Abstract Understanding the fluctuations by which phenomenological evolution equations with thermodynamic structure can be enhanced is the key to a general framework of nonequilibrium statistical mechanics. These fluctuations provide an idealized representation of microscopic details. We consider fluctuation-enhanced equations associated with Markov processes and elaborate the general recipes for evaluating dynamic material properties, which characterize force-flux constitutive laws, by statistical mechanics. Markov processes with continuous trajectories are conveniently characterized by stochastic differential equations and lead to Green–Kubo-type formulas for dynamic material properties. Markov processes with discontinuous jumps include transitions over energy barriers with the rates calculated by Kramers. We describe a unified approach to Markovian fluctuations and demonstrate how the appropriate type of fluctuations (continuous versus discontinuous) is reflected in the mathematical structure of the phenomenological equations.

中文翻译：

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非平衡统计力学框架。一、波动的作用和类型

摘要 理解可以增强具有热力学结构的现象学演化方程的涨落是非平衡统计力学一般框架的关键。这些波动提供了微观细节的理想化表示。我们考虑了与马尔可夫过程相关的波动增强方程，并详细阐述了通过统计力学评估动态材料特性的一般方法，这些特性表征力 - 通量本构定律。具有连续轨迹的马尔可夫过程可以方便地由随机微分方程表征，并导致动态材料特性的 Green-Kubo 型公式。具有不连续跳跃的马尔可夫过程包括能量势垒上的跃迁，其速率由 Kramers 计算。