We introduce a phenomenological theory for a new class of soft active fluids,
with the ability to synchronise. Our theoretical framework describes the
macroscopic behaviour of a collection of interacting anisotropic elements with
cyclic internal dynamics and a periodic phase variable. This system (i) can
spontaneously undergo a transition to a state with macroscopic orientational
order, with the elements aligned: a liquid crystal, (ii) attain another broken
symmetry state characterised by synchronisation 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 synchronisation can
promote the transition to a state with orientational order; and vice-versa.
Finally, we provide an explicit microscopic realisation: a suspension of
micro-swimmers driven by cyclic strokes.Comment: 5 pages, 3 figure
