  Counterdiabatic driving (CD) exploits auxiliary control fields to tailor the
nonequilibrium dynamics of a quantum system, making possible the suppression of
dissipated work in finite-time thermodynamics and the engineering of optimal
thermal machines with no friction. We show that while the mean work done by the
auxiliary controls vanishes, CD leads to a broadening of the work distribution.
We derive a fundamental inequality that relates nonequilibrium work
fluctuations to the operation time and quantifies the thermodynamic cost of CD
in both critical and noncritical systems.
