Brownian Motion in an External Field Revisited

• 作者: Angelo Plastino Mario Carlos Rocca Diana Monteoliva Alberto Hernando
• 来源期刊: 现代物理(英文)
• 学科: 数学
• 关键词: Divergent Partition Functions Statistical Mechanics Fisher Information
• 年，卷（期）: 2021,（2）
• 页码范围: 82-90
• 页数: 9页
• 分类号: O17

摘要

In many interesting physical examples, the partition function is divergent, as first pointed out in 1924 by Fermi (for the hydrogen-atom case). Thus, the usual toolbox of statistical mechanics becomes unavailable, notwithstanding the well-known fact that the pertinent system may appear to be in a thermal steady state. We tackle and overcome these difficulties hereby appeal to firmly established but not too well-known mathematical recipes and obtain finite values for a typical divergent partition function, that of a Brownian particle in an external field. This allows not only for calculating thermodynamic observables of interest, but for also instantiating other kinds of statistical mechanics’ novelties.