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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
