Hyperbolic Diffusion Functionals on a Ring with Finite Velocity

• Autores: Nizama Mendoza, Marco Alfredo
• Año de publicación: 2025
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: LATTICE; PERIODIC BOUNDARY CONDITIONS; FISHER’S INFORMATION; SHANNON’S ENTROPY; CRAMÉR–RAO BOUND; COMPLEXITY; POWER-LAW
• Institución: Consejo Nacional de Investigaciones Científicas y Técnicas

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.
Fil: Nizama Mendoza, Marco Alfredo. Universidad Nacional del Comahue. Facultad de Ingeniería. Departamento de Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Confluencia; Argentina