Shortcuts of freely relaxing systems using equilibrium physical observables

TL;DR

This paper develops a theoretical framework to design shortcuts for rapidly relaxing systems by exploiting equilibrium observables, focusing on anomalous behaviors like the Mpemba effect near first-order transitions.

Contribution

It introduces a strategy based on timescale separation and nonmonotonic temperature evolution to control relaxation times in mesoscopic systems, exemplified with the 1D Ising model.

Findings

The approach predicts conditions for anomalous relaxation behaviors.

Analytic and numerical results confirm the theory's applicability.

Strategies can be designed to accelerate system equilibration.

Abstract

Many systems, when initially placed far from equilibrium, exhibit surprising behavior in their attempt to equilibrate. Striking examples are the Mpemba effect and the cooling-heating asymmetry. These anomalous behaviors can be exploited to shorten the time needed to cool down (or heat up) a system. Though, a strategy to design these effects in mesoscopic systems is missing. We bring forward a description that allows us to formulate such strategies, and, along the way, makes natural these paradoxical behaviors. In particular, we study the evolution of macroscopic physical observables of systems freely relaxing under the influence of one or two instantaneous thermal quenches. The two crucial ingredients in our approach are timescale separation and a nonmonotonic temperature evolution of an important state function. We argue that both are generic features near a first-order transition. Our theory is exemplified with the one-dimensional Ising model in a magnetic field using analytic results and numerical experiments.