Probabilistic work extraction on a classical oscillator beyond the second law

Abstract

We demonstrate experimentally that, applying optimal protocols which drive the system between two equilibrium states characterized by a free energy difference $\Delta F$, we can maximize the probability of performing the transition between the two states with a work $W$ smaller than $\Delta F$. The second law holds only on average, resulting in the inequality $⟨W⟩\ge \Delta F$. The experiment is performed using an underdamped oscillator evolving in a double-well potential. We show that with a suitable choice of parameters the probability of obtaining trajectories with $W\le \Delta F$ can be larger than 95%. Very fast protocols are a key feature to obtain these results, which are explained in terms of the Jarzynski equality.