Gibbs-Preserving Maps outperform Thermal Operations in the quantum regime

TL;DR

This paper demonstrates that in quantum thermodynamics, Gibbs-Preserving Maps are more powerful than Thermal Operations because they can generate quantum coherence, unlike the latter.

Contribution

It reveals that Gibbs-Preserving Maps outperform Thermal Operations in the quantum regime by enabling coherence, challenging classical equivalence.

Findings

Gibbs-Preserving Maps can generate quantum coherence.

Thermal Operations cannot create superpositions of energy levels.

The quantum regime breaks classical equivalence between the frameworks.

Abstract

In this brief note, we compare two frameworks for characterizing possible operations in quantum thermodynamics. One framework considers Thermal Operations---unitaries which conserve energy. The other framework considers all maps which preserve the Gibbs state at a given temperature. Thermal Operations preserve the Gibbs state; hence a natural question which arises is whether the two frameworks are equivalent. Classically, this is true---Gibbs-Preserving Maps are no more powerful than Thermal Operations. Here, we show that this no longer holds in the quantum regime: a Gibbs-Preserving Map can generate coherent superpositions of energy levels while Thermal Operations cannot. This gap has an impact on clarifying a mathematical framework for quantum thermodynamics.