Network representations of nonequilibrium steady states: Cycle decompositions, symmetries, and dominant paths.
Network representations of nonequilibrium steady states: Cycle decompositions, symmetries, and dominant paths.
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非平衡稳态的网络表示：循环分解、对称性和主导路径。
DOI：
10.1103/physreve.85.041133
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
S. Herminghaus
中科院分区：
文献类型：
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作者：
B. Altaner;J. Vollmer;S. Grosskinsky;Lukas Katthan;M. Timme;S. Herminghaus
马尔可夫过程的非平衡定态会产生非平凡的循环概率流。循环分解的稳定状态提供了一个有效的描述这样的通量。在这里，我们提出了一个迭代循环分解，展示了自然的动态空间的周期，满足详细的平衡。可观测量的期望值可以表示为周期“平均值”，类似于动力系统中期望值的周期表示。我们说明了我们的方法中的类比一个简单的模型的公共交通动力学。对称性反映在我们的方法中，通过减少分解所需的最小循环数。这些功能证明了通过讨论一个变种的不对称排斥过程。有趣的是，网络中主导流动路径的连续变化会导致循环结构的变化以及循环权重的不连续跳跃。
Nonequilibrium steady states of Markov processes give rise to nontrivial cyclic probability fluxes. Cycle decompositions of the steady state offer an effective description of such fluxes. Here we present an iterative cycle decomposition exhibiting a natural dynamics on the space of cycles that satisfies detailed balance. Expectation values of observables can be expressed as cycle "averages," resembling the cycle representation of expectation values in dynamical systems. We illustrate our approach in terms of an analogy to a simple model of mass transit dynamics. Symmetries are reflected in our approach by a reduction of the minimal number of cycles needed in the decomposition. These features are demonstrated by discussing a variant of an asymmetric exclusion process. Intriguingly, a continuous change of dominant flow paths in the network results in a change of the structure of cycles as well as in discontinuous jumps in cycle weights.