Old Journal Club: S. W. Hawking, Black holes and thermodynamics

Christian Aoufia (IFT) will present S. W. Hawking, Black holes and thermodynamics, Phys. Rev. D, vol. 13, no. 2, pp. 191–197, 1976. doi: 10.1103/PhysRevD.13.191

The concept of entropy is examined with an eye toward gaining insight into the nature of black-hole thermodynamics. Definitions of entropy are given for ordinary classical and quantum-mechanical systems which lead to plausibility arguments for the ordinary laws of thermodynamics. The treatment of entropy for a classical system is in the spirit of the information-theory viewpoint, but by explicitly incorporating the coarse-grained observable into the definition of entropy, we eliminate any nonobjective features. The definition of entropy for a quantum-mechanical system is new, but directly parallels the classical treatment. We then apply these ideas to a self-gravitating quantum system which contains a black hole. Under some assumptions—which, although nontrivial, are by no means exotic—about the nature of such a system, it is seen that the same plausibility arguments which lead to the ordinary laws of thermodynamics for ordinary systems now lead to the laws of black-hole mechanics, including the generalised second law of thermodynamics. Thus, it appears perfectly plausible that black-hole thermodynamics is nothing more than ordinary thermodynamics applied to a self-gravitating quantum system.