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It is well established that it is possible to switch certain antiferromagnets electrically, yet the interplay of Neel-spin-orbit torques and thermal activation is only poorly understood. Combining ab initio calculations and atomistic spin dynamics simulations we develop a multiscale model to study the current-induced switching in Mn2Au. We compute from first principles the strength and direction of the electrically induced magnetic moments, caused by the Rashba-Edelstein effect, and take these into account in atomistic spin dynamics simulations. Our simulations reveal the switching paths as well as the timescales for switching. The size of the induced moments, however, turns out to be insufficient to lead to fully deterministic switching. Instead, we find that a certain degree of thermal activation is required to help overcome the relevant energy barrier.