Engineered Swift Equilibration (ESE) is a method to switch a system from one state to another much faster than its natural equilibration time. The initial and final states can be either in equilibrium or out of equilibrium.For example, one can perform the compression of a single brownian particle trapped in an harmonic potential by increasing its stiffness k. A step in k will equilibrate in the natural relaxation time of the system. Using ESE protocol for the time evolution of k, the same final state can be reached several order of magnitude faster. We will discuss the parameters which can be tuned in order to reach the desired dynamics and the stability of the protocol to external perturbation.
We will then discuss the application of ESE to the problem of first passage time. The resetting to the origin is one of the efficient theoretical strategies that allow a Brownian particle to reach a target in an optimal time. However we will show how in realistic situation the original assumptions used in these theoretical strategies must be modified in order to optimize the searching time. ESE is actually very useful to speed up the resetting.
Finally we will show how the ESE can speed up the force measurements in atomic force microscopies