  In arXiv:gr-qc/9504004 it was shown that the Einstein equation can be derived
as a local constitutive equation for an equilibrium spacetime thermodynamics.
More recently, in the attempt to extend the same approach to the case of $f(R)$
theories of gravity, it was found that a non-equilibrium setting is indeed
required in order to fully describe both this theory as well as classical GR
(arXiv:gr-qc/0602001). Here, elaborating on this point, we show that the
dissipative character leading to a non-equilibrium spacetime thermodynamics is
actually related -- both in GR as well as in $f(R)$ gravity -- to non-local
heat fluxes associated with the purely gravitational/internal degrees of
freedom of the theory. In particular, in the case of GR we show that the
internal entropy production term is identical to the so called tidal heating
term of Hartle-Hawking. Similarly, for the case of $f(R)$ gravity, we show that
dissipative effects can be associated with the generalization of this term plus
a scalar contribution whose presence is clearly justified within the
scalar-tensor representation of the theory. Finally, we show that the allowed
gravitational degrees of freedom can be fixed by the kinematics of the local
spacetime causal structure, through the specific Equivalence Principle
formulation. In this sense, the thermodynamical description seems to go beyond
Einstein's theory as an intrinsic property of gravitation.
