A local-global principle for nonequilibrium steady states.

Area of Science:

• Physics
• Complex Systems
• Statistical Mechanics

Background:

• Self-organization in equilibrium systems is explained by minimizing energy.
• Nonequilibrium systems lack a universal principle for self-organization.
• Rattling has emerged as a potential predictor of steady states in some nonequilibrium systems.

Purpose of the Study:

• To develop a theoretical framework for rattling in nonequilibrium systems.
• To determine the conditions under which rattling accurately predicts steady states.
• To explore the generality of rattling as a principle of self-organization.

Main Methods:

• Developed a theory of rattling based on Markov processes.
• Analyzed local-global relationships in steady states.
• Investigated random walks on random graphs, spin-glass dynamics, and animal collective behavior models.

Main Results:

• Rattling predicts a wider range of nonequilibrium steady states than previously claimed.
• The accuracy of rattling depends on the variance and correlation between local and global parts of a system.
• The theory provides precise conditions for rattling's predictive power.

Conclusions:

• Rattling is a more general principle of self-organization than previously understood.
• The Markov process theory clarifies the mechanisms behind rattling's success.
• Rattling's applicability extends to both equilibrium and nonequilibrium systems.