Importance sampling large deviations in nonequilibrium steady states. I.

Area of Science:

• Statistical Mechanics
• Non-equilibrium Physics
• Computational Physics

Background:

• Large deviation functions (LDFs) quantify stability and response in nonequilibrium steady states, analogous to free energies in equilibrium systems.
• Numerical evaluation of LDFs is challenging due to their dependence on exponentially rare events.
• Existing trajectory-based sampling methods face limitations in accurately computing LDFs.

Purpose of the Study:

• To evaluate various trajectory-based sampling methods for computing LDFs of time-integrated observables in nonequilibrium steady states.
• To identify convergence criteria and best practices for these computational methods.
• To analyze the performance limitations of popular sampling techniques.

Main Methods:

• Comparison of trajectory-based sampling methods, including transition path sampling and diffusion Monte Carlo.
• Application to diverse models: biased Brownian walker, driven lattice gas, and a self-assembly model.
• Analysis of convergence criteria and best practices for numerical evaluation.

Main Results:

• Transition path sampling and diffusion Monte Carlo exhibit exponentially diverging correlations in trajectory space when estimating LDFs.
• These divergences are dependent on the bias parameter, hindering accurate computation.
• The study highlights the need for enhanced sampling strategies.

Conclusions:

• Standard trajectory-based sampling methods are inefficient for computing LDFs in complex nonequilibrium systems.
• Guiding functions are essential for improving the efficiency of these algorithms.
• Further development of advanced sampling techniques is required for accurate LDF computation.