统计热力学Statistical mechanics

宏观状态对应大量微观状态，体系的平衡态是微观状态数 W 最多的状态，熵 S = k·ln W。吉布斯系综方法考虑大量处于相同宏观条件下的体系副本：微正则系综（N、V、E 固定）、正则系综（N、V、T 固定）和巨正则系综（μ、V、T 固定）。经典粒子服从玻尔兹曼统计，量子粒子中费米子服从费米-狄拉克统计（电子），玻色子服从玻色-爱因斯坦统计（光子、⁴He）。

A macrostate corresponds to vast numbers of microstates, and equilibrium is the macrostate with the most microstates W, with entropy S = k·ln W. Gibbs's ensemble method considers many copies of a system under the same macroscopic conditions: microcanonical (fixed N, V, E), canonical (fixed N, V, T) and grand canonical (fixed μ, V, T). Classical particles follow Boltzmann statistics, while quantum fermions such as electrons follow Fermi–Dirac statistics and bosons such as photons and ⁴He follow Bose–Einstein statistics.

19 世纪中叶克劳修斯和麦克斯韦发展了气体分子运动论。玻尔兹曼在 1870 年代建立统计解释，遭到马赫、奥斯特瓦尔德等人的强烈反对，他在 1906 年自杀，两年后佩兰的布朗运动实验证实了原子的存在。1902 年吉布斯出版《统计力学基本原理》，系统建立了系综理论。1924–1926 年玻色、爱因斯坦、费米和狄拉克建立了量子统计。

Clausius and Maxwell developed the kinetic theory of gases in the mid-nineteenth century. Boltzmann built the statistical interpretation in the 1870s against fierce opposition from Mach, Ostwald and others; he took his own life in 1906, two years before Perrin's Brownian-motion experiments confirmed the existence of atoms. Gibbs's Elementary Principles in Statistical Mechanics (1902) set out ensemble theory systematically, and Bose, Einstein, Fermi and Dirac founded quantum statistics in 1924–26.

统计热力学用于从光谱数据计算气体的熵、热容和平衡常数；解释固体热容的爱因斯坦模型和德拜模型；推导理想溶液和正规溶液理论、朗缪尔吸附等温式；高分子链构象统计（弗洛里）；过渡态理论和反应速率；以及分子模拟（分子动力学和蒙特卡罗方法）的理论基础。

Statistical mechanics computes gas entropies, heat capacities and equilibrium constants from spectroscopic data; explains the Einstein and Debye models of solid heat capacity; derives ideal- and regular-solution theory and the Langmuir isotherm; underlies Flory's statistics of polymer chain conformations, transition-state theory and reaction rates; and provides the theoretical basis of molecular simulation by molecular dynamics and Monte Carlo methods.