Fisher and Shannon Functionals for Hyperbolic Diffusion

被引：3

作者：

Caceres, Manuel O. ^{[1
,2
,3
]}

Nizama, Marco ^{[4
,5
]}

Pennini, Flavia ^{[6
,7
]}

机构：

[1] Ctr Atom Bariloche, Comis Nacl Energia Atom, Av E Bustillo 9500, RA-8400 San Carlos De Bariloche, Argentina

[2] Univ Nacl Cuyo, Inst Balseiro, Av E Bustillo 9500, RA-8400 San Carlos De Bariloche, Argentina

[3] Ctr Aton Bariloche, CONICET, Av E Bustillo 9500, RA-8400 San Carlos De Bariloche, Argentina

[4] Univ Nacl Comahue, Fac Ingn, Dept Fis, RA-8300 Neuquen, Argentina

[5] Univ Nacl Comahue, CONICET, RA-8300 Neuquen, Argentina

[6] Univ Nacl Mar del Plata UNMDP, Fac Ingn, Dept Fis, CONICET, RA-7600 Mar Del Plata, Argentina

[7] Univ Catolica Norte, Dept Fis, Av Angamos 0610, Antofagasta 1270709, Chile

来源：

ENTROPY | 2023年 / 25卷 / 12期

关键词：

hyperbolic diffusion; telegrapher's equation; Shannon entropy; Fisher information; Cramer-Rao bound; EQUATION; WAVES;

D O I：

10.3390/e25121627

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The complexity measure for the distribution in space-time of a finite-velocity diffusion process is calculated. Numerical results are presented for the calculation of Fisher's information, Shannon's entropy, and the Cramer-Rao inequality, all of which are associated with a positively normalized solution to the telegrapher's equation. In the framework of hyperbolic diffusion, the non-local Fisher's information with the x-parameter is related to the local Fisher's information with the t-parameter. A perturbation theory is presented to calculate Shannon's entropy of the telegrapher's equation at long times, as well as a toy model to describe the system as an attenuated wave in the ballistic regime (short times).

引用

页数：16

共 39 条

[21] On a property of Gauss's law [J].