathJax?](https://info.arxiv.org/help/mathjax.html))
