Entropy of continuous mixtures and the measure problem

P. Maynar 1, E. Trizac 2

Physical Review Letters 106 (2011) 160603

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.

  • 1. Fisica Teorica, Universidad de Sevilla,
    Universidad de Sevilla
  • 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
    CNRS : UMR8626 – Université Paris XI - Paris Sud