Work statistics in stochastically driven systems

We identify the conditions under which a stochastic driving that induces energy changes into a system coupled with a thermal bath can be treated as a work source. When these conditions are met, the work statistics satisfy the Crooks fluctuation theorem traditionally derived for deterministic drivings. We illustrate this fact by calculating and comparing the work statistics for a two-level system driven respectively by a stochastic and a deterministic piecewise constant protocol.