Black hole thermodynamics and information loss in two dimensions
  Black hole evaporation is investigated in a (1+1)-dimensional model of quantum gravity. Quantum corrections to the black hole entropy are computed, and the fine-grained entropy of the Hawking radiation is studied. A generalized second law of thermodynamics is formulated, and shown to be valid under suitable conditions. It is also shown that, in this model, a black hole can consume an arbitrarily large amount of information. 
Thomas M. Fiola, John Preskill, Andrew Strominger, and Sandip P.   Trivedi