Steady State Fluctuations in a 3D Particle Model Out of Equilibrium

We analyze, both analytically and numerically, a 3D billiard-like model introduced in Phys. Rev. Res. 5, 043063 (2023) to highlight some aspects of its steady state dynamics. First, we study the equation describing the interface between equilibrium and nonequilibrium phases in the parameter space and show that, in certain regimes, the solution can be expressed in an analytical form. Moreover, we also investigate the statistics of the fluctuations of the stationary particle current and try to establish a connection with the existing framework of the Fluctuation Relations.