Connections between efficient control and spontaneous transitions in an Ising model

TL;DR

This paper explores the relationship between externally controlled protocols designed to minimize work and the natural spontaneous transition paths in a 2D Ising model, revealing a preserved order of spin flips and energetic compensation mechanisms.

Contribution

It demonstrates a correspondence between minimum-work driving protocols and spontaneous transition mechanisms in an Ising model, highlighting the preservation of transition order despite control limitations.

Findings

Order of spin flips is preserved between driven and spontaneous transitions.

External control parameters compensate internal energy changes during protocols.

Minimum-work protocols reflect natural transition mechanisms.

Abstract

A system can be driven between metastable configurations by a time-dependent driving protocol, which uses external control parameters to change the potential energy of the system. Here we investigate the correspondence between driving protocols that are designed to minimize work and the spontaneous transition paths of the system in the absence of driving. We study the spin-inversion reaction in a 2D Ising model, quantifying the timing of each spin flip and heat flow to the system during both a minimum-work protocol and a spontaneous transition. The general order of spin flips during the transition mechanism is preserved between the processes, despite the coarseness of control parameters that are unable to reproduce more detailed features of the spontaneous mechanism. Additionally, external control parameters provide energy to each system component to compensate changes in internal energy, showing how control parameters are tuned during a minimum-work protocol to counteract underlying energetic features. This study supports a correspondence between minimum-work protocols and spontaneous transition mechanisms.