  Statistical mechanics explains thermodynamics in terms of (quantum) mechanics
by equating the entropy of a microstate of a closed system with the logarithm
of the number of microstates in the macrostate to which it belongs, but the
question `what is a macrostate?' has never been answered except in a vague,
subjective, way. However Hawking's discovery of black hole evaporation led to a
formula for black hole entropy with no subjective element. In this letter, we
argue from this result, together with the assumption that `black hole
thermodynamics is just ordinary thermodynamics applied to black holes', that a
macrostate for a general (quantum gravitational) closed system is an
equivalence class of matter-gravity microstates with the same expectation
values for the matter degrees of freedom alone. Not only does this finally
answer the question `what is entropy?', but it also predicts the equality of
the thermodynamic entropy of a black hole with the matter and the gravity
entropy-like quantities derived from the Euclidean path integral. Furthermore
it gives us a clear glimpse of an ultimate synthesis of quantum theory and
gravity in which we see that (a) gravity acts as a universal environment, thus
predicting that, if the initial state of the universe is unentangled, its
entropy must go on increasing forever, (b) the gravitational field has degrees
of freedom, but no observables, thus enabling gravity to perform the trick of
providing an objective continual process of decoherence. All the above rests on
the validity of unitarity. The `information-loss puzzle' had raised doubts
about that. But we suggest a resolution for this puzzle.
