Performance of near-optimal protocols in weak processes

Pierre Nazé

Published 2023-06-04Version 1

A natural criticism of the universal optimal protocol of the irreversible work found in the context of weak processes is its experimental difficulty to be implementable due to its singular part. In this work, I propose as a partial solution to this problem its continuous linear part as an acceptable near-optimal protocol. This is based on the analysis of several examples of the error committed to approximating the solution extended until its second order in its continuous linear part. The result seems to be universal: depending mainly on the ratio between switching time and waiting time $\tau/\tau_w$, the error for sudden and slowly-varying processes is less than $1\%$, while for $\tau\approx\tau_w$ it has a peak with an upper bound around $8\%$. Although implementing Dirac deltas could be an experimental challenge, I present also the error including those functions, where the results of these new near-optimal protocols become slightly better.