Computing Nonequilibrium Responses with Score-Shifted Stochastic Differential Equations.

Area of Science:

• Statistical Mechanics
• Physical Chemistry
• Computational Physics

Background:

• Linear response theory uses equilibrium fluctuations to interpret experiments and understand microscopic dynamics.
• Nonequilibrium systems require path ensemble averaging for response calculations, but this fails for perturbations affecting the diffusion tensor.
• Existing methods are insufficient for analyzing perturbations that alter the diffusion tensor in stochastic systems.

Purpose of the Study:

• To develop a novel method for calculating responses in stochastic systems to perturbations of the diffusion tensor.
• To enable accurate nonequilibrium response calculations for systems with unknown stationary distributions.
• To extend the applicability of response theory to a broader range of physical systems.

Main Methods:

• Introduction of an "effective" physical process to model diffusion-perturbed dynamics.
• Leveraging score matching algorithms to perform calculations.
• Applying the method to systems where the exact stationary distribution is unknown.

Main Results:

• The effective dynamics incorporate an additional drift term dependent on the system's instantaneous score.
• Accurate calculations of responses to changes in the diffusion tensor are achieved.
• The method is effective even when the exact stationary distribution is not known.

Conclusions:

• The developed "effective" physical process provides a powerful tool for analyzing nonequilibrium systems with diffusion tensor perturbations.
• Score matching algorithms are crucial for enabling these calculations.
• This work expands the toolkit for understanding complex stochastic systems and their responses.