  We consider the thermodynamics of rotating and charged asymptotically de
Sitter black holes. Using Hamiltonian perturbation theory techniques, we derive
three different first law relations including variations in the cosmological
constant, and associated Smarr formulas that are satisfied by such spacetimes.
Each first law introduces a different thermodynamic volume conjugate to the
cosmological constant. We examine the relation between these thermodynamic
volumes and associated geometric volumes in a number of examples, including
Kerr-dS black holes in all dimensions and Kerr-Newman-dS black holes in D=4. We
also show that the Chong-Cvetic-Lu-Pope solution of D=5 minimal supergravity,
analytically continued to positive cosmological constant, describes black hole
solutions of the Einstein-Chern-Simons theory and include such charged
asymptotically de Sitter black holes in our analysis. In all these examples we
find that the particular thermodynamic volume associated with the region
between the black hole and cosmological horizons is equal to the naive
geometric volume. Isoperimetric inequalities, which hold in the examples
considered, are formulated for the different thermodynamic volumes and
conjectured to remain valid for all asymptotically de Sitter black holes. In
particular, in all examples considered, we find that for fixed volume of the
observable universe, the entropy is increased by adding black holes. We
conjecture that this is true in general.
