  We define, by an integral of geometric quantities over a spherical shell of
arbitrary radius, an invariant gravitational entropy. This definition relies on
defining a gravitational energy and pressure, and it reduces at the horizon of
both black branes and black holes to Wald's Noether charge entropy. We support
the thermodynamic interpretation of the proposed entropy by showing that, for
some cases, the field theory duals of the entropy, energy and pressure are the
same as the corresponding quantities in the field theory. In this context, the
Einstein equations are equivalent to the field theory thermodynamic relation
TdS=dE+PdV supplemented by an equation of state.
