# Additivity and density fluctuations in Vicsek-like models of self-propelled particles

## TL;DR

This study investigates density fluctuations in Vicsek-like models of self-propelled particles, demonstrating an equilibrium-like chemical potential and a common mechanism for number fluctuations in these active systems.

## Contribution

It introduces a fluctuation-response relation based on additivity to accurately predict large-deviation probabilities in Vicsek-like models, revealing an equilibrium-like behavior.

## Key findings

- Large-deviation probabilities match microscopic simulations
- Existence of an equilibrium-like chemical potential
- Common mechanism for number fluctuations in active particles

## Abstract

We study coarse-grained density fluctuations in the disordered phase of the paradigmatic Vicsek-like models of self-propelled particles with alignment interactions and random self-propulsion velocities. By numerically integrating a fluctuation-response relation - the direct consequence of an additivity property, we compute logarithm of the large-deviation probabilities of the coarse-grained subsystem density, while the system is in the disordered fluid phase with vanishing macroscopic velocity. The large-deviation probabilities, computed within additivity, agree remarkably well with that obtained from direct microscopic simulations of the models. Our results provide an evidence of the existence of an equilibrium-like chemical potential, which governs the coarse-grained density fluctuations in the Vicsek-like models. Moreover, comparison of the particle-number fluctuations among several self-propelled particle systems suggests a common mechanism through which the number fluctuations arise in such systems.