Motility-Induced Phase Separation of Run-and-Tumble Particles under Local Stochastic Resetting

Pascal Grange

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arXiv · 2610.26149

Motility-Induced Phase Separation of Run-and-Tumble Particles under Local Stochastic Resetting

Pascal Grange

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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 $r_c$, 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.

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Pascal Grange. 2026-10-20. Motility-Induced Phase Separation of Run-and-Tumble Particles under Local Stochastic Resetting. https://arxiv.org/abs/2610.26149

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