Rules for transition rates in nonequilibrium steady states

Area of Science:

• Statistical Mechanics
• Non-equilibrium Thermodynamics
• Information Theory

Background:

• Canonical ensembles obey detailed balance, a fundamental principle governing transition rates.
• Driven systems exist in steady states far from equilibrium, where detailed balance does not hold.
• Understanding transition rates in these driven steady states is crucial for characterizing their behavior.

Purpose of the Study:

• To derive fundamental constraints on transition rates in driven steady states.
• To apply these constraints to specific physical systems, namely driven diffusion and sheared lattice fluids.
• To explore the potential of the derived ensemble to explain nonequilibrium phase behavior and emergent interactions.

Main Methods:

• Maximum information-entropy inference was employed to derive the constraints.
• The derived constraints were applied to analyze the steady states of driven diffusion models.
• The framework was also applied to a sheared lattice fluid model.

Main Results:

• Novel constraints on transition rates for driven steady states were successfully derived.
• The application to driven diffusion and sheared lattice fluids revealed specific implications of these constraints.
• For steady shear, the study identified stress-mediated long-range interactions.

Conclusions:

• The derived constraints provide a theoretical basis for understanding nonequilibrium steady states.
• The framework offers potential explanations for observed nonequilibrium phase behavior.
• The identification of stress-mediated interactions opens new avenues for research in driven soft matter and fluid dynamics.