Phase transition in protocols minimizing work fluctuations

TL;DR

This paper investigates the optimal control protocols for minimizing work fluctuations in driven mesoscopic systems, revealing a phase transition in protocol space for quantum dots and contrasting behavior with harmonic oscillators.

Contribution

It uncovers a phase transition in protocol space for quantum dots and compares it with harmonic oscillators, advancing understanding of work fluctuation minimization.

Findings

Quantum dot protocols exhibit a phase transition between two optimal strategies.

Harmonic oscillator protocols smoothly trade off between average work and fluctuations.

Optimal work fluctuation protocols do not become quasistatic even at infinite duration.

Abstract

For two canonical examples of driven mesoscopic systems - a harmonically-trapped Brownian particle and a quantum dot - we numerically determine the finite-time protocols that optimize the compromise between the standard deviation and the mean of the dissipated work. In the case of the oscillator, we observe a collection of protocols that smoothly trade-off between average work and its fluctuations. However, for the quantum dot, we find that as we shift the weight of our optimization objective from average work to work standard deviation, there is an analog of a first-order phase transition in protocol space: two distinct protocols exchange global optimality with mixed protocols akin to phase coexistence. As a result, the two types of protocols possess qualitatively different properties and remain distinct even in the infinite duration limit: optimal-work-fluctuation protocols never coalesce with the minimal work protocols, which therefore never become quasistatic.