Low-temperature thermodynamics with quantum coherence

TL;DR

This paper introduces 'cooling maps' as a low-temperature generalization of thermal operations, providing a complete characterization of state transitions involving quantum coherence, and suggests these maps could help understand broader thermodynamic processes.

Contribution

The paper derives necessary and sufficient conditions for state transitions under cooling maps and conjectures their equivalence to thermal operations, advancing the understanding of quantum coherence in thermodynamics.

Findings

Cooling maps can realize coherence transfer bounds.

Cooling maps are more tractable than Gibbs-preserving operations.

Conjecture: All cooling maps are thermal operations.

Abstract

Thermal operations are an operational model of non-equilibrium quantum thermodynamics. In the absence of coherence between energy levels, exact state transition conditions under thermal operations are known in terms of a mathematical relation called thermo-majorization. But incorporating coherence has turned out to be challenging, even under the relatively tractable model wherein all Gibbs state-preserving quantum channels are included. Here we find a mathematical generalization of thermal operations at low temperatures, "cooling maps", for which we derive the necessary and sufficient state transition condition. Cooling maps that saturate recently-discovered bounds on coherence transfer are realizable as thermal operations, motivating us to conjecture that all cooling maps are thermal operations. Cooling maps, though a less conservative generalization to thermal operations, are more tractable than Gibbs-preserving operations, suggesting that cooling map-like models at general temperatures could be of use in gaining insight about thermal operations.