Introductory note to 1900

pp. 286-299

in: Ernst Zermelo, Calculus of variations, applied mathematics, and physics/Variationsrechnung, angewandte mathematik und physik, Berlin, Springer, 2013

Abstract

Here Zermelo returns to the foundations of statistical physics. He refers to Boltzmann's assumption of molecular disorder which he understands as implying that various stages of molecular motion can be seen as probabilistically independent. This understanding seems to be suggested by the concern he expresses, namely, that due to the assumed equations of motion in the theory of gases these various stages are not mutually independent but functionally related. Zermelo proposes a definition of a probability measure on phase space and presents three theorems. The first is actually just the well-known Liouville theorem. The other two deal with the question whether any entropy-like function can be defined on phase space which might have the property of changing monotonically in time.