Configurational temperature in active matter. I. Lines of invariant physics in the phase diagram of the Ornstein-Uhlenbeck model

TL;DR

This paper introduces a method to use configurational temperature as an energy scale to maintain invariant structure and dynamics in active matter models across different densities, validated through simulations.

Contribution

It proposes a novel approach to adjust model parameters using configurational temperature for invariant properties in active Ornstein-Uhlenbeck models, supported by theoretical justification and simulations.

Findings

Lines of approximate invariance in structure and dynamics identified

Parameter adjustments based on configurational temperature are effective

Validated with simulations of Lennard-Jones AOUP model

Abstract

This paper shows that the configurational temperature of liquid-state theory, $\Tc$, defines an energy scale, which can be used for adjusting model parameters of active Ornstein-Uhlenbeck particle (AOUP) models in order to achieve approximately invariant structure and dynamics upon a density change. The required parameter changes are calculated from the variation of a single configuration's $\Tc$ for a uniform scaling of all particle coordinates. The resulting equations are justified theoretically for models involving a potential-energy function with hidden scale invariance. The validity of the procedure is illustrated by computer simulations of the Kob-Andersen binary Lennard-Jones AOUP model, demonstrating lines of approximate reduced-unit invariance of the radial distribution function and time-dependent mean-square displacement.