  It is well known that, for a wide class of spacetimes with horizons, Einstein
equations near the horizon can be written as a thermodynamic identity. It is
also known that the Einstein tensor acquires a highly symmetric form near
static, as well as stationary, horizons. We show that, for generic static
spacetimes, this highly symmetric form of the Einstein tensor leads quite
naturally and generically to the interpretation of the near-horizon field
equations as a thermodynamic identity. We further extend this result to generic
static spacetimes in Lanczos-Lovelock gravity, and show that the near-horizon
field equations again represent a thermodynamic identity in all these models.
These results confirm the conjecture that this thermodynamic perspective of
gravity extends far beyond Einstein's theory.
