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, driving strength /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 h (- W) 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.