Optimal finite-time heat engines under constrained control

TL;DR

This paper derives optimal control protocols for finite-time stochastic heat engines under realistic constraints, showing they are piecewise constant and can maximize efficiency and power, with practical experimental implications.

Contribution

It provides a general geometric proof that optimal protocols are piecewise constant under constraints, applicable to arbitrary dynamics, and demonstrates this for a Brownian heat engine.

Findings

Optimal protocols are piecewise constant, switching between maximum and minimum control values.

Protocols maximize efficiency and power under specific constraints.

Results are applicable to experimental systems like optical tweezers.

Abstract

We optimize finite-time stochastic heat engines with a periodically scaled Hamiltonian under experimentally motivated constraints on the bath temperature $T$ and the scaling parameter $\lambda$. We present a general geometric proof that maximum-efficiency protocols for $T$ and $\lambda$ are piecewise constant, alternating between the maximum and minimum allowed values. When $\lambda$ is restricted to a small range and the system is close to equilibrium at the ends of the isotherms, a similar argument shows that this protocol also maximizes output power. These results are valid for arbitrary dynamics. We illustrate them for an overdamped Brownian heat engine, which can experimentally be realized using optical tweezers with stiffness $\lambda$.