Entropy of continuous mixtures and the measure problem

P. Maynar (1) , E. Trizac (2)

1 Universidad de Sevilla = University of Seville
2 LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

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/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 entropy-like functional, that is free of the measure problem. This condition amounts to a factorization property of the Jacobian associated to the binary collision law, from which the proper weighting of phase space directly follows.

Domaines: Mécanique statistique [cond-mat.stat-mech]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

P. Maynar, E. Trizac. Entropy of continuous mixtures and the measure problem. Physical Review Letters, 2011, 106, pp.160603. ⟨10.1103/PhysRevLett.106.160603⟩. ⟨hal-00594546⟩