Communications: Can one identify nonequilibrium in a three-state system by analyzing two-state trajectories?

Area of Science:

• Statistical Mechanics
• Nonlinear Dynamics
• Physical Chemistry

Background:

• Distinguishing between equilibrium and nonequilibrium steady states is crucial in various physical systems.
• Previous criteria for identifying nonequilibrium states, such as oscillatory relaxation, may not capture all scenarios.

Purpose of the Study:

• To determine if effective two-state (on-off) trajectory data can reliably differentiate between equilibrium and nonequilibrium steady states in a three-state Markov system.
• To map the phase diagram of the system to identify regions consistent with nonequilibrium conditions.

Main Methods:

• Analysis of data from effective two-state (on-off) trajectories.
• Calculation of the full phase diagram for a three-state Markov system.
• Comparison of data consistency with equilibrium versus nonequilibrium steady states.

Main Results:

• Identification of a substantial region in the phase diagram where trajectory data is exclusively consistent with nonequilibrium steady states.
• This nonequilibrium regime is significantly larger than regions previously identified by oscillatory relaxation criteria.
• The findings demonstrate that two-state trajectory analysis can be a powerful tool for detecting nonequilibrium behavior.

Conclusions:

• Effective two-state trajectory data provides a robust method for discriminating between equilibrium and nonequilibrium steady states.
• The study expands the understanding of nonequilibrium phenomena by identifying a larger parameter space where such states exist.
• This work offers a new perspective on analyzing complex systems and their dynamic states.