Entropy of continuous mixtures and the measure problem
Statistical Mechanics
2011-06-08 v1 Mathematical Physics
math.MP
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/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.
Cite
@article{arxiv.1104.4914,
title = {Entropy of continuous mixtures and the measure problem},
author = {P. Maynar and E. Trizac},
journal= {arXiv preprint arXiv:1104.4914},
year = {2011}
}