Optimal work fluctuations for finite-time and weak processes

Pierre Nazé

Published 2023-04-24Version 1

The optimal protocols for the irreversible work achieve their maximum usefulness if their work fluctuations are the smallest ones. In this work, for isothermal processes subjected to finite-time and weak drivings, I show using the linear-response theory that the optimal protocol for the irreversible work is the same for the variance of work. This conclusion is based on the work fluctuation-dissipation theorem $\overline{W}=\Delta F+\beta \sigma_W^2/2$, extended now to finite-time and weak drivings. To illustrate such a relation, I analyze the example of an overdamped Brownian motion subjected to an anharmonic stiffening trap and white noise 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.