2025/12/03 by Ignacio S. Gomez, Gomez, Ignacio Sebastián, Guilherme Vieira Brito Junior +5
Physics and Astronomy · #Advanced Mathematical Theories and Applications #Chaos control and synchronization #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Mathematical Physics (math-ph) #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.2512.04202
openalex publication_date 2025/12/03 · openalex created_date 2025/12/06 · openalex updated_date 2026/08/03
In this work, we study the dynamics of the logistic map based on a probabilistic characterization in terms of the invariant density. We analyze the relevant regimes of the dynamics (regular, oscillatory, onset chaotic and fully chaotic) in terms of the Fisher information and the Crámer-Rao (CR) complexity. We have found that these informational quantifiers allow to distinguish the dynamical regions of the map, by maximizing the Fisher information in the regular behavior and with the CR complexity exhibiting variations and a maximum near to the Pameau-Maneville scenario. Fisher information as a function of time is examined in the light of Frieden's informational interpretation of the Second Law of Thermodynamics. We apply the Equipartition Theorem to propose a definition of temperature for the logistic map, providing a macroscopic signature of the dynamics.