Author(s)

Angelo Plastino^1,2, Mario Carlos Rocca^1,3,4, Diana Monteoliva^1,5, Alberto Hernando²

¹Departamento de Física, Universidad Nacional de La Plata, La Plata, Argentina.
²Kido Dynamics SA, Lausanne, Switzerland.
³Departamento de Mateática, Universidad Nacional de La Plata, La Plata, Argentina.
⁴Consejo Nacional de Investigaciones Científicas y Tecnológicas, (IFLP-CCT-CONICET)-C. C. 727, La Plata, Argentina.
⁵Comisión de Investigaciones Científicas, Provincia de Buenos Aires La Plata, La Plata, Argentina.

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.

Divergent Partition Functions, Statistical Mechanics, Fisher Information

Plastino, A. , Rocca, M. , Monteoliva, D. and Hernando, A. (2021) Brownian Motion in an External Field Revisited. Journal of Modern Physics, 12, 82-90. doi: 10.4236/jmp.2021.122008.