Abstract We continue our exploration of thermodynamics at long observational timescales, “slow time,” by including turbulent dynamics leading to a condition of fluctuating local equilibrium. Averaging these fluctuations in wind speed and temperature results in a velocity distribution with heavy tails which, however, are necessarily truncated at some large molecular speed preserving all moments of the velocity distribution including the energy. This leads to an expression for the ideal gas law in slow time which as its core has the superficially familiar term 3 2 N k θ\frac{3}{2}Nk\theta in addition to a term accounting for the large-scale fluctuations, which is also proportional to the particle number N; θ is a new temperature including thermalization of wind. The traditional temperature T no longer exists. Likewise, the additional energy term necessitates a new quantity that parallels entropy in the sense that it captures hidden degrees of freedom. Like entropy, it captures physical properties manifesting indirectly, but on scales larger than the familiar laboratory scales. We call this quantity epitropy.

中文翻译：

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慢时间的理想气体

摘要 我们通过包括导致局部平衡波动的条件的湍流动力学，继续在长观测时间尺度上对热力学进行探索，“慢时间”。对风速和温度的这些波动进行平均会导致带有重尾的速度分布，然而，在一些大分子速度下必须截断，以保留包括能量在内的速度分布的所有矩。这导致了慢时理想气体定律的表达式，其核心是表面上熟悉的术语 3 2 N k θ\frac{3}{2}Nk\theta 以及解释大规模波动的术语，这也与粒子数 N 成正比；θ 是新的温度，包括风的热化。传统的温度 T 不再存在。同样地，额外的能量项需要一个新的量，它与熵平行，因为它捕获了隐藏的自由度。与熵一样，它捕捉间接表现出来的物理特性，但其尺度大于熟悉的实验室尺度。我们称这个数量为外熵。