What it takes to shun equilibration

TL;DR

This paper explores how certain quantum states can be made resistant to equilibration by using resource systems, linking resource theories with quantum dynamics and examining implications for quantum thermodynamics.

Contribution

It introduces a measure of resilience against equilibration, establishing a resource-theoretic framework for understanding how to prevent or control quantum system equilibration.

Findings

Resilience against equilibration can be quantified and manipulated.

Large resource systems are needed to increase resilience.

Resilience can be redistributed or catalytically generated depending on correlations.

Abstract

Numerous works have shown that under mild assumptions unitary dynamics inevitably leads to equilibration of physical expectation values if many energy eigenstates contribute to the initial state. Here, we consider systems driven by arbitrary time-dependent Hamiltonians as a protocol to prepare systems that do not equilibrate. We introduce a measure of the resilience against equilibration of such states and show, under natural assumptions, that in order to increase the resilience against equilibration of a given system, one needs to possess a resource system which itself has a large resilience. In this way, we establish a new link between the theory of equilibration and resource theories by quantifying the resilience against equilibration and the resources that are needed to produce it. We connect these findings with insights into local quantum quenches and investigate the (im-)possibility of formulating a second law of equilibration, by studying how resilience can be either only redistributed among subsystems, if these remain completely uncorrelated, or in turn created in a catalytic process if subsystems are allowed to build up some correlations.