什么时候吉布斯相平均值和玻尔兹曼平衡值是一致的?

Q1 Arts and Humanities

Studies in History and Philosophy of Modern Physics Pub Date : 2020-11-01 DOI:10.1016/j.shpsb.2020.05.003

Charlotte Werndl , Roman Frigg

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引用次数: 4

摘要

本文旨在通过研究力学平均原理来阐明玻尔兹曼统计力学与吉本统计力学之间的关系。力学平均原理认为，在一定条件下，玻尔兹曼平衡值与吉本相平均值近似相等。这些条件是什么?我们确定了玻尔兹曼平衡值近似等于吉布斯相平均的三个条件:Khinchin条件和两个新定理(平均等效定理和消去定理)产生的两个条件。这些条件并不容易满足，而且统计力学的核心模型，如六顶点模型和伊辛模型，在这些模型中可能会失效。

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When do Gibbsian phase averages and Boltzmannian equilibrium values agree?

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.

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来源期刊

Studies in History and Philosophy of Modern Physics 物理-科学史与科学哲学

自引率

0.00%

发文量

审稿时长

13.3 weeks

期刊介绍： Studies in History and Philosophy of Modern Physics is devoted to all aspects of the history and philosophy of modern physics broadly understood, including physical aspects of astronomy, chemistry and other non-biological sciences. The primary focus is on physics from the mid/late-nineteenth century to the present, the period of emergence of the kind of theoretical physics that has come to dominate the exact sciences in the twentieth century. The journal is internationally oriented with contributions from a wide range of perspectives. In addition to purely historical or philosophical papers, the editors particularly encourage papers that combine these two disciplines. The editors are also keen to publish papers of interest to physicists, as well as specialists in history and philosophy of physics.