Optimal work fluctuations for finite-time and weak processes

Abstract: 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.