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By controlling in real-time the variance of the radiation pressure exerted onan optically trapped microsphere, we engineer temperature protocols thatshortcut thermal relaxation when transferring the microsphere from one thermalequilibrium state to an other. We identify the entropic footprint of suchaccelerated transfers and derive optimal temperature protocols that eitherminimize the production of entropy for a given transfer duration or accelerateas much as possible the transfer for a given entropic cost. Optimizing thetrade-off yields time-entropy bounds that put speed limits on thermalizationschemes. We further show how optimization expands the possibilities foraccelerating Brownian thermalization down to its fundamental limits. Ourapproach paves the way for the design of optimized, finite-time thermodynamiccycles at the mesoscale. It also offers a platform for investigatingfundamental connections between information geometry and finite-time processes.

Optimal time-entropy bounds and speed limits for Brownian thermal shortcuts