Complexity and disequilibrium in the dipole-type Hamiltonian mean-field model.

Area of Science:

• Statistical mechanics
• Information theory
• Computational physics

Background:

• The Hamiltonian mean-field (HMF) model is a fundamental system for studying phase transitions and complex dynamics.
• Understanding information properties like complexity and disequilibrium is crucial for characterizing physical systems.

Purpose of the Study:

• To investigate information-theoretic properties, specifically complexity and disequilibrium, within the dipole-type Hamiltonian mean-field model.
• To analytically derive and assess statistical, thermodynamical, and information measures for the model.

Main Methods:

• Utilizing the partition function in the canonical ensemble as a core analytical tool.
• Deriving statistical, thermodynamical, and information-theoretic measures from the partition function.
• Analyzing the temperature and particle number dependence of these derived measures.

Main Results:

• Information measures were found to be analytical and dependent on the number of particles.
• The derived measures align with theoretical predictions at high temperatures.
• Limitations were observed at low temperatures, indicating a deviation from expected behavior.

Conclusions:

• The study provides insights into the information-theoretic landscape of the HMF model.
• A specific temperature interval was identified where the model's classicality is well-represented.
• The findings highlight the utility of information measures in understanding system dynamics and limitations.