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A wide range of phenomena in the natural and social sciences involve largesystems of interacting particles, including plasmas, collections of galaxies,coupled oscillators, cell aggregations, and economic ``agents'. Kinetic methodsfor reducing the complexity of such systems typically involve the derivation ofnonlinear partial differential equations for the corresponding globaldensities. In recent years there has been considerable interest in the meanfield limit of interacting particle systems with long range interactions. Twomajor examples are interacting Brownian particles in the overdamped regime andthe Kuramoto model of coupled phase oscillators. In this paper we analyze thesesystems in the presence of local or global stochastic resetting, where theposition or phase of each particle independently or simultaneously resets toits original value at a random sequence of times generated by a Poissonprocess. In each case we derive the Dean-Kawasaki (DK) equation describinghydrodynamic fluctuations of the global density, and then use a mean fieldansatz to obtain the corresponding nonlinear McKean-Vlasov (MV) equation in thethermodynamic limit. In particular, we show how the MV equation for globalresetting is driven by a Poisson shot noise process, reflecting the fact thatresetting is common to all of the particles and thus induces correlations thatcannot be eliminated by taking a mean field limit. We then investigate theeffects of local and global resetting on nonequilibrium stationary solutions ofthe macroscopic dynamics and, in the case of the Kuramoto model, the reduceddynamics on the Ott-Antonsen manifold.

Global density equations for interacting particle systems with stochastic resetting: from overdamped Brownian motion to phase synchronization