  A fundamental and intrinsic property of any device or natural system is its
relaxation time relax, which is the time it takes to return to equilibrium
after the sudden change of a control parameter [1]. Reducing $tau$ relax , is
frequently necessary, and is often obtained by a complex feedback process. To
overcome the limitations of such an approach, alternative methods based on
driving have been recently demonstrated [2, 3], for isolated quantum and
classical systems [4--9]. Their extension to open systems in contact with a
thermostat is a stumbling block for applications. Here, we design a
protocol,named Engineered Swift Equilibration (ESE), that shortcuts
time-consuming relaxations, and we apply it to a Brownian particle trapped in
an optical potential whose properties can be controlled in time. We implement
the process experimentally, showing that it allows the system to reach
equilibrium times faster than the natural equilibration rate. We also estimate
the increase of the dissipated energy needed to get such a time reduction. The
method paves the way for applications in micro and nano devices, where the
reduction of operation time represents as substantial a challenge as
miniaturization [10]. The concepts of equilibrium and of transformations from
an equilibrium state to another, are cornerstones of thermodynamics. A textbook
illustration is provided by the expansion of a gas, starting at equilibrium and
expanding to reach a new equilibrium in a larger vessel. This operation can be
performed either very slowly by a piston, without dissipating energy into the
environment, or alternatively quickly, letting the piston freely move to reach
the new volume.
