# Elementary Thermal Operations. (arXiv:1607.00394v3 [quant-ph] UPDATED)

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.