论文标题
合奏理论的数学
The Mathematics of the Ensemble Theory
论文作者
论文摘要
这项研究表明，当系统通过某种数学形式的集合描述系统时，广义玻尔兹曼分布是数学上唯一与热力学一致的分布。这种数学形式非常笼统，因此规范，宏大的或等温 - 静态合奏理论都是这种形式的特殊情况。与统计力学（SM）的标准教科书形式主义相比，此方法不需要先前的分布，不假定熵的功能形式或最大化，并且采用更少的假设。因此，这种新的见解挑战了对先前分布在SM中的要求的信念，并提供了一种推导Boltzmann分布的新方法。这项研究还揭示了SM的基本组成部分的逻辑和数学约束。因此，它可能有可能使研究人员对非玻璃体gibbs SM和研究SM基础的哲学家有益。
This study shows that the generalized Boltzmann distribution is the only distribution mathematically consistent with thermodynamics when the system is described by an ensemble of a certain mathematical form. This mathematical form is very general, such that the canonical, grand-canonical, or isothermal-isobaric ensemble theories are all special cases of this form. Compared with the standard textbook formalism of the statistical mechanics (SM), this approach does not require a prior distribution, does not assume the functional form or maximization of entropy, and employs fewer assumptions. Therefore, this new insight challenges the belief on the requirement of a prior distribution in SM and provides a new way to derive the Boltzmann distribution. This study also reveals the logical and mathematical constraints of SM's fundamental components; therefore, it could potentially benefit researchers on non-Boltzmann-Gibbs SM and philosophers studying the foundations of SM.
