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We recall the existing string theory understanding of black hole entropy andargue it is incomplete but we put forward a modified version, based on theauthor's 'matter-gravity entanglement hypothesis', which, we claim, gives amore satisfactory understanding and also a resolution to the Information LossPuzzle. 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 purestate's matter-gravity entanglement entropy. We assume this equilibrium goesover, at weak string-coupling, to a pure state with similar energy consistingof a long string with a stringy atmosphere and that the matter-gravityentanglement entropy goes over to the entanglement entropy between(approximately) the long string and the stringy atmosphere. We also recallrecent work (in a non-gravitational context) towards modern foundations forthermodynamics, where, in place of a total microcanonical ensemble, one assumesthat a total system, consisting of a small (sub)system and an energy bath, isin a (random) pure state with energy in a given narrow range and shows that thesmall subsystem will then find itself in a thermal state. We present a new setof formulae, obtained in a companion paper, which generalize the setting ofthat work to cases where the system and energy bath are of comparable size. Weapply these formulae to a model for our string equilibrium where the densitiesof states of the long string (replacing our energy bath) and stringy atmosphere(replacing our system) both grow exponentially. We find, for our picture ofblack hole equilibrium, a temperature of the order of the Hawking temperatureand an entropy of the order of the Hawking entropy thus adding to the evidencefor the viablity of our matter-gravity entanglement hypothesis.

Modern foundations for thermodynamics and the stringy limit of black hole equilibria