Optimal finite-time processes in stochastic thermodynamics

TL;DR

This paper investigates the optimal control protocols for finite-time thermodynamic processes in small systems, deriving explicit solutions that reveal characteristic jumps at process boundaries.

Contribution

It provides explicit solutions for optimal protocols in stochastic thermodynamics, highlighting the presence of finite jumps at process start and end.

Findings

Optimal protocols often include finite jumps at boundaries.

Explicit solutions are derived for moving laser traps.

Jumps are typical at the beginning and end of the process.

Abstract

For a small system like a colloidal particle or a single biomolecule embedded in a heat bath, the optimal protocol of an external control parameter minimizes the mean work required to drive the system from one given equilibrium state to another in a finite time. In general, this optimal protocol obeys an integro-differential equation. Explicite solutions both for a moving laser trap and a time-dependent strength of such a trap show finite jumps of the optimal protocol to be typical both at the beginning and the end of the process.