Smooth Dynamics and New Theoretical Ideas in Nonequilibrium Statistical Mechanics
Smooth Dynamics and New Theoretical Ideas in Nonequilibrium Statistical Mechanics
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光滑动力学与非平衡统计力学的新理论思想
DOI：
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发表时间：
1998
期刊：
影响因子：
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通讯作者：
D. Ruelle
中科院分区：
文献类型：
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作者：
D. Ruelle
本文综述了光滑动力系统理论在非平衡统计力学概念问题中的各种应用。我们采用了近年来逐渐出现的一种新的观点，它认真考虑了微观时间演化的混沌特征。重点是在非平衡定态，而不是传统的方法平衡的玻尔兹曼的观点。非平衡稳态，在存在一个高斯恒温器，描述SRB措施。根据这些可以证明加拉沃蒂-科恩波动定理。人们也可以证明一个一般的线性响应公式，并研究其后果，这并不限于近平衡的情况。在均衡状态下，人们尤其可以恢复昂萨格互惠关系。在适当的条件下，非平衡定态满足Dettmann和Morriss的配对定理。到目前为止，刚刚提到的结果只适用于经典系统;它们不涉及大尺寸，即，它们没有热力学极限。
This paper reviews various applications of the theory of smooth dynamical systems to conceptual problems of nonequilibrium statistical mecanics. We adopt a new point of view which has emerged progressively in recent years, and which takes seriously into account the chaotic character of the microscopic time evolution. The emphasis is on nonequilibrium steady states rather than the traditional approach to equilibrium point of view of Boltzmann. The nonequilibrium steady states, in presence of a Gaussian thermostat, are described by SRB measures. In terms of these one can prove the Gallavotti–Cohen fluctuation theorem. One can also prove a general linear response formula and study its consequences, which are not restricted to near-equilibrium situations. At equilibrium one recovers in particular the Onsager reciprocity relations. Under suitable conditions the nonequilibrium steady states satisfy the pairing theorem of Dettmann and Morriss. The results just mentioned hold so far only for classical systems; they do not involve large size, i.e., they hold without a thermodynamic limit.