# Work extraction in an isolated quantum lattice system: Grand canonical and generalized Gibbs ensemble predictions

## TL;DR

This paper investigates work extraction in isolated quantum lattice systems using quenches and equilibration to GGE and GE, identifying conditions for maximal work extraction without entropy increase.

## Contribution

It introduces a class of quenches that preserve entropy and maximize work extraction in both noninteracting and weakly interacting quantum systems.

## Key findings

- Quenches that do not produce entropy enable maximal work extraction.
- Equilibration to GGE or GE can be achieved without entropy increase under certain quenches.
- Maximal work extraction is possible in both integrable and weakly interacting systems.

## Abstract

We study work extraction (defined as the difference between the initial and the final energy) in noninteracting and (effectively) weakly interacting isolated fermionic quantum lattice systems in one dimension, which undergo a sequence of quenches and equilibration. The systems are divided in two parts, which we identify as the subsystem of interest and the bath. We extract work by quenching the on-site potentials in the subsystem, letting the entire system equilibrate, and returning to the initial parameters in the subsystem using a quasi-static process (the bath is never acted upon). We select initial states that are direct products of thermal states of the subsystem and the bath, and consider equilibration to the generalized Gibbs ensemble (GGE, noninteracting case) and to the Gibbs ensemble (GE, weakly interacting case). We identify the class of quenches that, in the thermodynamic limit, results in GE and GGE entropies after the quench that are identical to the one in the initial state (quenches that do not produce entropy). Those quenches guarantee maximal work extraction when thermalization occurs. We show that the same remains true in the presence of integrable dynamics that results in equilibration to the GGE.