Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2011-04-26
Phys.Rev.Lett.106:160603,2011
Physics
Condensed Matter
Statistical Mechanics
Scientific paper
10.1103/PhysRevLett.106.160603
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.
Maynar P.
Trizac Emmanuel
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