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What complications arise when examining the statistical mechanics of a system under the influence of gravity? Is it significantly different from the classical treatment of statistical mechanics?

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    $\begingroup$ Could you be a bit more specific in what you actually want? Why do you think there are complications? Do you mean gravity as in "Newtonian gravity" or gravity as in "GR"? $\endgroup$
    – ACuriousMind
    Jul 17, 2014 at 17:12
  • $\begingroup$ There are many practical approaches to study systems for which gravity is important. E.g. a system can be in some steady state situation and you can then pretend that it is in thermal equilibrium, but then you need to invoke a negative heat capacity. But the fundamental issue here is that gravity is a long range force that unlike elctromagnetism won't be shielded, therefore internal energy entropy etc. won't be extensive. $\endgroup$ Jul 17, 2014 at 17:36
  • $\begingroup$ I think that most people are confused if you're asking about classical problems that appear in statistical mechanics of stars and clusters, where negative heat capacity, non-extensiveness and other "weird" behavior occurs or if you ask about the need to include the entropy of gravitational degrees of freedom (whatever that may be) in order not to violate the second law of thermodynamics in the presence of black holes. You could take a look at Donald Lynden-Bell's work on the first case, or inumerous discussions of Bekenstein's 1973 paper for the latter $\endgroup$ Jul 17, 2014 at 20:51
  • $\begingroup$ I was asking primarily about the classical problems that appear with regards to stars and galaxies, as I ran into some stuff about the negative heat capacity a few days ago but wasn't sure how it arose, and wanted to gain more insight into what role gravity plays in this. But the black hole stuff sounds interesting too, so I would appreciate some elucidation on that topic as well. $\endgroup$
    – ruadath
    Jul 17, 2014 at 20:58

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