Variational time reversal for free-energy estimation in nonequilibrium steady states

Area of Science:

• Statistical mechanics
• Non-equilibrium systems
• Soft matter physics

Background:

• Understanding systems in nonequilibrium steady states requires methods to quantify population shifts and free-energy landscape deformations under persistent currents.
• Stochastic thermodynamics provides a framework for analyzing these complex systems.

Purpose of the Study:

• To develop a variant of the Kawasaki-Crooks equality applicable to overdamped Langevin systems.
• To establish a general variational approach for evaluating nonequilibrium free-energy corrections.
• To accurately estimate order parameter distribution functions in driven and active matter models.

Main Methods:

• Applying stochastic thermodynamics to derive a modified Kawasaki-Crooks equality.
• Utilizing stochastic control theory for a variational approach to evaluate the equality.
• Employing molecular simulation to compute heat dissipation statistics along time-reversed trajectories.

Main Results:

• A novel method is established to relate nonequilibrium free-energy corrections to heat dissipation.
• The variational approach provides a general framework for evaluating the modified Kawasaki-Crooks equality.
• Substantial accuracy improvements were achieved in estimating order parameter distributions compared to perturbative methods.

Conclusions:

• The developed method offers a powerful tool for studying nonequilibrium steady states.
• This work advances the understanding of free-energy landscapes in driven and active matter systems.
• The approach demonstrates significant potential for applications in molecular simulations and theoretical physics.