双稳势中游走-翻滚粒子的空间密度、首次通过时间与熵
Spatial density, first passage times, and entropy of run and tumble particles in a bistable potential
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中文总结 AI 辅助
研究双稳势中游走-翻滚粒子的动力学，求得稳态与时间依赖分布、弛豫前沿弹道运动及首次通过时间，并指出粗粒化为二分马尔可夫过程会丢失熵产生信息。
中文摘要 AI 辅助
我们研究了与热浴接触的双稳势中游走-翻滚粒子（RTP）的动力学。我们求得了稳态位置分布的精确形式，以及其在拉普拉斯空间中的时间依赖形式。利用这一结果，我们研究了空间概率密度的弛豫性质，发现密度从中心向外收敛至稳态，且弛豫前沿随时间做弹道运动。从物理上讲，这种弹道行为出现在观察密度尾部的弛豫性质时，此时粒子距原点的距离大于描述RTP稳态的长度尺度。我们还求得了平均首次通过时间的精确形式，以及首次通过时间分布的长时间行为。这使我们能够将动力学粗粒化为一个二分马尔可夫过程，这是广泛一类双稳过程的范式。然而，粗粒化以信息损失为代价：尽管RTP即使在稳态下也具有有限的熵产生，但其粗粒化描述的熵产生恒为零。
英文摘要
We study the dynamics of a run and tumble particle (RTP) in a bistable potential, in contact with a heat bath. We find the exact form of the steady state position distribution as well as its time-dependent form in Laplace space. We use this result to study relaxation properties of the spatial probability density and find that it converges to the steady state from the center outwards, with the relaxation front moving ballistically in time. Physically this ballistic behavior arises when observing relaxation properties at the tails of the density, where the distance of the particle from the origin is larger than the length-scale describing the steady state of the RTP. We also find the exact form of the mean first passage time, and the long-time behavior of the first passage time distribution. This allows us to coarse-grain the dynamics as a dichotomous Markov process, a paradigm for a wide class of bistable processes. Coarse-graining, however, comes at the cost of a loss of information: while the RTP possesses a finite entropy production even at steady state, it identically vanishes for its coarse-grained description.
发表机构
- Banaras Hindu University（贝拿勒斯印度教大学）
- University of Louisiana at Lafayette（路易斯安那大学拉斐特分校）
机构由 AI 辅助整理，请以论文原文为准。
