摘要翻译：
我们考虑确定随机非平衡系统稳态的一般问题，例如那些被用来建模（除其他外）生物运输和交通流的随机非平衡系统。我们首先对这类驱动扩散系统进行了广泛的概述--包括排斥过程--侧重于有趣的物理性质，如激波和相变。然后，我们将注意力专门转向那些可以用矩阵积形式表示稳态中微态的精确分布的模型。除了对这种矩阵积方法的温和介绍，它是如何工作的，以及它是如何与在其他物理环境中出现的类似构造联系起来的，我们提出了一个统一的，教育性的各种方法的说明，通过这些方法，宏观物理量的统计力学计算实际上是执行的。我们还回顾了一些更高级的主题，包括非平衡自由能泛函，涉及多粒子物种的排斥过程的分类，给定模型的矩阵积态的存在性证明，以及允许处理各种并行动力学的矩阵积态的更复杂的变体。最后，我们简要讨论了有待进一步研究的问题。
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英文标题：
《Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide》
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作者：
R. A. Blythe and M. R. Evans
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最新提交年份：
2007
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分类信息：

一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
  We consider the general problem of determining the steady state of stochastic nonequilibrium systems such as those that have been used to model (among other things) biological transport and traffic flow. We begin with a broad overview of this class of driven diffusive systems - which includes exclusion processes - focusing on interesting physical properties, such as shocks and phase transitions. We then turn our attention specifically to those models for which the exact distribution of microstates in the steady state can be expressed in a matrix product form. In addition to a gentle introduction to this matrix product approach, how it works and how it relates to similar constructions that arise in other physical contexts, we present a unified, pedagogical account of the various means by which the statistical mechanical calculations of macroscopic physical quantities are actually performed. We also review a number of more advanced topics, including nonequilibrium free energy functionals, the classification of exclusion processes involving multiple particle species, existence proofs of a matrix product state for a given model and more complicated variants of the matrix product state that allow various types of parallel dynamics to be handled. We conclude with a brief discussion of open problems for future research.
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PDF链接：
https://arxiv.org/pdf/706.1678