Thermodynamics and Gravity

ads_ballI 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.


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18 Responses to Thermodynamics and Gravity

  1. Aaron Bergman says:

    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.

    But this is what drives me nuts. We throw around terms from thermodynamics, and I have no idea what any of the words mean. Worse, people freely mix up entanglement entropy, microcanonical entropy and canonical entropy when they’re not always the same thing, especially for gravitating systems.

  2. Clifford says:

    I do agree that there’s a bit of noise there. Indeed that could do with a lot of cleaning up too. But are you unhappy with the basic maps of the thermodynamics of large black holes to those of the plasma, and the terms used there? (Hawking-Page-Witten, if you like.)


  3. Aaron Bergman says:

    If I don’t think too hard about it, I’m happy. But whenever I try to dig in and really figure out what’s going on, so to speak, I end up hopelessly confused.

  4. Elliot says:

    I always wondered about the idea of a closed box with a gas in thermal equilibrium in an increasing gravitational field. At some point the strength of the gravitational field “reduces” the entropy of the gas in the box by pulling all the gas molecules to one side.

    I suspect this is just a naive view of things but it seems curious to me.


  5. Slim P. says:

    “as Witten first taught us in 2008”
    You meant 1998.

  6. wolfgang says:


    I am not sure how AdS/CFT will help you with thermodynamics of quantum gravity (the AdS side).
    If the CFT part of the duality is in a pure state, the associated entropy is zero – and yet the AdS side contains (virtual) black holes etc. in the bulk.

  7. Clifford says:

    Slim P. – Thanks! fixed.

    wolfgang – I don’t think I understand why you’re saying it does not help. The system is thermodynamic on both sides in the situations I’m thinking of. I have a black hole with well defined temperature and entropy, etc, on the AdS side, and the plasma has also a well defined temperature and entropy. I would say that this is a nice example of AdS/CFT helping us with the thermodynamics of quantum gravity in the sense that it gives us a firm handle on it by relating it to the thermodynamics of more familiar non-gravitational systems.


  8. wolfgang says:

    > in the situations I’m thinking of
    Yes, but my argument is that it seems possible to have a pure state on one side and it should still have (virtual) black holes etc. on the other side.
    Thus I think the entropy on one side does not tell you much about the other side without additional assumptions.

  9. wolfgang says:

    I think I should be more explicit: My argument points out that a pure quantum gravity state (corresponding to the pure CFT state) has zero entropy even if it involves virtual black holes (but maybe I am wrong about that).
    Now you can have entropy on both sides by considering mixed states, but what do you learn from it about the entropy associated with black holes etc. ?

  10. wolfgang says:


    after re-reading your post I have to conclude that my comments do not apply to your argument.

    I am sorry for wasting your time; Is there a way to delete my previus comments?

  11. Clifford says:

    I don’t see any need to delete them. All part of the discussion. No worries.


  12. Plato says:

    As a lay person I have a question.

    Are scientists only providing perspective( Boltzmann Brains, mathematics, theoretics of gravity inherent) from an approximation?

    Would this not be considered “as noise” knowing that there maybe some “truth inherent” about the “real universe” that we can all speculate and are all not aware of?

  13. Clifford says:

    Hi Plato,

    I “don’t understand” your “question”. 🙂

    We’re working to understand the universe. This starts by thinking about it, and building on what we already know about the universe, constructing mathematical toolboxes and models, in frameworks such as string theory. The next step is to extract new conclusions form these models and see if these match what we see or have seen in experiments and observations. With issues in quantum gravity, we are mostly at the first stage, not the second. However, reading what I said in my earlier posts (linked above) about relationships to QCD in newly discovered phases of nuclear matter (plasmas made of quarks and gluons), you can see that perhaps we’ve begun to see signs of rather cute experimental routes for testing some of these tools and models from string theory. We in this way may get a handle on issues in quantum gravity – so far it is not the gravity of our universe, but some of us find it encouraging (if it works at all) that we can get insights into any such theory, so we’re excited.

    I “hope” that gets at what you’re “asking”.


  14. Plato says:

    Hi Clifford,

    With issues in quantum gravity, we are mostly at the first stage, not the second

    Yes that does help clarify.

    you can see that perhaps we’ve begun to see signs of rather cute experimental routes for testing some of these tools and models from string theory

    Yes I had been following for sometime.

    so far it is not the gravity of our universe,

    Now, that indeed is confusing. It seems to imply that there is other gravities, when “may be” really just one?

    Do you acknowledge “any relativistic interpretation” in the QGP?


  15. Clifford says:

    Please read the posts again. I think the duality is reasonably well explained in them. I can’t write it all again.

    Not even the slightest clue what your last question means. Sorry.


  16. Plato says:

    I’m sorry Clifford. I am really trying to take my time.

    An astronomer might say, and I gathered from my reading, that the “spherical cow” is a method by which, “an approximation” is made about “an event.”

    Then we are witness too, “the physics of expression from those events.” I wanted to know if there is a “mathematical way” to describe “each and every event” as a rule, as it is expressed in our cosmos under the “string theory structure?”

    A “Heat death” would seem to me to be a finality. I would like to think there is an “open the door in the face of reductionism” to what existed “before.” Wishful thinking?:)

    IN that context “gravity is the same” before the universe or after, in the geometrical expression. I do not mean too, demean the word gravity, other then what you want it to be as a science expression.

    My last question above was with regard to the nature of the macroscopic world(relativity) being inconsistent with the microcosm. That such a inconsistency “has been removed” once taken to the QGP level? I was thinking in terms of Navier Stokes.

    Thanks for your time.


  17. Peter Fred says:

    The sun is not only the most massive body in the solar system; it is also the the most luminous. Also at the center of a galaxy where the high rotation of the central stars lead our scientist to believe that 10^10 solar mass black hole exists is also the seat of a very high source of luminosity. If you think this is just a mere coincidence, why can I repeatedly demonstrate experimentally that spreading infrared radiation is gravitationally attractive.

    Pardon me for interrupting. Please go on and on about thermodynamics and gravity. Do not suspect that heat and gravity are causally related. The dimming of the universe started around z =1 and the acceleration of the universe started around z = 0.6. Of course, you scientists think this is just another mere coincidence.
    Newton and Einstein could not be wrong? Could they? We will find the dark matter and resolve the dark energy problem? Won’t we? So this business about 95% of the universe being composed of something we know nothing about is not anything to be worried about.

  18. ed says:

    Hi intellectual type folk,

    I am less than a lay person. I like to read all of the theories of the universe that are out there. OUT THERE sometimes being the operative word.

    I may be misunderstanding greatly but it seems you guys just discount the force of a vacuum, the vacuum of space.

    In a large explosion, you know like the big bang, wouldn’t the vacuum created be an awsome counter force. At the original source of an explosion as well as around each subsequant explosion. The creation of each new star, sun etc.

    Stupid me but with all this counter force of the low presure created by the consumption all the available fuel, hydrogen whatever, at each point of combustion through out the entire universe does this have any relation to dark matter or dark energy???

    Does this have any relation to the force holding the planets seemingly in place??? Gravity. In place seems to be just a perception.

    Is living in our universe like existing in a time lapse fireworks display??

    Thanks for the time,