  In theories of semi-classical quantum gravity where the cosmological constant
is considered a thermodynamic variable, the gravitational mass of a black hole
has been shown to correspond to the enthalpy of the thermodynamic system,
rather than the energy. We propose that this should be extended to all
spacetime solutions, and consider the meaning of this extension of
gravitational thermodynamics for the Taub-NUT and Taub-Bolt geometries in four
dimensional locally anti-de Sitter spacetime. We present formulae for their
thermodynamic volumes. Surprisingly, Taub-NUT has negative volume, for which
there is a natural dynamical explanation in terms of the process of formation
of the spacetime. A special case corresponds to pure AdS_4 with an S^3 slicing.
The same dynamical setting can explain the negative entropy known to exist for
these solutions for a range of parameters.
