Model-Free Learning of Probability Flows: Elucidating the Nonequilibrium Dynamics of Flocking

Area of Science:

• Physics
• Complex Systems
• Statistical Mechanics

Background:

• Active systems are characterized by autonomous energy dissipation and nonequilibrium dynamics.
• Estimating the entropy production rate (EPR) is crucial for understanding these systems but is computationally challenging due to high-dimensional phase spaces.

Purpose of the Study:

• To develop a novel deep learning approach for estimating EPR in high-dimensional active systems.
• To establish a direct physical connection between probability currents and local EPR definitions for inertial systems.
• To visualize and characterize nonequilibrium dynamics in a canonical flocking model.

Main Methods:

• A deep learning technique was employed to directly estimate probability currents from stochastic system trajectories.
• The method was applied to a canonical model of flocking to analyze spatial and temporal entropy production.
• A new physical link was derived between probability currents and local EPR definitions.

Main Results:

• The study successfully estimated EPR using deep learning, overcoming limitations of traditional methods.
• Entropy production and consumption were visualized on the spatial interface of a flock.
• The interplay between alignment and fluctuation was shown to dynamically create and annihilate order within the flock.

Conclusions:

• The developed methodology enables direct visualization of when and where systems are out of equilibrium.
• This approach is anticipated to significantly advance the understanding of complex nonequilibrium dynamics.
• The findings offer new insights into the fundamental processes governing active matter and self-organization.