A Generalization of the Concavity of Renyi Entropy Power | |
Guo, Laigang1; Yuan, Chun-Ming2,3; Gao, Xiao-Shan2,3 | |
刊名 | ENTROPY |
2021-12-01 | |
卷号 | 23期号:12页码:18 |
关键词 | Renyi entropy entropy power inequality nonlinear heat equation |
DOI | 10.3390/e23121593 |
英文摘要 | Recently, Savare-Toscani proved that the Renyi entropy power of general probability densities solving the p-nonlinear heat equation in R n is a concave function of time under certain conditions of three parameters n , p , mu , which extends Costa's concavity inequality for Shannon's entropy power to the Renyi entropy power. In this paper, we give a condition f ( n , p , mu ) of n , p , mu under which the concavity of the Renyi entropy power is valid. The condition f ( n , p , mu ) contains Savare-Toscani's condition as a special case and much more cases. Precisely, the points ( n , p , mu ) satisfying Savare-Toscani's condition consist of a two-dimensional subset of R (3) , and the points satisfying the condition f ( n , p , mu ) consist a three-dimensional subset of R (3) . Furthermore, f ( n , p , mu ) gives the necessary and sufficient condition in a certain sense. Finally, the conditions are obtained with a systematic approach. |
资助项目 | NSFC[11688101] ; NSFC[NKRDP 2018YFA0704705] ; Beijing Natural Science Foundation[Z190004] ; Fundamental Research Funds for the Central Universities[2021NTST32] |
WOS研究方向 | Physics |
语种 | 英语 |
出版者 | MDPI |
WOS记录号 | WOS:000738892800001 |
内容类型 | 期刊论文 |
源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/59850] |
专题 | 中国科学院数学与系统科学研究院 |
通讯作者 | Gao, Xiao-Shan |
作者单位 | 1.Beijing Normal Univ, Sch Math Sci, Lab Math & Complex Syst, Minist Educ, Beijing 100875, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, KLMM, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Beijing 100049, Peoples R China |
推荐引用方式 GB/T 7714 | Guo, Laigang,Yuan, Chun-Ming,Gao, Xiao-Shan. A Generalization of the Concavity of Renyi Entropy Power[J]. ENTROPY,2021,23(12):18. |
APA | Guo, Laigang,Yuan, Chun-Ming,&Gao, Xiao-Shan.(2021).A Generalization of the Concavity of Renyi Entropy Power.ENTROPY,23(12),18. |
MLA | Guo, Laigang,et al."A Generalization of the Concavity of Renyi Entropy Power".ENTROPY 23.12(2021):18. |
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