ABSTRACT

A former theoretical picture, presented to relate geometry and statistics in chemical physics, is addressed to deal with real gases, cellular froths and simple liquids. In previous studies, scaling laws for macromolecules in solution were derived from a relativistic theory of self-diffusion in a liquid and then geometrically reformulated to link statistics at different length scales.  The analogy between polymer chain and geodesic path led successively to an equivalence principle for Boltzmann and Lobachevskij factors and a partition function concept for geometry. In this paper, statistics (wave and partition functions) and kinetics (time) are related to geometry (metric and curvature) and topology (Euler-Poincaré characteristic) by means of quantities defined here as metric wave and topological curvature.