ArticleEntropy (Basel, Switzerland)2025
Hyperbolic Diffusion Functionals on a Ring with Finite Velocity.
Article in Entropy (Basel, Switzerland), 2025. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.
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Abstract
I study a lattice with periodic boundary conditions using a non-local master equation that evolves over time. I investigate different system regimes using classical theories like Fisher information, Shannon entropy, complexity, and the Cramér-Rao bound. To simulate spatial continuity, I employ a large number of sites in the ring and compare the results with continuous spatial systems like the Telegrapher's equations. The Fisher information revealed a power-law decay of t-ν, with ν=2 for short times and ν=1 for long times, across all jump models. Similar power-law trends were also observed for complexity and the Fisher information related to Shannon entropy over time. Furthermore, I analyze toy models with only two ring sites to understand the behavior of the Fisher information and Shannon entropy. As expected, a ring with a small number of sites quickly converges to a uniform distribution for long times. I also examine the Shannon entropy for short and long times.
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