Optimal speed-up of multi-step Pontus-Mpemba protocols

TL;DR

This paper explores multi-step Pontus-Mpemba protocols in open quantum systems, identifying optimal conditions for speed-up and revealing rich dynamical regimes including non-Markovian effects.

Contribution

It introduces a framework for optimizing speed-up in quantum protocols using time-dependent dissipation rates, bridging quasi-static and sudden-quench regimes.

Findings

Optimal parameters for speed-up identified in two-parameter family of rates.

Continuous protocols derived as the limit of many discrete steps.

Non-Markovian dynamics can be induced by time-dependent dissipation.

Abstract

The classical Mpemba effect is the counterintuitive phenomenon where hotter water freezes faster than colder water due to the breakdown of Newton's law of cooling after a sudden temperature quench. The genuine nonequilibrium post-quench dynamics allows the system to evolve along effective shortcuts absent in the quasi-static regime. When the time needed for preparing the (classical or quantum) system in the hotter initial state is included, we encounter so-called Pontus-Mpemba effects. We here investigate multi-step Pontus-Mpemba protocols for open quantum systems whose dynamics is governed by non-autonomous (aka time-inhomogeneous) Lindblad master equations. In the limit of infinitely many steps, one arrives at continuous Pontus-Mpemba protocols. We study the crossover between the quasi-static and the sudden-quench regime, showing the presence of dynamically generated shortcuts achieved for time-dependent dissipation rates. Considering a two-parameter family of time-dependent rates, the parameters allowing for optimal speed-up conditions are determined. Time-dependent rates can also cause non-Markovian behavior, highlighting the existence of rich dynamical regimes accessible beyond the Markovian framework.