# Mechanical pressure and momentum conservation in dry active matter

## TL;DR

This paper investigates how the lack of momentum conservation in dry active matter systems causes the breakdown of equations of state for mechanical pressure, highlighting the role of boundary interactions and conditions for restoring an equation of state.

## Contribution

It demonstrates the connection between momentum non-conservation and pressure equations of state, and identifies conditions under which an equation of state can be recovered in active matter.

## Key findings

- Mechanical pressure depends on container interactions.
- Decoupling particle orientation dynamics restores the equation of state.
- Active impulse divergence relates to the mean active force density.

## Abstract

We relate the breakdown of equations of states for the mechanical pressure of generic dry active systems to the lack of momentum conservation in such systems. We show how sources and sinks of momentum arise generically close to confining walls. These typically depend on the interactions of the container with the particles, which makes the mechanical pressure a container-dependent quantity. We show that an equation of state is recovered if the dynamics of the orientation of active particles are decoupled from other degrees of freedom and lead to an apolar bulk steady-state. This is related to the fact that the mean steady-state active force density is the divergence of the flux of "active impulse", an observable which measures the mean momentum particles will receive from the substrate in the future.