Fluctuation-optimization theorem

A fluctuation theorem relating the work to its optimal average work is presented. The function mediating the relation is increasing and convex, and depends on the switching time $\tau$, driving strength $\delta\lambda/\lambda_0$, and protocol $g(t)$. The result is corroborated by an example of an overdamped white noise Brownian motion subjected to a moving laser harmonic trap. Observing also that the fluctuation-optimization theorem is an Euler-Lagrange equation, I conclude that the function minimizing $\langle h(-\beta W)\rangle$ obeys the relation proposed. The optimal work can now be calculated with numerical methods without knowing the optimal protocol, using only a work distribution of an arbitrary protocol.