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.
Lower bounds on multivariate higher order derivatives of differential entropy
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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.