  We develop an abstract model of atomic clocks that fully describes the
dynamics of repeated synchronization between a classical oscillator and a
quantum reference. We prove existence of a stationary state of the model and
study its dependence on the control scheme, the interrogation time and the
stability of the oscillator. For unbiased atomic clocks, we derive a
fundamental bound on atomic clocks long time stability for a given local
oscillator noise. In particular, we show that for a local oscillator noise with
integrated frequency variance scaling as $T^\alpha$ for short times $T$, the
optimal clock time variance scales as $F^{-(\alpha +1)/(\alpha +2)}$ with
respect to the quantum Fisher information, $F$, associated to the quantum
reference.
