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Entropy 2017, 19(1), 9; doi:10.3390/e19010009

A Dissipation of Relative Entropy by Diffusion Flows

Department of Information Sciences, Ochanomizu University, 2-1-1, Otsuka, Bunkyo-ku, Tokyo 112-8610, Japan
Academic Editor: Angelo Plastino
Received: 5 October 2016 / Revised: 18 December 2016 / Accepted: 22 December 2016 / Published: 27 December 2016
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Abstract

Given a probability measure, we consider the diffusion flows of probability measures associated with the partial differential equation (PDE) of Fokker–Planck. Our flows of the probability measures are defined as the solution of the Fokker–Planck equation for the same strictly convex potential, which means that the flows have the same equilibrium. Then, we shall investigate the time derivative for the relative entropy in the case where the object and the reference measures are moving according to the above diffusion flows, from which we can obtain a certain dissipation formula and also an integral representation of the relative entropy. View Full-Text
Keywords: relative entropy; relative Fisher information; Fokker–Planck equation; entropy dissipation; entropy gap relative entropy; relative Fisher information; Fokker–Planck equation; entropy dissipation; entropy gap
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Yoshida, H. A Dissipation of Relative Entropy by Diffusion Flows. Entropy 2017, 19, 9.

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