Yang-Lee theory for a nonequilibrium phase transition

Area of Science:

• Statistical Mechanics
• Non-equilibrium Thermodynamics
• Complex Systems Analysis

Background:

• Phase transitions are critical phenomena observed in many physical systems.
• The Yang-Lee theory describes equilibrium phase transitions via roots of the partition function.
• Understanding nonequilibrium phase transitions is crucial for complex systems.

Purpose of the Study:

• To extend the Yang-Lee theory of phase transitions to nonequilibrium systems.
• To analyze phase transitions in a one-dimensional diffusion model.
• To identify and characterize different phases and their coexistence.

Main Methods:

• Studying the grand canonical partition function in terms of complex fugacity.
• Analyzing the real and positive roots of the partition function.
• Investigating a one-dimensional diffusion model with periodic boundary conditions.

Main Results:

• Real and positive roots of the partition function were found to mark phase transitions in the nonequilibrium system.
• Two distinct regions of analyticity, corresponding to different phases, were identified based on diffusion rates.
• The coexistence of these phases was observed within a specific parameter space region.
• The condensation point was computed with high accuracy.

Conclusions:

• The Yang-Lee approach is applicable to analyzing nonequilibrium phase transitions.
• The diffusion model exhibits distinct phases and phase coexistence.
• The study provides a method for accurately computing the condensation point in such systems.