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Nicholas M Boffi1, Eric Vanden-Eijnden1

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This study introduces a deep learning framework to efficiently calculate key metrics in active matter systems, revealing how particles drive nonequilibrium states. The method accurately quantifies entropy production and probability currents in complex systems like motility-induced phase separation.

Keywords:
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Area of Science:

  • Statistical Mechanics
  • Active Matter Physics
  • Machine Learning Applications

Background:

  • Active matter systems convert energy to work, exhibiting nonequilibrium physics beyond equilibrium statistical mechanics.
  • Quantifying nonequilibrium states using entropy production and probability currents is challenging due to reliance on unknown probability densities.
  • Efficient computation of these metrics is crucial for understanding complex active matter dynamics.

Purpose of the Study:

  • Develop a deep learning framework to efficiently estimate the score of high-dimensional probability densities in active matter systems.
  • Enable accurate calculation of entropy production rate and probability current from microscopic equations of motion.
  • Decompose these nonequilibrium measures into local contributions from individual particles.

Main Methods:

  • Utilized advances in generative modeling to create a deep learning framework for density score estimation.
  • Introduced a spatially local transformer network architecture to learn particle interactions and preserve permutation symmetry.
  • Applied the framework to high-dimensional active particle systems, including those exhibiting motility-induced phase separation (MIPS).

Main Results:

  • The deep learning framework successfully estimates the score, providing access to entropy production rate and probability current.
  • The method allows for the decomposition of these quantities into local particle contributions.
  • A single trained network demonstrated generalization across varying particle numbers (up to 32,768) and packing fractions in MIPS systems.

Conclusions:

  • The developed deep learning approach offers a scalable and efficient method for quantifying nonequilibrium phenomena in active matter.
  • The framework's ability to generalize highlights its potential for broad applications in complex physical systems.
  • This work provides new insights into the spatial structure of nonequilibrium departures in MIPS.