  The static patch of de Sitter spacetime and the Rindler wedge of Minkowski
spacetime are causal diamonds admitting a true Killing field, and they behave
as thermodynamic equilibrium states under gravitational perturbations. We
explore the extension of this gravitational thermodynamics to all causal
diamonds in maximally symmetric spacetimes. Although such diamonds generally
admit only a conformal Killing vector, that seems in all respects to be
sufficient. We establish a Smarr formula for such diamonds and a "first law"
for variations to nearby solutions. The latter relates the variations of the
bounding area, spatial volume of the maximal slice, cosmological constant, and
matter Hamiltonian. The total Hamiltonian is the generator of evolution along
the conformal Killing vector that preserves the diamond. To interpret the first
law as a thermodynamic relation, it appears necessary to attribute a negative
temperature to the diamond, as has been previously suggested for the special
case of the static patch of de Sitter spacetime. With quantum corrections
included, for small diamonds we recover the "entanglement equilibrium" result
that the generalized entropy is stationary at the maximally symmetric vacuum at
fixed volume, and we reformulate this as the stationarity of free conformal
energy with the volume not fixed.
