  The optimal protocols for the irreversible work achieve their maximum
usefulness if their work fluctuations are the smallest ones. In this work, for
classical and isothermal processes subjected to finite-time and weak drivings,
I show that the optimal protocol for the irreversible work is the same for the
variance of work. This conclusion is based on the fluctuation-dissipation
relation $\overline{W}=\Delta F+\beta \sigma_W^2/2$, extended now to
finite-time and weak drivings. To illustrate it, I analyze a white noise
overdamped Brownian motion subjected to an anharmonic stiffening trap for fast
processes. By contrast with the already known results in the literature for
classical systems, the linear-response theory approach of the work
probabilistic distribution is not a Gaussian reduction.
