This paper aims to shed light on the relation between Boltzmannian statistical mechanics and Gibbsian statistical mechanics by studying the Mechanical Averaging Principle, which says that, under certain conditions, Boltzmannian equilibrium values and Gibbsian phase averages are approximately equal. What are these conditions? We identify three conditions each of which is individually sufficient (but not necessary) for Boltzmannian equilibrium values to be approximately equal to Gibbsian phase averages: the Khinchin condition, and two conditions that result from two new theorems, the Average Equivalence Theorem and the Cancelling Out Theorem. These conditions are not trivially satisfied, and there are core models of statistical mechanics, the six-vertex model and the Ising model, in which they can fail.

本文旨在通过研究机械平均原理来阐明玻尔兹曼统计力学与吉布斯统计力学之间的关系，该原理指出，在一定条件下，玻尔兹曼平衡值和吉布斯相平均近似相等。这些条件是什么？我们确定三个条件，每个条件足以使玻尔兹曼平衡值大约等于吉布斯相平均：Khinchin条件，以及两个新定理产生的两个条件：平均当量定理和抵消定理。这些条件不能完全满足，并且存在统计力学的核心模型，六顶点模型和Ising模型，在这些模型中它们可能会失败。