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We introduce a phenomenological theory for a new class of soft active fluids with the ability to synchronize. Our theoretical framework describes the macroscopic behavior of a collection of interacting anisotropic elements with cyclic internal dynamics and a periodic phase variable. This system can (i) spontaneously undergo a transition to a state with macroscopic orientational order, with the elements aligned, a liquid crystal, (ii) attain another broken symmetry state characterized by synchronization of their phase variables, or (iii) a combination of both types of order. We derive the equations describing a spatially homogeneous system and also study the hydrodynamic fluctuations of the soft modes in some of the ordered states. We find that synchronization can promote or inhibit the transition to a state with orientational order, and vice versa. We provide an explicit microscopic realization: a suspension of microswimmers driven by cyclic strokes.
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