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.