Entropy density of spacetime and thermodynamic interpretation of field
  equations of gravity in any diffeomorphism invariant theory
  I argue that the field equations of any theory of gravity which is
diffeomorphism invariant must be expressible as a thermodynamic identity,
TdS=dE around any event in the spacetime. This fact can be demonstrated
explicitly (and rather easily) if: (a) one accepts the Noether current of the
theory as providing the definition for local entropy density and (b) one is
allowed to introduce the local notions of a Rindler frame, acceleration horizon
and a Killing vector (related to translation in Rindler time) around any event.
It is conceptually incorrect - in general - to invert this argument and obtain
the field equations of the theory from the thermodynamic identity. I discuss
under what conditions this may be possible. Several subtleties related to these
arguments are described.
