  Since the 1970's it has been known that black hole (and other) horizons are
truly thermodynamic in nature. More generally, surfaces which are not horizons
have also been conjectured to behave thermodynamically. Initially, for surfaces
microscopically expanded from a horizon to so-called stretched horizons, and
more recently, for more general ordinary surfaces in the emergent gravity
program. To test these conjectures we ask whether such surfaces satisfy an
analogue to the first law of thermodynamics (as do horizons). For static
asymptotically-flat spacetimes we find that such a first law holds on horizons.
We rigorously prove that this law remains an excellent approximation for
stretched horizons, but perhaps counter-intuitively this result illustrates the
insufficiency of the laws of black hole mechanics alone from implying truly
thermodynamic behavior. For surfaces away from horizons in the emergent gravity
program the first law fails (with the exception of fully spherically symmetric
scenarios) thus undermining the key thermodynamic assumption of this program.
