tag:blogger.com,1999:blog-8883034.post3666773713099780510..comments2024-03-23T23:26:40.813+01:00Comments on atdotde: Thermodynamics of gravitational systemsRoberthttp://www.blogger.com/profile/06634377111195468947noreply@blogger.comBlogger12125tag:blogger.com,1999:blog-8883034.post-47111164691314625532010-07-16T18:23:36.570+02:002010-07-16T18:23:36.570+02:00Hi Robert,
I can recommend you the very *thoughtf...Hi Robert,<br /><br />I can recommend you the very *thoughtful* review about these issues (entropy formula's in relativity, laws of thermodynamics, unitarity and hawking radiation, the holographic principle) written by Bob wald :<br /><br />http://arxiv.org/PS_cache/gr-qc/pdf/9912/9912119v2.pdf<br /><br />Concerning the averaging procedure in cosmology which you mention, I recall that Thomas Buchert has done some nice work about that.<br /><br />Best,<br /><br />JohnAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-8883034.post-8997207235621801752009-02-16T07:01:00.000+01:002009-02-16T07:01:00.000+01:00In the book of Landau& Lifschitz "statist...In the book of Landau& Lifschitz "statistical physics" (vol V of his famouse course in theorethical physics)youcan find concise, elegant and short answers to most of your questions.<BR/><BR/> Specifically you should read sections 25, 26 (optionally), 27 and 38. I guess it would take among 5 or 15 minuts to do so.<BR/><BR/> Aditionally I remember to have readed that a collection of bodies interactin only by a purely newtonian potential cant go into equilibrium, ut I donĀ“t remember the exact reference (I think that it was in Lectures on phase transitions and the renormalization group <BR/> Goldenfeld, Nigel , but I am not totally sure.Javierhttps://www.blogger.com/profile/17845977289427117418noreply@blogger.comtag:blogger.com,1999:blog-8883034.post-91158732048818888182009-01-12T12:53:00.000+01:002009-01-12T12:53:00.000+01:00Hi Robert, I'm a Ph.D studet in stat mech. I wante...Hi Robert, I'm a Ph.D studet in stat mech. I wanted to write a comment but it was getting too long, so I wrote a verbose post <A HREF="http://tomate.blogsome.com/2009/01/12/gravitation-and-thermodynamics/#more-66" REL="nofollow">here</A> trying to examine your two questions which I dubbed the "growing information paradox" and the "tidy equilibrium paradox". Hope it might be helpful, either for me or for you.tomatehttps://www.blogger.com/profile/09711368972086055059noreply@blogger.comtag:blogger.com,1999:blog-8883034.post-21110180929755636852009-01-05T08:50:00.000+01:002009-01-05T08:50:00.000+01:00Wow, being away from the internet for a day makes ...Wow, being away from the internet for a day makes me nearly miss being knighted by Lubos in one of his trademark praises. <BR/><BR/>And no, I am too modest to thank him personally and visibly on his site for enlightening me as in the past he has demonstrated he is too busy to actually consider such thanks but would rather spill out more of his praise.<BR/><BR/>Later today, however, I will respond to some of the good points made here. Thanks a lot, honstely!Roberthttps://www.blogger.com/profile/06634377111195468947noreply@blogger.comtag:blogger.com,1999:blog-8883034.post-20089205932799667742009-01-05T03:49:00.000+01:002009-01-05T03:49:00.000+01:00As CVJ said, there is plenty of evidence that our ...As CVJ said, there is plenty of evidence that our normal expectations regarding entropy will continue to hold in the gravitational case. There will be plenty of complications and surprises as the notion of gravitational entropy is clarified, but there is *no* reason to think that the overall picture will be really strange.<BR/><BR/>The basic point is this. If our Universe had been born in a "completely random" way, then of course it ought to have been born in a state of maximal entropy, that being the most probable state of any system. Maximal entropy would mean: the matter degrees of freedom nearly in equilibrium, and the spacetime geometry very anisotropic and inhomogeneous. Note that in the absence of *geometric* homogeneity, we have no right to expect any kind of uniformity in the matter, even when the latter is at equilibrium [This is the one sensible point made by LM in his lengthy, chaotic, and mostly utterly *wrong* diatribe in response to your post.] <BR/><BR/>Now of course the real world was not born anything like that; obviously it was born in a fantastically non-generic, low entropy state. The matter degrees of freedom *were* born nearly in equilibrium, but the gravitational degrees of freedom certainly were not. For some reason the universe was born very very isotropic, that is, with extremely low *gravitational* entropy. Under these circumstances, of course the matter [near equilibrium] was nice and uniform. But the *total* entropy was low. Indeed, it is *only* the concept of gravitational entropy [however exactly it is defined] that allows us to make sense of the thermal history of the early universe. In Newtonian gravity, what we see would make no sense at all.