Elementary Thermal Operations

TL;DR

This paper introduces elementary thermal operations based on 2-level energy interactions, showing they impose stricter physical constraints than traditional thermal operations, with implications for quantum thermodynamics and cooling protocols.

Contribution

It defines elementary thermodynamic gates, connects them to Jaynes-Cummings interactions, and demonstrates their tighter constraints on state transformations compared to standard thermal operations.

Findings

Elementary thermal operations are well modeled by Jaynes-Cummings interactions.

They impose stricter constraints than traditional thermal operations.

New tools and conditions for state transformation feasibility are provided.

Abstract

To what extent do thermodynamic resource theories capture physically relevant constraints? Inspired by quantum computation, we define a set of elementary thermodynamic gates that only act on 2 energy levels of a system at a time. We show that this theory is well reproduced by a Jaynes-Cummings interaction in rotating wave approximation and draw a connection to standard descriptions of thermalisation. We then prove that elementary thermal operations present tighter constraints on the allowed transformations than thermal operations. Mathematically, this illustrates the failure at finite temperature of fundamental theorems by Birkhoff and Muirhead-Hardy-Littlewood-Polya concerning stochastic maps. Physically, this implies that stronger constraints than those imposed by single-shot quantities can be given if we tailor a thermodynamic resource theory to the relevant experimental scenario. We provide new tools to do so, including necessary and sufficient conditions for a given change of the population to be possible. As an example, we describe the resource theory of the Jaynes-Cummings model. Finally, we initiate an investigation into how our resource theories can be applied to Heat Bath Algorithmic Cooling protocols.