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arXiv · 2512.00440

First Passage Resetting Gas

Marco Biroli·Satya N. Majumdar·Gregory Schehr
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Abstract

We study a one-dimensional gas of $N$ Brownian particles that diffuse independently but are simultaneously reset whenever any of them reaches a fixed threshold located at $L > 0$. For any $N > 2$, the system reaches a non-equilibrium stationary state (NESS) at long-times with strong long-range correlations. These correlations emerge purely from the dynamics, and not from built-in interactions. Despite being strongly correlated, the NESS has a solvable structure that allows for an exact computation of several physical observables, both global and local. These include the average density profile, the distribution of the position of the $k$-th ordered particles, the distribution of the gap between two consecutive particles and the full counting statistics, i.e., the distribution of the number of particles in a finite interval around the origin.

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Marco Biroli, Satya N. Majumdar, Gregory Schehr. 2025-11-29. First Passage Resetting Gas. https://doi.org/10.1209/0295-5075%2Fae3f4f

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