Dixit Purushottam D
Department of Systems Biology, Columbia University, New York, New York 10032, United States.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Oct;92(4):042149. doi: 10.1103/PhysRevE.92.042149. Epub 2015 Oct 23.
Maximum-entropy (ME) inference of state probabilities using state-dependent constraints is popular in the study of complex systems. In stochastic systems, how state space topology and path-dependent constraints affect ME-inferred state probabilities remains unknown. To that end, we derive the transition probabilities and the stationary distribution of a maximum path entropy Markov process subject to state- and path-dependent constraints. A main finding is that the stationary distribution over states differs significantly from the Boltzmann distribution and reflects a competition between path multiplicity and imposed constraints. We illustrate our results with particle diffusion on a two-dimensional landscape. Connections with the path integral approach to diffusion are discussed.
使用依赖于状态的约束对状态概率进行最大熵（ME）推断在复杂系统研究中很流行。在随机系统中，状态空间拓扑结构和依赖于路径的约束如何影响ME推断的状态概率仍然未知。为此，我们推导了受状态和路径依赖约束的最大路径熵马尔可夫过程的转移概率和平稳分布。一个主要发现是，状态上的平稳分布与玻尔兹曼分布有显著差异，并且反映了路径多重性和施加的约束之间的竞争。我们用二维空间中的粒子扩散来说明我们的结果。还讨论了与扩散的路径积分方法的联系。
