V2EX grand canonical ensemble

Grand Canonical Ensemble

定义 Definition

巨正则系综:统计物理中描述一种与“粒子库”和“热库”相接触的系统的概率集合。系统的温度 \(T\)体积 \(V\)化学势 \(\mu\) 固定,而系统内的粒子数 \(N\)能量 \(E\) 都允许涨落。它常用于研究开放体系、吸附、相变以及量子多体系统等。
(注:在不同语境下还会涉及“巨配分函数/巨正则配分函数”等相关概念。)

发音 Pronunciation (IPA)

/rnd knnkl nsmbl/

例句 Examples

A grand canonical ensemble allows particle number to fluctuate.
巨正则系综允许粒子数发生涨落。

In the grand canonical ensemble, equilibrium properties follow from the grand partition function at fixed \(T\), \(V\), and \(\mu\).
在巨正则系综中,平衡性质可由在固定 \(T\)、\(V\)、\(\mu\) 条件下的巨配分函数推出。

词源 Etymology

grand 在此并非“宏伟”,而是表示“更一般、更扩展的”;canonical 源自“规范/正则”的含义,用来指一类标准化的统计描述;ensemble 来自法语,意为“集合、整体”。合起来表示:相较于“正则系综”(固定 \(N\))更“扩展”的那种统计集合因为它把粒子数也纳入可变范围。

相关词 Related Words

文学与名著用例 Literary Works

  • Statistical Mechanics(R. K. Pathria & Paul D. Beale):系统介绍系综理论,巨正则系综是核心章节之一。
  • Statistical Mechanics(Kerson Huang):在量子统计与多体问题中频繁使用巨正则系综表述。
  • Statistical Physics(Landau & Lifshitz, Course of Theoretical Physics):以理论物理风格讨论系综与热力学势,包含巨正则框架。
  • McQuarrie’s Statistical Mechanics(Donald A. McQuarrie):面向化学与物理学习者,常用巨正则系综处理粒子交换体系。
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