Computing diffusivities from particle models out of equilibrium.

Area of Science:

• Statistical Mechanics
• Computational Physics
• Nonlinear Dynamics

Background:

• Extracting macroscopic properties like diffusivity from microscopic particle behavior is crucial.
• Stochastic particle systems often exhibit complex out-of-equilibrium dynamics.
• Understanding the connection between microscopic fluctuations and macroscopic transport is a key challenge.

Purpose of the Study:

• To develop a numerical method for extracting the diffusivity of diffusion equations from stochastic particle systems.
• To validate the method's applicability to systems undergoing arbitrary out-of-equilibrium evolutions.
• To provide a tool for analyzing experimental particle data.

Main Methods:

• The method relies on the principle that large particle systems formally obey stochastic partial differential equations of gradient flow type.
• It requires the system to be in local equilibrium and exhibit Gaussian fluctuations.
• The fluctuation-dissipation relation is a key component of the theoretical framework.

Main Results:

• The proposed method successfully extracts diffusivity from three classic particle models: independent random walkers, zero-range process, and symmetric simple exclusion process.
• Comparisons with analytic solutions confirm the accuracy of the numerical extraction.
• The method demonstrates robustness for systems in arbitrary out-of-equilibrium states.

Conclusions:

• A new numerical strategy enables the extraction of diffusivity from stochastic particle systems, even under non-equilibrium conditions.
• The method is validated against established models, showing good agreement with analytical results.
• This technique offers a promising approach for analyzing experimental data from particle-based systems.