Thermodynamics of Black holes
From the beginning, it was suspected that the four laws of black hole dynamics, formulated by Bardeen, Carter and Hawking in 1973, were related to the laws of thermodynamics. The analogy with glasses, that is to say, systems with two well separated timescales and two temperatures, proved successful, see [L32]. One temperature is the Hawking temperature of the black hole, the other, for isolated holes, the 3K cosmic microwave background temperature. Within this approach, the zero'th, first and second laws find their natural connection. It appeared, however, that the third law of the dynamics, which deals with extremal black holes (maximal rotation or maximal charge; vanishing Hawking temperature) describes other physics than the third law of thermodynamics, which is relevant for vanishing temperature of the environment, in which case all black holes evaporate.
[L33] Th.M. N., Thermodynamics of black holes: an analogy with glasses, Phys. Rev. Lett. 81 (1998) 2201-2204
[C21] Th.M. N., Thermodynamics Far from Equilibrium: from Glasses to Black Holes Proceedings Marcel Grossmann IX (World Scientific, 2001). Short version: 4 pages, extended version for CD-rom: 11 pages
[C19] Th.M. N., Thermodynamics and Gravitation: From Glasses to Black Holes and Globular Star Clusters, Proceedings of ``The Chaotic Universe'', eds. V.G.Gurzadyan and R.Ruffini, World Scientific, 2000 cond-mat/9911121
Black hole information paradox
In 1975 Steven Hawking showed that black holes evaporate, creating a thermal spectrum, as if it
were a black body. This poses the information paradox: information about the matter that went in the black hole, does not seem to come out.
One of the biggest mysteries of the macroscopic world is irreversibility/relaxation. Hawking has the opinion that there is conservation of information in theories with unitary dynamics. Actually this assertion is far from being obvious. There are various types of information (entropy) which behave differently under unitary dynamics. The problem is studied in statistical physics starting with Boltzmann.
Even for ordinary gases it is not solved yet. One of the basic advances in the study of this problem is the Bogoliubov idea about two relaxation timescales.
In this paper, we consider the black hole information problem as an example of the famous irreversibility problem in statistical physics and mention various fine grained and coarse grained entropies that play a role. Next we outline a derivation of an analogue of the Boltzmann equation in quantum gravity along the lines of Bogoliubov's derivation for gases.
ITFA-2005-35: Th. M. Nieuwenhuizen and I.V. Volovich,
Role of Various Entropies in the Black Hole Information Loss Problem,
hep-th/0507272.