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Updated: May 25, 2025

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Summary
This summary is machine-generated.

This study analyzes a lattice system using master equations and classical theories. Fisher information shows a power-law decay over time, indicating system dynamics across different models.

Keywords:
Cramér–Rao boundFisher’s informationShannon’s entropycomplexitylatticeperiodic boundary conditionspower-law

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Area of Science:

  • Statistical Physics
  • Information Theory
  • Computational Physics

Background:

  • Investigating complex systems dynamics is crucial for understanding phenomena across various scientific disciplines.
  • Classical information measures provide valuable insights into system behavior and evolution.
  • Master equations are fundamental tools for modeling time-dependent probabilistic systems.

Purpose of the Study:

  • To analyze the dynamics of a lattice system with periodic boundary conditions using a non-local master equation.
  • To explore system regimes by applying classical information theories: Fisher information, Shannon entropy, complexity, and the Cramér-Rao bound.
  • To compare discrete lattice simulations with continuous spatial systems, such as Telegrapher's equations.

Main Methods:

  • Utilizing a non-local master equation to model a time-evolving lattice system with periodic boundary conditions.
  • Employing classical information-theoretic measures (Fisher information, Shannon entropy, complexity) to characterize system states.
  • Simulating spatial continuity with a large number of lattice sites and comparing with continuous models like Telegrapher's equations.
  • Analyzing simplified two-site toy models to understand fundamental behaviors.

Main Results:

  • Fisher information exhibits a power-law decay of t-ν, with ν=2 for short times and ν=1 for long times, consistent across all jump models.
  • Complexity and Fisher information related to Shannon entropy also display similar power-law decay trends over time.
  • Small lattice systems rapidly converge to a uniform distribution at long times.
  • Distinct behaviors of Fisher information and Shannon entropy were observed for short and long time scales.

Conclusions:

  • The study demonstrates consistent power-law decay in key information measures, revealing universal dynamics in the lattice system.
  • Classical information theories effectively characterize system evolution and provide a link between discrete and continuous models.
  • The findings offer insights into the statistical properties and emergent behaviors of complex systems evolving over time.