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Microscopically reversible kinetic theory of flocking.

¹University of Amsterdam, University of Amsterdam, University of Amsterdam, Institute for Theoretical Physics, 1090 GL Amsterdam, The Netherlands; Dutch Institute for Emergent Phenomena, 1090 GL Amsterdam, The Netherlands; and Institute for Advanced Study, Oude Turfmarkt 147, 1012 GC Amsterdam, The Netherlands.

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Summary

This study models self-propelling "birds" in "air" using kinetic theory. A flocking transition emerges when reactive collisions drive the system out of equilibrium, altering momentum damping.

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Area of Science:

Physics
Statistical Mechanics
Kinetic Theory

Background:

Modeling active matter systems is crucial for understanding emergent behaviors.
Reactive collisions can convert chemical energy into kinetic energy, driving self-propulsion.
Understanding non-equilibrium systems is key to explaining complex phenomena.

Purpose of the Study:

To develop a kinetic theory for a two-species system with reactive collisions.
To investigate the emergence of flocking behavior in a self-propelled particle system.
To analyze the role of non-equilibrium conditions and interspecies collisions.

Main Methods:

Formulation of a kinetic theory for hard spheres with reactive collisions.
Imposing microscopic reversibility on reactive dynamics.
Utilizing a chemostat to drive the system out of equilibrium.
Analyzing grazing interspecies collisions.

Main Results:

A kinetic theory model for active and passive species (birds and air) was established.
Self-propulsion arises from reactive collisions converting chemical to kinetic energy.
A flocking transition was observed when the system is driven out of equilibrium by a strong chemostat, with a sign change in the momentum damping coefficient for birds during grazing collisions.

Conclusions:

The kinetic theory successfully models self-propelled particle systems with reactive collisions.
Non-equilibrium conditions and specific collision types (grazing interspecies) are critical for emergent flocking.
The model provides a framework for understanding how microscopic reactive events can lead to macroscopic collective behavior.