# Pressure in an exactly solvable model of active fluid

## TL;DR

This paper investigates the pressure in three active particle models, revealing universal behaviors and establishing formulas that connect different models, with explicit examples showing consistent pressure calculations across methods.

## Contribution

It derives a universal pressure formula for active particle models and demonstrates equivalence of pressure calculations across different models and methods.

## Key findings

- Pressure formulas for active particle models are connected and universal.
- Pressure calculations via virial, thermodynamic, and mechanical methods agree across models.
- Explicit example with elastic dumbbells confirms theoretical predictions.

## Abstract

We consider the pressure in the steady-state regime of three stochastic models characterized by self-propulsion and persistent motion and widely employed to describe the behavior of active particles, namely the Active Brownian particle (ABP) model, the Gaussian colored noise (GCN) model and the unified colored noise model (UCNA). Whereas in the limit of short but finite persistence time the pressure in the UCNA model can be obtained by different methods which have an analog in equilibrium systems, in the remaining two models only the virial route is, in general, possible. According to this method, notwithstanding each model obeys its own specific microscopic law of evolution, the pressure displays a certain universal behavior. For generic interparticle and confining potentials, we derive a formula which establishes a correspondence between the GCN and the UCNA pressures. In order to provide explicit formulas and examples, we specialize the discussion to the case of an assembly of elastic dumbbells confined to a parabolic well. By employing the UCNA we find that, for this model, the pressure determined by the thermodynamic method coincides with the pressures obtained by the virial and mechanical methods. The three methods when applied to the GCN give a pressure identical to that obtained via the UCNA. Finally, we find that the ABP virial pressure exactly agrees with the UCNA and GCN result.