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A Counter Example to Cercignani’s Conjecture for the d Dimensional Kac Model
(SpringerJournal of Statistical Physics, 2012-08-21)
Kac’s d dimensional model gives a linear, many particle, binary collision model from which, under suitable conditions, the celebrated Boltzmann equation, in its spatially homogeneous form, arise as a mean field limit. The ...
On Villani's conjecture concerning entropy production for the Kac Master equation
(America Institute of Mathematical SciencesKinetic and Related Models, 2011-06-01)
In this paper we take an idea presented in recent paper by Carlen, Carvalho, Le Roux, Loss, and Villani ([3]) and push it one step forward to find an exact estimation on the entropy production. The new estimation essentially ...