TITLE:
Brownian Motion in an External Field Revisited
AUTHORS:
Angelo Plastino, Mario Carlos Rocca, Diana Monteoliva, Alberto Hernando
KEYWORDS:
Divergent Partition Functions, Statistical Mechanics, Fisher Information
JOURNAL NAME:
Journal of Modern Physics,
Vol.12 No.2,
January
18,
2021
ABSTRACT: 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.