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The entropy production is not always monotone for the Kac equation
In 1966, McKean conjectured that the entropy production of Kac's caricature of a Maxwellian gas is nonincreasing in time \cite{McKean66}. We disprove this conjecture for the standard uniform-angle Kac equation. Our counterexamples are smooth, strictly positive, even mixtures of two Gaussians at diff
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