Motility-Induced Phase Separation of Run-and-Tumble Particles under Local Stochastic Resetting
Abstract
We investigate the non-equilibrium stationary states of a one-dimensional active gas composed of run-and-tumble particles (RTPs) undergoing motility-induced phase separation (MIPS) and subjected to local stochastic resetting at the origin. Unlike global resetting, local resetting maintains a mass-injection flux at the origin while preserving large-scale spatial self-organization. We demonstrate that above a critical resetting rate rc, the active system undergoes a transition toward a stationary two-phase state featuring a dense liquid droplet centered at the origin coexisting with a surrounding gas phase. Using kinetic evolution equations, we derive the exact steady-state density profile expressed in terms of the Lambert function. The size of the droplet has a non-monotonic dependence on the resetting rate r, and attains its maximum. Furthermore, we analyze the dynamical stability of the supersaturated gas phase and show that a nucleated droplet relaxes exponentially toward its steady-state size with a relaxation timescale of 1/r. We extend our framework to model a finite resetting velocity, proving that the stationary droplet size is invariant with respect to the resetting velocity.
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BibTeX
@misc{grange2026motilityinduced,
title = {{Motility-Induced Phase Separation of Run-and-Tumble Particles under Local Stochastic Resetting}},
author = {Pascal Grange},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26149},
eprint = {2610.26149},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26149},
}
RIS
TY - UNPB
TI - Motility-Induced Phase Separation of Run-and-Tumble Particles under Local Stochastic Resetting
AU - Pascal Grange
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.26149
UR - https://arxiv.org/abs/2610.26149
AB - We investigate the non-equilibrium stationary states of a one-dimensional active gas composed of run-and-tumble particles (RTPs) undergoing motility-induced phase separation (MIPS) and subjected to local stochastic resetting at the origin. Unlike global resetting, local resetting maintains a mass-injection flux at the origin while preserving large-scale spatial self-organization. We demonstrate that above a critical resetting rate r_c, the active system undergoes a transition toward a stationary two-phase state featuring a dense liquid droplet centered at the origin coexisting with a surrounding gas phase. Using kinetic evolution equations, we derive the exact steady-state density profile expressed in terms of the Lambert function. The size of the droplet has a non-monotonic dependence on the resetting rate r, and attains its maximum. Furthermore, we analyze the dynamical stability of the supersaturated gas phase and show that a nucleated droplet relaxes exponentially toward its steady-state size with a relaxation timescale of 1/r. We extend our framework to model a finite resetting velocity, proving that the stationary droplet size is invariant with respect to the resetting velocity.
ER -