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Statistical complexity as indicator of the classical-quantum crossover
M Escobar1, F Pennini1,2, A Plastino3
1Departamento de Física, Universidad Católica del Norte, Av. Angamos 0610, Antofagasta, Chile.
Chaos (Woodbury, N.Y.)
|July 14, 2025
Summary
Statistical complexity (C) may indicate when thermodynamic systems transition from classical to quantum behaviors. A maximum in C was observed at a characteristic temperature (Tc) across ideal and van der Waals gases, suggesting C as a quantum crossover proxy.
Area of Science:
- Thermodynamics
- Statistical Mechanics
- Quantum Physics
Background:
- Classical and quantum statistics describe thermodynamic systems differently.
- Identifying the crossover point where quantum effects emerge is crucial for understanding system behavior.
- Statistical complexity measures quantify system disorder and structure.
Purpose of the Study:
- To investigate statistical complexity (C) as an indicator of the classical-to-quantum behavior crossover in thermodynamic systems.
- To analyze the behavior of C and disequilibrium (D) in ideal and van der Waals gases near quantum regimes.
- To determine if C can serve as a proxy for detecting quantum effects.
Main Methods:
- Utilized the López-Ruiz, Mancini, and Calbet (LMC) statistical complexity measure (C).
- Analyzed C and disequilibrium (D) for ideal and van der Waals gases.
- Examined system behavior as it approaches quantum statistical significance.
Main Results:
- Statistical complexity (C) exhibited a well-defined maximum at a characteristic temperature (Tc) for all analyzed models.
- The numerical value of C at Tc was consistent across different gas models.
- The van der Waals gas showed a shift in Tc dependent on the excluded volume parameter (b), indicating interaction influence.
Conclusions:
- Statistical complexity (C) may effectively signal the transition from classical to quantum regimes in thermodynamic systems.
- The consistent maximum value of C at Tc suggests it captures fundamental structural changes related to quantum emergence.
- C shows promise as a tool for detecting quantum statistical effects in many-body systems.
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