Computing stationary distributions in equilibrium and nonequilibrium systems with forward flux sampling

Area of Science:

• Statistical mechanics
• Computational chemistry
• Chemical kinetics

Background:

• Activated processes in equilibrium and nonequilibrium systems often require complex calculations for stationary distributions and rate constants.
• Existing methods may necessitate separate computations for these two key properties, increasing complexity.
• Understanding these distributions is crucial for modeling phenomena like nucleation and genetic switches.

Purpose of the Study:

• To present a unified method for computing stationary distributions of activated processes.
• To demonstrate that stationary distributions can be obtained directly from forward and backward reaction rate constant calculations.
• To validate the method's applicability across diverse systems, including equilibrium and nonequilibrium scenarios.

Main Methods:

• Forward Flux Sampling (FFS) was employed to directly calculate stationary distributions.
• The method integrates the computation of stationary distributions with rate constant calculations.
• No separate calculations for stationary distribution or rate constant are required.

Main Results:

• The presented method successfully computes stationary distributions for activated processes.
• The approach was applied to a nonequilibrium rare event problem (Maier and Stein), nucleation in a 2D Ising system, and genetic switch flipping.
• The results demonstrate the method's efficiency and broad applicability.

Conclusions:

• The forward flux sampling method offers a direct and efficient way to compute stationary distributions for activated processes.
• This unified approach simplifies the analysis of complex chemical kinetics and rare events.
• The method's successful application to diverse systems highlights its potential for broader use in computational science.