Statistical quantifiers and nonlinear conservative-dissipative classical transition

Gaspar Gonzalez Acosta; Andrés M. Kowalski; Gaspar Gonzalez Acosta; Andrés M. Kowalski

doi:10.3934/math.2025913

AIMS Mathematics

2025, Volume 10, Issue 9: 20443-20465. doi: 10.3934/math.2025913

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Statistical quantifiers and nonlinear conservative-dissipative classical transition

Gaspar Gonzalez Acosta ^1,2,
Andrés M. Kowalski ^{1,2
,
,}

1.
Instituto de Física La Plata-CONICET/UNLP, 1900, Buenos Aires, Argentina
2.
Comision de Investigaciones Científicas (CIC)

Received: 05 May 2025 Revised: 23 August 2025 Accepted: 25 August 2025 Published: 05 September 2025

We investigated the dynamics of a regular nonlinear semiclassical system by employing Shannon entropy together with two associated formulations of statistical complexity: the López-Ruiz–Mancini–Calbet (LMC) and Jensen–Shannon approaches. Additionally, Tsallis entropy was used as an alternative quantifier. In this context, quantum variables interacted with a classical environment, and both conservative and dissipative regimes were considered. To compute information-theoretic quantifiers, probability distributions were extracted from the system's temporal evolution using the Bandt–Pompe permutation method. The classical limit was characterized by a motion invariant linked to the uncertainty principle. Our analysis revealed three distinct zones that characterized the structure of transitions across the classical–quantum boundary. These findings confirmed earlier results obtained in markedly different dynamical systems. This consistency supported the idea of a possible generalization, which, if established, would have significant implications for both semiclassical and quantum theories.
- quantum-classical interaction,
- conservative and dissipative regimes,
- classical limit,
- statistical complexity,
- Bandt-Pompe method
Citation: Gaspar Gonzalez Acosta, Andrés M. Kowalski. Statistical quantifiers and nonlinear conservative-dissipative classical transition[J]. AIMS Mathematics, 2025, 10(9): 20443-20465. doi: 10.3934/math.2025913

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Abstract

We investigated the dynamics of a regular nonlinear semiclassical system by employing Shannon entropy together with two associated formulations of statistical complexity: the López-Ruiz–Mancini–Calbet (LMC) and Jensen–Shannon approaches. Additionally, Tsallis entropy was used as an alternative quantifier. In this context, quantum variables interacted with a classical environment, and both conservative and dissipative regimes were considered. To compute information-theoretic quantifiers, probability distributions were extracted from the system's temporal evolution using the Bandt–Pompe permutation method. The classical limit was characterized by a motion invariant linked to the uncertainty principle. Our analysis revealed three distinct zones that characterized the structure of transitions across the classical–quantum boundary. These findings confirmed earlier results obtained in markedly different dynamical systems. This consistency supported the idea of a possible generalization, which, if established, would have significant implications for both semiclassical and quantum theories.

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