The cost of cooling (quantum) beer

November 16, 2017

Some two weeks ago, we had a new paper out on the arXiv, which I haven’t had the time to write about until now: It has been under way for quite a while, but now we finally managed to put it all on (virtual) paper and get it out there.

This work contributes to building a consistent picture of thermodynamics at the quantum scale.

Thermodynamics explains how machines like steam engines and fridges work. It describes how heat can be moved around or transformed into other useful forms of energy, such as motion in a locomotive. And it tells us the fundamental limits on how well any such machine can perform, no matter how clever and intricate. In turn, the study of ideal machines has taught us fundamental things about nature, such as the second law of thermodynamics, which says that the entropy of an isolated system can never decrease (often thought of as stating the the ‘mess’ of the universe can only get bigger over time). Or the third law, which says that cooling to absolute theory requires infinite resources.

Traditionally, thermodynamics deals with big systems (think, steam locomotive), whose components are well described by classical physics. However, if we would look at smaller and smaller scales, then eventually we will need quantum physics to describe these components, and quantum phenomena will start to become important. What does thermodynamics look like at this quantum scale? Do the well known laws still hold? Can we make sense of such microscopic thermal processes? These are interesting theoretical questions. And by now, experimental techniques are getting so advanced that we can actually begin to build something like steam engines and fridges on the nanoscale. So they are starting to be relevant in practice as well.

A lot is already known about quantum thermodynamics, including generalisations of the Second and Third Laws and many results about the behaviour of thermal machines. However, it is fair to say that it is still work in progress – we do not yet have a full, coherent picture of quantum thermodynamics. Different approaches have been developed and it is not always clear how they fit together.

One point where classical and quantum thermodynamics differ is on how much it ‘costs’ to have control over a system, in terms of work energy (think of work as energy in an ordered, useful form as opposed to disordered heat energy). In the classical world the work cost of control can usually be neglected. Not so in the quantum world. There the cost of control can be a significant part of the cost of operating a machine.

In our paper, we add a piece towards completing the puzzle of quantum thermodynamics by studying the role of control for cooling. By looking at small fridges with more or less available control, we are able to compare different paradigms, which have been developed in the field, and compare how much one can cool under each of them, and how much it costs.

Published paper:

This paper eventually got split into two parts. One focusing on a universal limit to cooling quantum systems, and one focused on the work cost of cooling.

The first paper was published in PRL here:

The second was published in PRE here: