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.
Highlights
In recent years, ideas first appearing in the field of physical chemistry [1,2,3,4] have been used in conjunction with information theory to analyse thermodynamics in the quantum and nano-scale regimes
This stronger result follows from the fact that set of q that can be achieved in the resource theory of elementary thermal operations (ETOs) is a closed set; in turn, this is a by-product of the considerations of the section, in which we develop necessary and sufficient conditions for a transformation to be possible in the resource theory of ETOs
In this paper we have introduced the thermodynamic resource theory of elementary thermal operations (ETOs) and shown that for certain parameter regimes that they can be well reproduced by a simple Jaynes-Cummings interaction
Summary
Ideas first appearing in the field of physical chemistry [1,2,3,4] have been used in conjunction with information theory to analyse thermodynamics in the quantum and nano-scale regimes. Many of these results are based upon the definition of a restricted set of quantum operations known as thermal operations (TO) These aim to capture all processes that can be realised without an external source of work or coherence and derive fundamental limitations and bounds on thermodynamic processes and transformations. While at infinite temperature thermodynamic theories are largely universal, i.e. the specific constraints at hand do not matter in terms of the thermodynamic laws arising, this is no longer the case at finite temperature This implies that every restriction will lead to a different resource theory; luckily, some of these can be solved using the same tools we develop here for ETOs. For example, we can give necessary and sufficient conditions for the population dynamics achievable in the resource theory of 2-level Jaynes-Cummings interactions in RWA, which is a theory strictly contained in ETOs. For example, we can give necessary and sufficient conditions for the population dynamics achievable in the resource theory of 2-level Jaynes-Cummings interactions in RWA, which is a theory strictly contained in ETOs This is important since, for large enough systems and/or specific choices of physical parameters, we expect the two theories to depart from each other. We discuss an application of this framework to an algorithmic cooling protocol, showing that a particular ETO can be used to speed up recently proposed protocols
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