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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

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Maxwell-Boltzmann velocity distribution for noninteracting active matter.

Pedro Herrera¹, Mario Sandoval¹

¹Department of Physics, Universidad Autonoma Metropolitana-Iztapalapa, Mexico City 09340, Mexico.

Physical Review. E

|February 19, 2021

Summary

We discovered a Maxwell-Boltzmann-like velocity distribution for noninteracting active matter (NAM). This finding, derived from the Fokker-Planck equation, reveals inertia

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Area of Science:

Statistical Mechanics
Soft Matter Physics
Active Matter Dynamics

Background:

Noninteracting active matter (NAM) lacks a well-defined velocity distribution under Fokker-Planck formalism.
Previous models often overlook inertial effects in active matter systems.

Purpose of the Study:

To derive and analyze the velocity distribution for the underdamped scenario of NAM.
To incorporate inertial effects into the Fokker-Planck formalism for active matter.

Main Methods:

Theoretical derivation and computational analysis of the noninteracting active Fokker-Planck equation (NAFP).
Incorporation of mass and moment of inertia into the NAFPF.
Generalization of the Brinkman hierarchy for NAFP.

Main Results:

A novel, bimodal symmetric velocity distribution for NAM was found.
The derived distribution explicitly includes the impact of inertia on transport properties.
The analytical results were validated against experimental data from vibrobots.

Conclusions:

This study provides the first Fokker-Planck solution for the underdamped scenario of NAM.
The findings represent a significant advancement in characterizing active matter via nonequilibrium statistical mechanics.
The work bridges theoretical models with experimental observations in active matter systems.