Modern foundations for thermodynamics and the stringy limit of black   hole equilibria
  We recall the existing string theory understanding of black hole entropy and argue it is incomplete but we put forward a modified version, based on the author's 'matter-gravity entanglement hypothesis', which, we claim, gives a more satisfactory understanding and also a resolution to the Information Loss Puzzle. This hypothesis pictures a black hole equilibrium as an, overall pure, state, with given energy, consisting of a black hole with its (mostly matter) atmosphere in a box and identifies the black hole's entropy with the pure state's matter-gravity entanglement entropy. We assume this equilibrium goes over, at weak string-coupling, to a pure state with similar energy consisting of a long string with a stringy atmosphere and that the matter-gravity entanglement entropy goes over to the entanglement entropy between (approximately) the long string and the stringy atmosphere. We also recall recent work (in a non-gravitational context) towards modern foundations for thermodynamics, where, in place of a total microcanonical ensemble, one assumes that a total system, consisting of a small (sub)system and an energy bath, is in a (random) pure state with energy in a given narrow range and shows that the small subsystem will then find itself in a thermal state. We present a new set of formulae, obtained in a companion paper, which generalize the setting of that work to cases where the system and energy bath are of comparable size. We apply these formulae to a model for our string equilibrium where the densities of states of the long string (replacing our energy bath) and stringy atmosphere (replacing our system) both grow exponentially. We find, for our picture of black hole equilibrium, a temperature of the order of the Hawking temperature and an entropy of the order of the Hawking entropy thus adding to the evidence for the viablity of our matter-gravity entanglement hypothesis. 
Bernard S. Kay (York)
gr-qc cond-mat.stat-mech hep-th quant-ph