Dresden 2020 – wissenschaftliches Programm
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DY 21.1: Hauptvortrag
Dienstag, 17. März 2020, 09:30–10:00, HÜL 186
From Non-normalizable Boltzmann-Gibbs statistics to infinite-ergodic theory — •ELi Barkai — Physics Department, Bar-Ilan University, Ramat-Gan, Israel
We consider a single particle coupled to a a thermal heat bath, when the system approaches in the long time limit a non-normalised Boltzmann state. This could be a particle interacting with a wall, the force field falling off faster than one over the particle-wall distance. We show how infinite ergodic theory is a useful tool, the infinite invariant measure (the non-normalised state) is given by Boltzmann-Gibbs theory. Time averages of integrable observables are described by the Aaronson-Darling-Kac theorem. We derive our main results using an entropy maximum principle, and discuss the virial theorem when Boltzmann-Gibbs measure is non-normalisable.