嵌套重置过程中稳态的趋近方法
Approach to Steady-State in Nested Resetting Processes
浏览论文内容
中文总结 AI 辅助
本研究解析了嵌套重置过程趋近非平衡稳态的动力学，发现弛豫以波前传播且由最小重置率决定，为分层随机重置系统提供了首达时间的全面描述。
中文摘要 AI 辅助
我们通过推导系统的累积时间，刻画了嵌套重置过程中非平衡稳态的趋近，该累积时间量化了局部建立稳态的有效首达时间。对于相等重置率，我们获得了闭式表达式，表明弛豫以波前形式传播，其延迟沿重置链线性增加。随后，我们将此分析扩展到异质重置率，推导了简并和非简并重置率下的精确稳态分布、空间矩和累积时间。我们表明，最终趋近稳态由系统中的最小重置率决定，在简并系统中，还由其多重性决定。这些结果为分层耦合随机重置系统中的非平衡稳态首达提供了全面的解析描述，并可能应用于生物系统中的弛豫和输运过程。
英文摘要
We characterise the approach to nonequilibrium steady state in nested resetting processes by deriving accumulation times for the system, which quantify the effective first-passage time for the local establishment of steady state. For equal resetting rates, we obtain closed-form expressions showing that relaxation propagates as a wavefront with a delay that increases linearly along the resetting chain. We then extend this analysis to heterogeneous resetting rates, deriving exact steady-state distributions, spatial moments and accumulation times for both degenerate and non-degenerate resetting rates. We show that relaxation to steady state is ultimately governed by the minimum resetting rate in the system and, in degenerate systems, its multiplicity. These results provide a comprehensive analytical description of first-passage to nonequilibrium steady state in hierarchically coupled stochastic resetting systems, with potential applications to relaxation and transport processes in biological systems.
发表机构
- Laboratoire de physique de l’École normale supérieure, CNRS, PSL University, Sorbonne Université, and Université Paris-Cité（巴黎高等师范学院物理实验室，法国国家科学研究中心，巴黎文理研究大学，索邦大学，巴黎西岱大学）
机构由 AI 辅助整理，请以论文原文为准。
