Numerical comparison of a constrained path ensemble and a driven quasisteady state

Area of Science:

• Statistical mechanics
• Non-equilibrium physics
• Dynamical systems

Background:

• Understanding systems driven far from equilibrium is a key challenge in statistical mechanics.
• Nonequilibrium ensembles offer a theoretical framework to describe such systems.
• The validity of path-based ensembles for driven systems needs empirical verification.

Purpose of the Study:

• To investigate the correspondence between a nonequilibrium path ensemble and a boundary-driven system.
• To determine if the path ensemble adequately describes the physics of driven systems.
• To establish protocols for analyzing transition rates in nonequilibrium quasisteady states.

Main Methods:

• A one-dimensional model of rotors with Newtonian dynamics and conservative interactions was used.
• Transition rates between potential wells and phase-space elements were measured.
• Rates were compared with predictions from the nonequilibrium path ensemble.

Main Results:

• Transition rates between potential wells and phase-space elements exhibit distinct properties.
• Coarse-grained potential wells were found to be further from equilibrium.
• Results from the boundary-driven system closely matched path-ensemble predictions.

Conclusions:

• The nonequilibrium path ensemble provides a good approximation for boundary-driven systems.
• Distinct behaviors were observed for different coarse-graining levels.
• The precise equivalence between the path ensemble and driven systems remains an open question.