Dr. Dogan Comez
Department of Mathematics
Modern ergodic theory; from a physics hypothesis to a mathematical theory
In their pursuit to lay firm foundations for statistical mechanics, late 19th century physicists Boltzmann, Gibbs, Maxwell, Ehrenfest and others introduced concepts that tie the behavior of ensembles typically arising in statistical mechanics to the properties of single systems. One peculiar such concept, due to Boltzmann and Ehrenfest, has been known as the ergodic hypothesis. Roughly speaking, it states that “a system that is left to itself in its actual state of motion, will sooner or later, pass through every phase points compatible with the total energy of the system.” Since its introduction, the ergodic hypothesis has been a controversial one; and hence, it has been under scrutiny by its skeptics as well as adherents. It turns out that, in the form it was formulated, it is not a valid; however, with some “minimal modification”, namely the quasi-ergodic hypothesis, has been fruitful. Indeed, it led to a well-developed and an active mathematical theory today: the ergodic theory. Since the speaker is a mathematician with very rudimentary physics background, this talk aims to provide an account of the developments in ergodic theory starting with its humble beginnings till current results.