<BR/><BR/>Bottom line: you are right, gravitational entropy is confusing and very badly understood. But despite this there is good reason to think that it *is* a valid concept. Anyone who argues otherwise is essentially suggesting that the second law of thermodynamics is violated in the early universe. The principal task is to understand *why* gravitational entropy was so low at the creation.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-8883034.post-42861672214075037832009-01-04T21:05:00.000+01:002009-01-04T21:05:00.000+01:00I take it your question is genuine?http://en.wikip...I take it your question is genuine?<BR/><BR/>http://en.wikipedia.org/wiki/Lubo%C5%A1_Motl<BR/><BR/>http://motls.blogspot.com/Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-8883034.post-61260863827502318522009-01-04T20:43:00.000+01:002009-01-04T20:43:00.000+01:00who is Lubos Motl?who is Lubos Motl?Bruce Routhttps://www.blogger.com/profile/07070314799576659579noreply@blogger.comtag:blogger.com,1999:blog-8883034.post-50787023739820137692009-01-04T15:13:00.000+01:002009-01-04T15:13:00.000+01:00Hi Robert,may I suggest that you reply and defend ...Hi Robert,<BR/><BR/>may I suggest that you reply and defend yourself over at Lubos Motl's blog? I admit, I wouldn't want to defend your text against his, but surely you feel differently, don't you?<BR/><BR/>Best,<BR/>MichaelAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-8883034.post-28297819622819477122009-01-03T16:05:00.000+01:002009-01-03T16:05:00.000+01:00As far as Penrose's Weyl curvature proposal goes, ...As far as Penrose's Weyl curvature proposal goes, an easy way to see it can't work is to look in 2+1 dimensions.<BR/><BR/>In 2+1 dimensions the Weyl curvature vanishes identically, but in 2+1 dimensions one has a black hole with entropy proportional to its circumference.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-8883034.post-77406058231936321532009-01-03T10:05:00.000+01:002009-01-03T10:05:00.000+01:00Robert,what is sometimes confusing about thermodyn...Robert,<BR/><BR/>what is sometimes confusing about thermodynamics of gravitating systems (Newtonian gravity) is the fact that their heat capacity is negative.<BR/><BR/>e.g. A star radiating energy away is heating up (due to gravitational contraction). <BR/><BR/>When it comes to general relativity, we simply do not know how to calculate the entropy of an (arbitrary) space-time.<BR/>Penrose proposed to use the Weyl curvature, but one can show that there are problems with his initial proposal.<BR/><BR/>But I think when people talk about the low entropy of the universe near the big bang, they refer (implicitly) to the fact that the Weyl curvature is/was small there (at least according to our current understanding).Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-8883034.post-12851413499282224122009-01-03T03:14:00.000+01:002009-01-03T03:14:00.000+01:00Yo Bob. Very good post with exceptionally good que...Yo Bob. Very good post with exceptionally good questions. How do we approach the question of the entropy of a black hole? Furthermore, is information conserved across an event horizon?<BR/><BR/>Entropy increases. If it doesn't then no work can be done. It's highly related to the efficiency of a system. Gravity is pretty efficient.<BR/><BR/>It all makes sense unless you assume an expanding universe, in which case, anything goes, including the most bizarre theories imaginable.<BR/><BR/>Apparently, a popular cosmology is that we are in a left-handed orthogonal triad in which time goes forward, the universe expands and entropy increases. Personally, I think it's garbage. Overall entropy increases in a system if it does anything. Time goes forward. I doubt very much that the universe is expanding.Bruce Routhttps://www.blogger.com/profile/07070314799576659579noreply@blogger.comtag:blogger.com,1999:blog-8883034.post-63824752253401803502009-01-02T20:26:00.000+01:002009-01-02T20:26:00.000+01:00Hi Robert. Happy New Year. I like a lot of what yo...Hi Robert. <BR/><BR/>Happy New Year. I like a lot of what you're saying but I do think we have some evidence that the familiar laws of thermodynamics can work with gravity. Various gauge/gravity duals of the AdS/CFT class and related. This class of examples does not get at all the issues you mention (not even close) but surely there are some useful lessons there. I think that Holography is key to some of these issues. See a quick post I did in response to yours <A HREF="http://asymptotia.com/2009/01/02/thermodynamics-and-gravity/" REL="nofollow">here</A>.<BR/><BR/>Best,<BR/><BR/>-cvjcvjhttps://www.blogger.com/profile/11877721142551713474noreply@blogger.com