  Discrete time crystals are periodically driven systems that display
spontaneous symmetry breaking of time translation invariance in the form of
indefinite subharmonic oscillations. We introduce a thermodynamically
consistent model for a discrete time crystal and analyze it using the framework
of stochastic thermodynamics. In particular, we evaluate the rate of energy
dissipation of this many body system of interacting noisy subharmonic
oscillators in contact with a heat bath. Our model displays the novel phenomena
of subharmonic synchronization, which corresponds to collective subharmonic
oscillations of the individual units.
