Stability and ensemble inequivalence in a globally coupled system

Area of Science:

• Statistical mechanics
• Nonlinear dynamics
• Physics of complex systems

Background:

• Globally coupled rotors are a fundamental model for studying synchronization phenomena.
• Understanding the stability of different phases is crucial for characterizing system behavior.
• Ensemble inequivalence can arise in systems with long-range interactions.

Purpose of the Study:

• To analyze the stability of the incoherent phase in a system of globally coupled rotors.
• To investigate the Fokker-Planck equation's solutions for microcanonical and canonical ensembles.
• To elucidate the physical basis for quasistationarity in numerical simulations.

Main Methods:

• Derivation and analysis of the Fokker-Planck equation for globally coupled rotors.
• Examination of the system's solutions under different ensemble conditions (microcanonical and canonical).
• Temperature-dependent stability analysis of the derived solutions.

Main Results:

• The Fokker-Planck equation yields distinct solutions for the microcanonical and canonical ensembles.
• The stability of these solutions exhibits differential dependence on temperature.
• This temperature-driven inequivalence between ensembles is demonstrated.

Conclusions:

• The study confirms the inequivalence of microcanonical and canonical ensembles for this rotor system.
• The observed differences in solution stability provide a physical explanation for quasistationarity.
• Findings highlight the importance of ensemble choice in statistical mechanics of coupled systems.