  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.
