I noticed that Robert Helling shared some thoughts about thermodynamics and gravity today on his blog. He is understandably confused about several aspects of the issue, especially when applied to cosmological issues. (What is the entropy of our universe? Does the Second Law really apply? Does equilibrium thermodynamics even apply here?)
I’ve nothing remarkable to add to the discussion at this time except to note that a blanket statement that thermodynamics and gravity don’t seem to go together (which I don’t think he’s strongly saying) is not one I’d make, since we have a major class of working counterexamples.
The context is the gauge/gravity duals I’ve talked about here a lot, starting with AdS/CFT and beyond. There we know that the gravitational systems are essentially able to display the more garden variety thermodynamics by being immersed in the (regulating-box-like) anti-De Sitter type backgrounds. Then we see that black holes (large enough to see the AdS setup) have positive specific heat (the essential Hawking-Page result), and are just the right sorts of things to model the thermodynamics of ordinary gauge theories (as Witten first taught us in 1998 when beautifully refining Maldacena’s AdS/CFT conjecture into a computational tool), and hence -for complicated enough duals- the class of dynamics that quarks and gluons in the lab will exhibit (as some of us have been emphasizing and working on for a decade now)! (For a post on these latter issues, see here, and recall I even made a little movie of some slides that you can see here.)
So the methods we’ve been using in string theory seem to be able to help us make some sense of thermodynamics and gravity in a way that seems to fit together rather well. This is just a small corner though…. I’ll agree with Robert that there’s a lot more to do. This tells us nothing about non-equilibrium systems, and whether (or when) it makes sense in to treat the universe as an equilibrium system when it comes to thermodynamic issues. So the AdS/CFT (and related) examples may well be irrelevant for such cosmological issues. But…
But we know that the usual gravitational thermodynamics is embedded in the same AdS story for small enough scales (negative specific heat black holes of the ordinary Schwarzschild type and so forth), and by the duality must probably also make sense in ordinary thermodynamics too. Probably they play a role in some part of a non-equilibrium story… those small black holes are unstable due to Hawking evaporation. A good handle on the role of such objects on the gauge theory (quark-gluon plasma) side is still lacking, last time I looked (but maybe that has changed?) but it is probably only a matter of time. So maybe at least a broad lesson is that “it’s in there”, which is reassuring, and all we need is better tools to learn how to extract the specifics. I may well be way too optimistic here. Not only might we need to go back to the drawing board, we may need a whole new drawing board. But I do feel that the recent work on gauge/gravity duals – and holography in general – are pointing the right way.
All worth chewing over.