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Updated: Jul 7, 2025

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
Published on: September 26, 2016
Fisher and Shannon Functionals for Hyperbolic Diffusion
Manuel O Cáceres1,2, Marco Nizama3, Flavia Pennini4,5
1Comision Nacional de Energia Atomica, Centro Atomico Bariloche and Instituto Balseiro, Universidad Nacional de Cuyo, Av. E. Bustillo 9500, Bariloche CP 8400, Argentina.
Abstract:
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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