General Theory of Static Response for Markov Jump Processes,Physical Review Letters

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General Theory of Static Response for Markov Jump Processes
Physical Review Letters ( IF 8.1 ) Pub Date : 2024-09-05 , DOI: 10.1103/physrevlett.133.107103
Timur Aslyamov ₁ , Massimiliano Esposito ₁

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We consider Markov jump processes on a graph described by a rate matrix that depends on various control parameters. We derive explicit expressions for the static responses of edge currents and steady-state probabilities. We show that they are constrained by the graph topology (i.e., the incidence matrix) by deriving response relations (i.e., linear constraints linking the different responses) and topology-dependent bounds. For unicyclic networks, all scaled current responses are between zero and one and must sum to one. Applying these results to stochastic thermodynamics, we derive explicit expressions for the static response of fundamental currents (which carry the full dissipation) to fundamental thermodynamic forces (which drive the system away from equilibrium).

中文翻译：

马尔可夫跳跃过程静态响应的一般理论

我们在由取决于各种控制参数的速率矩阵描述的图上考虑马尔可夫跳跃过程。我们推导出边缘电流和稳态概率的静态响应的显式表达式。我们通过推导响应关系（即连接不同响应的线性约束）和依赖于拓扑的边界来证明它们受到图拓扑（即关联矩阵）的约束。对于单环网络，所有缩放的电流响应都在零和一之间，并且总和必须为一。将这些结果应用到随机热力学中，我们得出了基本电流（携带完全耗散）对基本热力学力（使系统远离平衡）的静态响应的显式表达式。

更新日期：2024-09-05

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