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.
A review of mathematical topics in collisional kinetic theory.Handbook of mathematical fluid dynamics, 1:71–74
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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.