We associate to the p-th Ré ́nyi entropy a definition of entropy power, which is the natural extension of Shannon’s entropy power and exhibits a nice behaviour along solutions to the p-nonlinear heat equation in Rn. We show that the Rényi entropy power of general probability densities solving such equations is always a concave function of time, whereas it has a linear behaviour in correspondence to the Barenblatt source- type solutions. This result extends Costa’s concavity inequality for Shannon’s entropy power to Rényi entropies. The research that led to the present paper was partially supported by a grant of the group GNFM of INdAM.

The concavity of Renyi entropy power

SAVARE', GIUSEPPE;TOSCANI, GIUSEPPE
2014-01-01

Abstract

We associate to the p-th Ré ́nyi entropy a definition of entropy power, which is the natural extension of Shannon’s entropy power and exhibits a nice behaviour along solutions to the p-nonlinear heat equation in Rn. We show that the Rényi entropy power of general probability densities solving such equations is always a concave function of time, whereas it has a linear behaviour in correspondence to the Barenblatt source- type solutions. This result extends Costa’s concavity inequality for Shannon’s entropy power to Rényi entropies. The research that led to the present paper was partially supported by a grant of the group GNFM of INdAM.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11571/866438
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