Work to insert a particle into an active fluid

¹ Applied Physics Program, University of Michigan - Ann Arbor, MI 48109, USA
² Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée, LPTMC F-75005 Paris, France
³ Department of Biophysics, University of Michigan - Ann Arbor, MI 48109, USA
⁴ Center for the Study of Complex Systems, University of Michigan - Ann Arbor, MI 48109, USA
⁵ Department of Physics, University of Michigan - Ann Arbor, MI 48109, USA

Received: 10 September 2025
Accepted: 17 February 2026

Abstract

The chemical potential is defined as the work to quasi-statically add a particle to an equilibrium system. Inspired by this definition, we investigate how the work to add a particle to an active fluid depends on the activity, density, and insertion protocol. We find that the average work is protocol dependent and decreases with activity. Moreover, the work fluctuations retain asymmetric non-Gaussian tails even for slow particle insertions. We then compare the average particle-insertion work to the steady-state densities observed when two active fluids are brought into diffusive contact and observe opposing trends between density and work.