We develop nonequilibrium theory by using averages in time and space as a generalized way to upscale thermodynamics in nonergodic systems. The approach offers a classical perspective on the energy dynamics in fluctuating systems. The rate of entropy production is shown to be explicitly scale dependent when considered in this context. We show that while any stationary process can be represented as having zero entropy production, second law constraints due to the Clausius theorem are preserved due to the fact that heat and work are related based on conservation of energy. As a demonstration, we consider the energy dynamics for the Carnot cycle and for Maxwell's demon. We then consider nonstationary processes, applying time-and-space averages to characterize nonergodic effects in heterogeneous systems where energy barriers such as compositional gradients are present. We show that the derived theory can be used to understand the origins of anomalous diffusion phenomena in systems where Fick's law applies at small length scales, but not at large length scales. We further characterize fluctuations in capillary-dominated systems, which are nonstationary due to the irreversibility of cooperative events.

中文翻译：

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基于时空平均值的波动热力学

我们通过使用时间和空间的平均值作为提升非遍历系统中的热力学的通用方法来开发非平衡理论。该方法为波动系统中的能量动力学提供了经典视角。在这种情况下考虑时，熵产生率显示为明确地依赖于规模。我们表明，虽然任何平稳过程都可以表示为具有零熵产生，但由于热量和功基于能量守恒相关这一事实，由于克劳修斯定理的第二定律约束得以保留。作为演示，我们考虑卡诺循环和麦克斯韦妖的能量动力学。然后我们考虑非平稳过程，应用时间和空间平均值来表征存在能量障碍（例如成分梯度）的异构系统中的非遍历效应。我们表明，派生的理论可用于理解菲克定律适用于小长度尺度但不适用于大长度尺度的系统中异常扩散现象的起源。我们进一步描述了毛细管主导系统的波动，由于合作事件的不可逆性，这些波动是非平稳的。