This is one of my more technical posts about research activity. It is not written with wide readability in mind, but you may still get a lot out of it since the first part especially talks about about research life.

Some years ago (you’ll perhaps recall), I came up with an interesting construction that I called a “Holographic Heat Engine”. Basically, it arises as a natural concept when you work in what I call “extended” gravitational thermodynamics where you allow the spacetime cosmological constant to be dynamical. It is natural to associate the cosmological constant with a dynamical pressure (in the usual way it appears as a pressure in Einstein’s equations) and if you work it though it turns out that there’s a natural conjugate quantity playing the role of volume, etc. Black hole thermodynamics (that you get when you turn on quantum effects, giving entropy and temperature) then get enhanced to include pressure and volume, something that was not present for most of the history of the subject. It was all worked out nicely in a paper by Kastor et. al. in 2009. So…anyway, once you have black holes in that setup it seemed to me (when I encountered this extended framework in 2014) that it would be wilful neglect to not define heat engines: closed cycles in the p-V plane that take in heat, output heat, and do mechanical work. So I defined them. See three old posts of mine, here, here, and here, and there are others if you search.

Well, one of the things that has been a major quest of mine since 2014 is to see if I can make sense of the extended thermodynamics for quantum field theory, and then go further and translate the heat engines and their properties into field theory terms. This seemed possible to me all the way back then since for positive pressure, the cosmological constant is negative, and when you have gravity with negative cosmological constant you’ve got duality to strongly coupled field theories. So those heat engines must be some kind of special tour in the field theories. the efficiency of an engine must mean something about the tour. Moreover, since the efficiency of the engine is bounded by the Carnot efficiency, it seems we have a naturally defined dimensionless number that has a fundamental bound… Alarm bells ringing! – Opportunity knocking to learn something new and powerful! Maybe even important!

So I chipped away at this for some time, over years, doing various projects that […] Click to continue reading this post →