An explicit non-Gaussian probability measure on R makes the fifth time derivative of entropy positive along the heat flow, disproving the Gaussian completely monotone conjecture and related claims.
Gaussian optimality for derivatives of differential entropy using linear matrix inequalities
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A Counterexample to the Gaussian Completely Monotone Conjecture
An explicit non-Gaussian probability measure on R makes the fifth time derivative of entropy positive along the heat flow, disproving the Gaussian completely monotone conjecture and related claims.