# Occupation time statistics of a gas of interacting diffusing particles

## TL;DR

This paper uses Macroscopic Fluctuation Theory to analyze how interactions among diffusing particles affect their occupation time statistics, revealing possible phase transitions and linking to large deviation principles.

## Contribution

It extends occupation time analysis from non-interacting to interacting particles using MFT, uncovering interaction-induced singularities and phase transitions.

## Key findings

- Interactions significantly alter occupation time statistics.
- Singularities in large-deviation functions indicate dynamical phase transitions.
- Connection established between many-particle and single-particle occupation statistics.

## Abstract

The time which a diffusing particle spends in a certain region of space is known as the occupation time, or the residence time. Recently the joint occupation time statistics of an ensemble of non-interacting particles was addressed using the single-particle statistics. Here we employ the Macroscopic Fluctuation Theory (MFT) to study the occupation time statistics of many \emph{interacting} particles. We find that interactions can significantly change the statistics and, in some models, even cause a singularity of the large-deviation function describing these statistics. This singularity can be interpreted as a dynamical phase transition. We also point out to a close relation between the MFT description of the occupation-time statistics of non-interacting particles and the level 2 large deviation formalism which describes the occupation-time statistics of a single particle.