Time-extensive classical and quantum correlations in thermal machines

TL;DR

This paper investigates how classical and quantum correlations develop over time in a driven quantum thermal machine, revealing two key processes responsible for long-term correlation growth.

Contribution

It identifies the specific resonant and nonresonant processes that generate time-extensive correlations in the environment of a quantum thermal machine.

Findings

Mutual information and quantum discord grow quadratically over time.

Entanglement production becomes time-extensive.

Two main processes drive long-term correlations in the environment.

Abstract

We study intraenvironmental classical and quantum correlations in a thermal machine, which is modeled as a driven quantum system coupled with thermal reservoirs. We compute the mutual information, the quantum discord, and the entanglement between two parts of the environment formed by oscillators centered around two different frequencies. We show that there are only two processes that generate time-extensive correlations in the long-time limit. First, there is a resonant process which is responsible for the transport of excitations between different environmental modes due to the absorption (or emission) of energy from (or into) the driving field. Second, there is a nonresonant process that transforms the energy from the external driving into pairs of excitations in two environmental modes. We show that there is a regime when the mutual information and the quantum discord between the parts of the environment correlated by these two processes grow quadratically in time, while entanglement production is time-extensive.