title: Entropy of continuous mixtures and the measure problem.
abstract: In its continuous version, the entropy functional measuring the information content of a given probability density may be plagued by a "measure" problem that results from improper weighting of phase space. This issue is addressed considering a generic collision process whereby a large number of particles or agents randomly and repeatedly interact in pairs, with prescribed conservation law(s). We find a sufficient condition under which the stationary single-particle distribution function maximizes an entropylike functional, that is free of the measure problem. This condition amounts to a factorization property of the Jacobian associated with the binary collision law, from which the proper weighting of phase space directly follows.
authors: Física Teórica, Universidad de Sevilla, Apartado de Correos, Sevilla, Spain.
authors: Pablo
authors: P
authors: Maynar
authors: Emmanuel
authors: E
authors: Trizac