The Ehrenfest fleas

from model to theory

D. Costantini

U. Garibaldi

pp. 107-142

in: Synthese 139 (1), 2004.

Abstract

A generalization of Ehrenfest's urn model is suggested. This will allow usto treat a wide class of stochastic processes describing the changes ofmicroscopic objects. These processes are homogeneous Markov chains. Thegeneralization proposed is presented as an abstract conditional (relative)probability theory. The probability axioms of such a theory and some simpleadditional conditions, yield both transition probabilities and equilibriumdistributions. The resulting theory interpreted in terms of particles andsingle-particle states, leads to the usual formulae of quantum and classicalstatistical mechanics; in terms of chromosomes and allelic types, it allowsthe deduction of many genetical models including the Ewens sampling formula;in terms of agents' strategies, it gives a justification of the ``herdbehaviour'' typical of a population of heterogeneous economic agents.