随机切换朗之万系统中有效热平衡的数值计算
Numerical computation of effective thermal equilibrium in Stochastically Switching Langevin Systems
AI总结：
本文针对力按连续时间马尔可夫链切换的过阻尼朗之万系统推导准势以刻画有效热平衡，并结合弦方法计算最概然转变路径，通过算法改进克服新出现的数值挑战并验证了准势垒与蒙特卡洛转变时间的一致性。
摘要：
随机切换的力项经常出现在蛋白质等活性因子作用下的生物系统模型中。切换力与布朗运动的相互作用可以产生“有效热平衡”，即使系统并不服从某个势函数。为了将能量景观分析领域扩展到理解切换系统中的稳定性与转变，我们针对一个一般的过阻尼朗之万系统推导了定义该有效平衡的准势，其中力按照连续时间马尔可夫链过程进行切换。结合用于计算最概然转变路径的弦方法，我们将该方法应用于一个理想化系统，并展示了此前未被报道的数值挑战。我们提出了对算法的修改以克服这些挑战，并通过证明我们计算得到的准势垒与系统中的渐近蒙特卡洛转变时间之间的一致性来验证其有效性。
英文摘要：
Stochastically switching force terms appear frequently in models of biological systems under the action of active agents such as proteins. The interaction of switching force and Brownian motion can create an "effective thermal equilibrium" even though the system does not obey a potential function. In order to extend the field of energy landscape analysis to understand stability and transitions in switching systems, we derive the quasipotential that defines this effective equilibrium for a general overdamped Langevin system with a force switching according to a continuous-time Markov chain process. Combined with the string method for computing most-probable transition paths, we apply our method to an idealized system and show the appearance of previously unreported numerical challenges. We present modifications to the algorithms to overcome these challenges, and show validity by demonstrating agreement between our computed quasipotential barrier and asymptotic Monte Carlo transition times in the system.
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