Ideal gas of active particles in a box
Abstract
Extending a fundamental concept of thermodynamics to the nonequilibrium realm of active matter, we derive an ideal gas law for a suspension of noninteracting active particles confined to a finite rectangular box. The law is exact for run-and-tumble particles (RTPs) in one dimension and established by a systematic analytical expansion of the steady-state probability density for active Ornstein-Uhlenbeck particles in any dimension. It also agrees well with numerical results for active Brownian particles and RTPs in higher dimensions and recovers previously known relations for the limit of large system sizes. Together, these results demonstrate the applicability of the ideal active gas law to the three most widely studied theoretical models of colloidal active matter. As an application, we analyze thermodynamic processes involving active matter on a macroscopic level, without recourse to microscopic particle trajectories or self-propulsion fluctuations.
Related
- Geodesic Trapping and Escape of Active Particles on Curved Surfaces
- Morphological instability and negative geometric friction from contact with active and driven particles
- Emergent Self-Organisation of Intelligent Active Particles
- Partial Entropy production of active particles with hidden states in potentials
- Active model B+ from run-and-tumble particles on a triangular lattice
BibTeX
@misc{li2026ideal,
title = {{Ideal gas of active particles in a box}},
author = {Siran Li and Ralf Eichhorn and Lennart Dabelow},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01287},
eprint = {2610.01287},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01287},
}
RIS
TY - UNPB
TI - Ideal gas of active particles in a box
AU - Siran Li
AU - Ralf Eichhorn
AU - Lennart Dabelow
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.01287
UR - https://arxiv.org/abs/2610.01287
AB - Extending a fundamental concept of thermodynamics to the nonequilibrium realm of active matter, we derive an ideal gas law for a suspension of noninteracting active particles confined to a finite rectangular box. The law is exact for run-and-tumble particles (RTPs) in one dimension and established by a systematic analytical expansion of the steady-state probability density for active Ornstein-Uhlenbeck particles in any dimension. It also agrees well with numerical results for active Brownian particles and RTPs in higher dimensions and recovers previously known relations for the limit of large system sizes. Together, these results demonstrate the applicability of the ideal active gas law to the three most widely studied theoretical models of colloidal active matter. As an application, we analyze thermodynamic processes involving active matter on a macroscopic level, without recourse to microscopic particle trajectories or self-propulsion fluctuations.
ER -