Optimal protocols and universal time-energy bound in Brownian thermodynamics

Abstract

We propose an optimization strategy to control the dynamics of a stochastic system transferred from one thermal equilibrium to another and apply it experimentally to a Brownian particle in an optical trap under compression. Based on a variational principle that treats the transfer duration and the expended work on an equal footing, our strategy leads to a family of protocols that are either optimally cheap for a given duration or optimally fast for a given energetic cost. This approach unveils a universal relation $\hat{I}”t\hat{I}”W\ge (\hat{I}”t\hat{I}”W{)}_{\mathrm{opt}}$ between the transfer duration and the expended work. We verify experimentally that the lower bound is reached only with the optimized protocols.

10 pages, 14 figures