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Quantum Statistical Complexity Measure as a Signaling of Correlation Transitions.

Entropy (Basel, Switzerland)·2022

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Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

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A Complexity-Based Approach to Quantum Observable Equilibration.

Marcos G Alpino¹, Tiago Debarba², Reinaldo O Vianna¹

¹Departamento de Física, ICEx, Universidade Federal de Minas Gerais, Av. Pres. Antônio Carlos 6627, Belo Horizonte 31270-901, MG, Brazil.

Entropy (Basel, Switzerland)

|August 28, 2025

Summary

We introduce a statistical complexity measure to track equilibration in isolated quantum systems. This measure effectively distinguishes complex dynamics from non-complex, quasi-periodic behavior, aiding the study of quantum system equilibration.

Keywords:

equilibration non-integrable Hamiltonians observable equilibration statistical complexity

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Area of Science:

Quantum physics
Statistical mechanics
Complex systems

Background:

Unitary dynamics in isolated quantum systems preserve global purity.
Observable expectation values often exhibit equilibration-like behavior despite global purity preservation.
The emergence of equilibrium from unitary dynamics is a key question in quantum mechanics.

Purpose of the Study:

To investigate the role of statistical complexity in assigning equilibration in isolated quantum systems.
To examine how quantum state complexity evolves during the transition from coherence to equilibrium.
To develop a complexity measure sensitive to non-complex dynamics, such as quasi-periodic behavior.

Main Methods:

Definition of a classical statistical complexity measure based on observable entropy and deviation from equilibrium.
Analysis of quantum state complexity evolution.
Numerical simulations using an Ising-like non-integrable Hamiltonian spin-chain model.

Main Results:

The proposed statistical complexity measure effectively tracks the dynamical progression towards equilibration.
The measure successfully distinguishes between complex and non-complex (quasi-periodic) quantum dynamics.
Simulations support the measure's ability to identify systems exploring limited Hilbert space regions while preserving coherence.

Conclusions:

Statistical complexity offers a meaningful tool for studying the emergence of equilibrium in isolated quantum systems.
Complexity analysis provides insight into the transition from initial coherence to equilibrium states.
This approach advances the understanding of how classicality emerges from microscopic quantum systems.