A counterexample demonstrates that entropy production is not always monotone decreasing for the space-homogeneous Boltzmann equation with a non-standard collision kernel, disproving McKean's conjecture.
Differentials of entropy and fisher information along heat flow: a brief review of some conjectures.Preprint, 2022
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The entropy production is not always monotone in the space-homogeneous Boltzmann equation
A counterexample demonstrates that entropy production is not always monotone decreasing for the space-homogeneous Boltzmann equation with a non-standard collision kernel, disproving McKean's conjecture.