A derivation of the master equation from path entropy maximization.
A derivation of the master equation from path entropy maximization.
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DOI：
10.1063/1.4743955
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发表时间：
2012-06
期刊：
影响因子：
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通讯作者：
Julian Lee;S. Pressé
中科院分区：
文献类型：
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作者：
Julian Lee;S. Pressé
主方程和更一般的马尔可夫过程通常被用作随机过程的模型。它们通常是基于随机化和粗粒度假设来证明的。相反，在这里，我们推导出n阶马尔可夫过程和主方程作为反问题的唯一解。我们发现，当约束不足以唯一确定的随机模型，一个n阶马尔可夫过程出现作为唯一的最大熵解，否则欠定问题。这给出了一个严格的替代证明这样的模型，同时提供了一个系统的配方推广广泛接受的随机模型通常假设遵循的第一原则。
The master equation and, more generally, Markov processes are routinely used as models for stochastic processes. They are often justified on the basis of randomization and coarse-graining assumptions. Here instead, we derive nth-order Markov processes and the master equation as unique solutions to an inverse problem. We find that when constraints are not enough to uniquely determine the stochastic model, an nth-order Markov process emerges as the unique maximum entropy solution to this otherwise underdetermined problem. This gives a rigorous alternative for justifying such models while providing a systematic recipe for generalizing widely accepted stochastic models usually assumed to follow from the first principles.