Black Hole Evaporation as a Nonequilibrium Process
  When a black hole evaporates, there arises a net energy flow from the black hole into its outside environment due to the Hawking radiation and the energy accretion onto black hole. Exactly speaking, due to the net energy flow, the black hole evaporation is a nonequilibrium process. To study details of evaporation process, nonequilibrium effects of the net energy flow should be taken into account. In this article we simplify the situation so that the Hawking radiation consists of non-self-interacting massless matter fields and also the energy accretion onto the black hole consists of the same fields. Then we find that the nonequilibrium nature of black hole evaporation is described by a nonequilibrium state of that field, and we formulate nonequilibrium thermodynamics of non-self-interacting massless fields. By applying it to black hole evaporation, followings are shown: (1) Nonequilibrium effects of the energy flow tends to accelerate the black hole evaporation, and, consequently, a specific nonequilibrium phenomenon of semi-classical black hole evaporation is suggested. Furthermore a suggestion about the end state of quantum size black hole evaporation is proposed in the context of information loss paradox. (2) Negative heat capacity of black hole is the physical essence of the generalized second law of black hole thermodynamics, and self-entropy production inside the matter around black hole is not necessary to ensure the generalized second law. Furthermore a lower bound for total entropy at the end of black hole evaporation is given. A relation of the lower bound with the so-called covariant entropy bound conjecture is interesting but left as an open issue. 
Hiromi Saida