  Adiabatic processes are important for studying the dynamics of a
time-dependent system. Conventionally, the adiabatic processes can only be
achieved by varying the system slowly. We speed up both classical and quantum
adiabatic processes by adding control protocols. In classical systems, we work
out the control protocols by analyzing the classical adiabatic approximation.
In quantum systems, we follow the idea of transitionless driving by Berry [J.
Phys. A: Math. Theor. Vol.42 365303 (2009)]. Such fast-forward adiabatic
processes can be performed at arbitrary fast speed, and in the meanwhile reduce
the work fluctuation. In both systems, we use a time-dependent harmonic
oscillator model to work out explicitly the work function and the work
fluctuation in three types of processes: fast-forward adiabatic processes,
adiabatic processes, and non-adiabatic processes. We show the significant
reduction on work fluctuation in fast-forward adiabatic process. We further
illustrate how the fast-forward process improved the converging rate of the
Jarzynski equality between the work function and the free energy. As an
application, we show that the fast-forward process not only maximizes the
output power but also improve the efficiency of a quantum engine.
