AI 中文总结
该研究建立连续时间马尔可夫过程中MFPT响应的系统理论，通过映射MFPT瞬态响应到辅助系统稳态响应的对应关系，推导精确响应关系并阐明生物系统相关悖论，兼具理论与计算优势。
AI 中文摘要
平均首次通过时间（MFPT）是物理、化学及生物系统中输运、反应、搜索和切换过程的通用时间度量。因此，理解MFPT对扰动的响应对预测和控制至关重要，但此前一直缺乏系统理论。我们建立了连续时间马尔可夫过程中线性与非线性MFPT响应的紧凑理论框架，核心工具是将MFPT的本质瞬态响应映射到辅助系统稳态响应的精确对应关系。该对应关系给出了任意状态对之间MFPT的精确通用响应关系，完全由未受扰MFPT和稳态概率表达。随后，我们将MFPT响应分解为线性上游、线性下游及非线性贡献的因子化物理项。进一步的推论包括响应曲线推断规则、MFPT响应的基本边界、MFPT和稳态概率的高阶响应解析表达式，以及多速率响应公式。此外，我们的结果在计算MFPT和稳态分布方面具有计算优势。最后，我们分析了一个受生物启发的折叠网络，并阐明了最近报道的关于MFPT的一个悖论。
英文摘要
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.
Comments7+10 pages, 3 figures. See also our companion paper [arXiv:2608.06368]
