First-passage resetting gas

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 nonequilibrium 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 conditionally independent 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. This system is the first example of a conditionally independent structure where the conditioning distribution is explicitly dependent on N.