Fisher and Shannon Functionals for Hyperbolic Diffusion
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  • Release Date: 2024-08-05
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Playlist
  • hyperbolic diffusion
  • telegrapher’s equation
  • Shannon entropy
  • Fisher information
  • Cramer-Rao bound
Video Introduction

This video is adapted from 10.3390/e25121627

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 Cramér–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).

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If you have any further questions, please contact Encyclopedia Editorial Office.
Caceres, M.O.; Nizama, M.; Pennini, F. Fisher and Shannon Functionals for Hyperbolic Diffusion. Encyclopedia. Available online: https://encyclopedia.pub/video/video_detail/1329 (accessed on 21 December 2024).
Caceres MO, Nizama M, Pennini F. Fisher and Shannon Functionals for Hyperbolic Diffusion. Encyclopedia. Available at: https://encyclopedia.pub/video/video_detail/1329. Accessed December 21, 2024.
Caceres, Manuel Osvaldo, Marco Nizama, Flavia Pennini. "Fisher and Shannon Functionals for Hyperbolic Diffusion" Encyclopedia, https://encyclopedia.pub/video/video_detail/1329 (accessed December 21, 2024).
Caceres, M.O., Nizama, M., & Pennini, F. (2024, August 05). Fisher and Shannon Functionals for Hyperbolic Diffusion. In Encyclopedia. https://encyclopedia.pub/video/video_detail/1329
Caceres, Manuel Osvaldo, et al. "Fisher and Shannon Functionals for Hyperbolic Diffusion." Encyclopedia. Web. 05 August, 2024.
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