  For two canonical examples of driven mesoscopic systems - a
harmonically-trapped Brownian particle and a quantum dot - we numerically
determine the finite-time protocols that optimize the compromise between the
standard deviation and the mean of the dissipated work. In the case of the
oscillator, we observe a collection of protocols that smoothly trade-off
between average work and its fluctuations. However, for the quantum dot, we
find that as we shift the weight of our optimization objective from average
work to work standard deviation, there is an analog of a first-order phase
transition in protocol space: two distinct protocols exchange global optimality
with mixed protocols akin to phase coexistence. As a result, the two types of
protocols possess qualitatively different properties and remain distinct even
in the infinite duration limit: optimal-work-fluctuation protocols never
coalesce with the minimal work protocols, which therefore never become
quasistatic.
