Principles of maximum entropy and maximum caliber in statistical physics
Principles of maximum entropy and maximum caliber in statistical physics
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DOI：
10.1103/revmodphys.85.1115
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发表时间：
2013-07-16
影响因子：
44.1
通讯作者：
Dill, Ken A.
中科院分区：
文献类型：
--
作者：
Presse, Steve;Ghosh, Kingshuk;Dill, Ken A.
回顾了称为最大熵(MaxEnt)和最大口径(MaxCal)的变分原理。MaxEnt起源于玻尔兹曼和吉布斯的统计物理学，是预测热系统平衡态的理论工具。后来，熵最大化也被应用于信息、信号传输和图像重建等问题。最近，自从Shore和Johnson的工作以来，MaxEnt一直被认为是一个比物理学或单纯的信息更广泛的原理。MaxEnt是一种确保从随机数据中得出的推论满足基本自洽要求的过程。回顾了关于熵S=-Sigma(I)p(I)logp(I)的不同历史证明及其相应的变分原理。作为最大熵原理扩展范围的一个例证，最大口径，即应用于动力系统轨迹的路径熵最大化，也被回顾。给出了用最大口径来解释生物和纳米尺度上的动力学涨落的例子，如分子马达、化学反应、生物反馈电路和微流控装置中的扩散。
The variational principles called maximum entropy (MaxEnt) and maximum caliber (MaxCal) are reviewed. MaxEnt originated in the statistical physics of Boltzmann and Gibbs, as a theoretical tool for predicting the equilibrium states of thermal systems. Later, entropy maximization was also applied to matters of information, signal transmission, and image reconstruction. Recently, since the work of Shore and Johnson, MaxEnt has been regarded as a principle that is broader than either physics or information alone. MaxEnt is a procedure that ensures that inferences drawn from stochastic data satisfy basic self-consistency requirements. The different historical justifications for the entropy S = -Sigma(i)p(i) log p(i) and its corresponding variational principles are reviewed. As an illustration of the broadening purview of maximum entropy principles, maximum caliber, which is path entropy maximization applied to the trajectories of dynamical systems, is also reviewed. Examples are given in which maximum caliber is used to interpret dynamical fluctuations in biology and on the nanoscale, in single-molecule and few-particle systems such as molecular motors, chemical reactions, biological feedback circuits, and diffusion in microfluidics devices.