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We present a novel method to compute the phase space distribution in thenonequilibrium stationary state of a wide class of mean-field systems involvingrotators subject to quenched disordered external drive and dissipation. Themethod involves a series expansion of the stationary distribution in inverse ofthe damping coefficient; the expansion coefficients satisfy recursion relationswhose solution requires computing a sparse matrix, making numerical evaluationsimple and efficient. We illustrate our method for the paradigmatic Kuramotomodel of spontaneous collective synchronization and for its two modegeneralization, in presence of noise and inertia, and demonstrate an excellentagreement between simulations and theory for the phase space distribution.

Nonequilibrium inhomogeneous steady state distribution in disordered, mean-field rotator systems