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摘要翻译：
这篇综述的目的是提供更好的理解已提出的处理统计力学中的非平衡（含时）过程的几种方法，重点是理论之间的相互关系。J.W.Gibbs提出的系综方法在平衡统计力学中具有很强的通用性和广泛的适用性。不同的宏观环境约束导致不同类型的集合，并具有特定的统计特征。本文讨论了基于非平衡系综形式的非平衡过程统计理论。从不可逆性的基本理论的观点出发，指出了动力学多体问题的动力学方法。重点介绍了D.N.Zubarev提出的非平衡统计算子(NSO)方法。NSO方法使我们可以将Gibbs系综方法推广到非平衡情况，并构造一个非平衡统计算子，使我们可以根据相关函数得到输运方程和计算输运系数，在平衡情况下，该算子转入Gibbs分布。虽然有一些空间用于NSO方法的形式结构，但重点是它的效用。在具体问题上的应用，如广义输运方程和动力学方程，以及一些松弛和耗散过程的例子，表明了该方法的可操作性。
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英文标题：
《Theory of Transport Processes and the Method of the Nonequilibrium
Statistical Operator》
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作者：
A. L. Kuzemsky
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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：
The aim of this review is to provide better understanding of a few approaches that have been proposed for treating nonequilibrium (time-dependent) processes in statistical mechanics with the emphasis on the inter-relation between theories. The ensemble method, as it was formulated by J. W. Gibbs, have the great generality and the broad applicability to equilibrium statistical mechanics. Different macroscopic environmental constraints lead to different types of ensembles, with particular statistical characteristics. In the present work, the statistical theory of nonequilibrium processes which is based on nonequilibrium ensemble formalism is discussed. The kinetic approach to dynamic many-body problems, which is important from the point of view of the fundamental theory of irreversibility, is alluded to. The emphasis is on the method of the nonequilibrium statistical operator (NSO) developed by D. N. Zubarev. The NSO method permits one to generalize the Gibbs ensemble method to the nonequilibrium case and to construct a nonequilibrium statistical operator which enables one to obtain the transport equations and calculate the transport coefficients in terms of correlation functions, and which, in the case of equilibrium, goes over to the Gibbs distribution. Although some space is devoted to the formal structure of the NSO method, the emphasis is on its utility. Applications to specific problems such as the generalized transport and kinetic equations, and a few examples of the relaxation and dissipative processes, which manifest the operational ability of the method, are considered.
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PDF链接：
https://arxiv.org/pdf/707.0753
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