Recovery of mechanical pressure in a gas of underdamped active dumbbells with Brownian noise

TL;DR

This study numerically explores how increasing Brownian noise in a gas of underdamped active dumbbells affects the recovery of mechanical pressure, revealing complex behaviors and multiple mechanisms influencing force equilibrium.

Contribution

It demonstrates how Brownian noise can restore pressure in active dumbbell gases and uncovers subtle, unexpected effects of noise and damping on force balance and system equilibrium.

Findings

Moderate noise suffices for force equilibration at low damping.

Stronger noise needed for higher damping.

Displacement of the wall can be non-monotonic with noise increase.

Abstract

In contrast with a gas at thermodynamic equilibrium, the mean force exerted on a wall by a gas of active particles usually depends on the confining potential, thereby preventing a proper definition of mechanical pressure. In this paper, we investigate numerically the properties of a gas of underdamped self-propelled dumbbells subject to Brownian noise of increasing intensity, in order to understand how the notion of pressure is recovered as noise progressively masks the effects of self-propulsion and the system approaches thermodynamic equilibrium. The simulations performed for a mobile asymmetric wall separating two chambers containing an equal number of active dumbbells highlight some subtle and unexpected properties of the system. First, Brownian noise of moderate intensity is sufficient to let mean forces equilibrate for small values of the damping coefficient, while much stronger noise is required for larger values of the damping coefficient. Moreover, the displacement of the mean position of the wall upon increase of the intensity of the noise is not necessarily monotonous and may instead display changes of direction. Both facts actually reflect the existence of several mechanisms leading to the rupture of force balance, which tend to displace the mean position of the wall towards different directions and display different robustness against an increase of the intensity of Brownian noise. This work therefore provides a clear illustration of the fact that driving an autonomous system towards (or away from) thermodynamic equilibrium may not be a straightforward process, but may instead proceed through the variations of the relative weights of several conflicting mechanisms.