Hazoglou Michael J, Walther Valentin, Dixit Purushottam D, Dill Ken A
Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794, USA.
Department of Systems Biology, Columbia University, New York, New York 10032, USA.
J Chem Phys. 2015 Aug 7;143(5):051104. doi: 10.1063/1.4928193.
There has been interest in finding a general variational principle for non-equilibrium statistical mechanics. We give evidence that Maximum Caliber (Max Cal) is such a principle. Max Cal, a variant of maximum entropy, predicts dynamical distribution functions by maximizing a path entropy subject to dynamical constraints, such as average fluxes. We first show that Max Cal leads to standard near-equilibrium results—including the Green-Kubo relations, Onsager's reciprocal relations of coupled flows, and Prigogine's principle of minimum entropy production—in a way that is particularly simple. We develop some generalizations of the Onsager and Prigogine results that apply arbitrarily far from equilibrium. Because Max Cal does not require any notion of "local equilibrium," or any notion of entropy dissipation, or temperature, or even any restriction to material physics, it is more general than many traditional approaches. It also applicable to flows and traffic on networks, for example.
人们一直对寻找非平衡统计力学的一般变分原理感兴趣。我们提供证据表明最大口径(Max Cal)就是这样一种原理。Max Cal是最大熵的一种变体,它通过在诸如平均通量等动力学约束条件下最大化路径熵来预测动力学分布函数。我们首先表明,Max Cal以一种特别简单的方式得出标准的近平衡结果,包括格林 - 久保关系、耦合流的昂萨格互易关系以及普里戈金的最小熵产生原理。我们对昂萨格和普里戈金的结果进行了一些推广,这些推广在远离平衡的任意情况下都适用。由于Max Cal不需要任何“局部平衡”的概念,也不需要任何熵耗散、温度的概念,甚至对物质物理学没有任何限制,所以它比许多传统方法更具一般性。例如,它也适用于网络上的流和交通。