# Clausius relation for active particles: what can we learn from fluctuations?

## TL;DR

This paper compares different theoretical definitions of heat and entropy production in active particles, emphasizing an 'active heat' that satisfies the Clausius relation and can be experimentally tested.

## Contribution

It analyzes and compares three recent proposals for defining heat and entropy production in active particle models, highlighting an experimentally verifiable active heat.

## Key findings

- Active heat satisfies the Clausius relation.
- Comparison of three definitions clarifies their physical meaning.
- Active heat can be experimentally measured.

## Abstract

Many kinds of active particles, such as bacteria or active colloids, move in a thermostatted fluid by means of self-propulsion. Energy injected by such a non-equilibrium force is eventually dissipated as heat in the thermostat. Since thermal fluctuations are much faster and weaker than self-propulsion forces, they are often neglected, blurring the identification of dissipated heat in theoretical models. For the same reason, some freedom - or arbitrariness - appears when defining entropy production. Recently three different recipes to define heat and entropy production have been proposed for the same model where the role of self-propulsion is played by a Gaussian coloured noise. Here we compare and discuss the relation between such proposals and their physical meaning. One of these proposals takes into account the heat exchanged with a non-equilibrium active bath: such an "active heat" satisfies the original Clausius relation and can be experimentally verified.