Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2411.13761

Statistical permutation quantifiers in the classical transition of conservative-dissipative systems

Gaspar Gonzalez, A.M. Kowalski

Published Nov 21, 2024• 0 citations
arXivHTMLPDF

Abstract

We study the behavior of a nonlinear semiclassical system using Shannon entropy and two approaches to statistical complexity. These systems involve the interaction between classical variables (representing the environment) and quantum ones. Both conservative and dissipative regimes are explored. To calculate the information metrics, probability distributions are derived from the temporal evolution via the Bandt-Pompe permutation method. Additionally, we describe the classical limit in terms of a motion invariant linked to the uncertainty principle. Our analysis reveals three distinct regions, including a mesoscopic one, along with other notable findings.

DOI
10.48550/arxiv.2411.13761

Related papers

Statistical quantifiers and nonlinear conservative-dissipative classical transition

Gaspar Gonzalez, Instituto de Física La Plata-CONICET/UNLP, 1900, Buenos Aires, Argentina, Andrés M. Kowalski +1 more

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.

AIMS Mathematics•Jan 1, 2025•0 citations

INFORMATION ENTROPY AND NONLINEAR SEMIQUANTUM DYNAMICS

Claudia M. Sarris, Araceli N. Proto

We describe how, departing from the Shannon entropy, it is possible to deal with semiquantum time-independent nonlinear Hamiltonians. The interplay between the quantal and classical degrees of freedom can be easily seen, and the set of differential equations that govern the temporal evolution of the quantal mean values and the classical variables is obtained. We find invariants of motion and, particularly, we describe under which conditions, the uncertainty principle remains as an invariant of motion too. Through the analysis of these invariants, it is possible to follow the transition of the system from quantum to classical regime and to conclude that the uncertainty principle behaves as an indicator telling us whether the system is in regular or irregular regime. A simple example is shown.

International Journal of Bifurcation and Chaos•Oct 1, 2009•6 citations

Chaos and complexity in the classical-quantum transition

A.M. Kowalski, M.T. Martín, Angelo Plastino +1 more

By recourse to the concept of Statistical Complexity we study here the classical-quantum transition in a special system that represents the matter-field interaction. Our work con-siders two distinct disequilibrium forms based on Euclidean norm and Jensen-Shannon divergence, on the one hand, and analyzes things, on the other one, by using two differ-ent numerical approaches for probability distribution, namely, relative wavelet energy and permutation patterns.

International Journal of Applied Mathematics & Statistics/International journal of applied mathematics and statistics•Feb 2, 2012•5 citations

Dynamical classic limit: Dissipative vs conservative systems

Gaspar Gonzalez, Angelo Plastino, A.M. Kowalski

We analyze the nonlinear dynamics of a quartic semiclassical system able to describe the interaction of matter with a field. We do it in both dissipative and conservative scenarios. In particular, we study the classical limit of both frameworks and compare the associated features. In the two environments, we heavily use a system's invariant, related to the Uncertainty Principle, that helps to determine how the dynamics tends to the pertinent classical limit. We exhibit the convergence to the classical limit and also verify that the Uncertainty Principle is complied with during the entire process, even in the presence of dissipation.

Chaos An Interdisciplinary Journal of Nonlinear Science•Jan 1, 2023•3 citations

The Quantum-Classical Transition as an Information Flow

A.M. Kowalski, Maria T. Martin, Luciano Zunino +2 more

We investigate the classical limit of the semiclassical evolution with reference to a well-known model that represents the interaction between matter and a given field. This is done by recourse to a special statistical quantifier called the “symbolic transfer entropy”. We encounter that the quantum-classical transition gets thereby described as the sign-reversal of the dominating direction of the information flow between classical and quantal variables.

Entropy•Jan 26, 2010•5 citations

Chaos in the quantum Duffing oscillator in the semiclassical regime under parametrized dissipation

Andrew Maris, Bibek Pokharel, Sharan Ganjam Seshachallam +2 more

We study the quantum dissipative Duffing oscillator across a range of system sizes and environmental couplings under varying semiclassical approximations. Using spatial complexity metrics based on Kullback-Leibler distances between phase-space attractors and temporal complexity metrics based on the Lyapunov exponent, we isolate the effect of the environment on quantum-classical differences. Moreover, we quantify the system sizes where quantum dynamics cannot be simulated using semiclassical or noise-added classical approximations. We find that a remarkable parametrically invariant meta-attractor emerges at a specific length scale and noise-added classical models deviate strongly from quantum dynamics below this scale. We also generalize the previous surprising result that classically regular orbits can have the greatest quantum-classical differences in the semiclassical regime and show that the dynamical growth of quantum-classical differences is not determined by the degree of classical chaos.

arXiv:2011.00118•Physical review. E•Aug 6, 2021•4 citations
We study the behavior of a nonlinear semiclassical system using Shannon entropy and two approaches to statistical complexity. These systems involve the interaction between classical variables (representing the environment) and quantum ones. Both conservative and dissipative regimes are explored. To calculate the information metrics, probability distributions are derived from the temporal evolution via the Bandt-Pompe permutation method. Additionally, we describe the classical limit in terms of a motion invariant linked to the uncertainty principle. Our analysis reveals three distinct regions, including a mesoscopic one, along with other notable findings.
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.
We describe how, departing from the Shannon entropy, it is possible to deal with semiquantum time-independent nonlinear Hamiltonians. The interplay between the quantal and classical degrees of freedom can be easily seen, and the set of differential equations that govern the temporal evolution of the quantal mean values and the classical variables is obtained. We find invariants of motion and, particularly, we describe under which conditions, the uncertainty principle remains as an invariant of motion too. Through the analysis of these invariants, it is possible to follow the transition of the system from quantum to classical regime and to conclude that the uncertainty principle behaves as an indicator telling us whether the system is in regular or irregular regime. A simple example is shown.
We analyze the nonlinear dynamics of a quartic semiclassical system able to describe the interaction of matter with a field. We do it in both dissipative and conservative scenarios. In particular, we study the classical limit of both frameworks and compare the associated features. In the two environments, we heavily use a system's invariant, related to the Uncertainty Principle, that helps to determine how the dynamics tends to the pertinent classical limit. We exhibit the convergence to the classical limit and also verify that the Uncertainty Principle is complied with during the entire process, even in the presence of dissipation.
We study the quantum dissipative Duffing oscillator across a range of system sizes and environmental couplings under varying semiclassical approximations. Using spatial complexity metrics based on Kullback-Leibler distances between phase-space attractors and temporal complexity metrics based on the Lyapunov exponent, we isolate the effect of the environment on quantum-classical differences. Moreover, we quantify the system sizes where quantum dynamics cannot be simulated using semiclassical or noise-added classical approximations. We find that a remarkable parametrically invariant meta-attractor emerges at a specific length scale and noise-added classical models deviate strongly from quantum dynamics below this scale. We also generalize the previous surprising result that classically regular orbits can have the greatest quantum-classical differences in the semiclassical regime and show that the dynamical growth of quantum-classical differences is not determined by the degree of classical chaos.