  We consider stationary, non-extremal black holes in 11-dimensional
supergravity having isometry group $\mathbb{R} \times U(1)^8$. We prove that
such a black hole is uniquely specified by its angular momenta, its electric
charges associated with the various 7-cycles in the manifold, together with
certain moduli and vector valued winding numbers characterizing the topological
nature of the spacetime and group action. We furthermore establish interesting,
non-trivial, relations between the thermodynamic quantities associated with the
black hole. These relations are shown to be a consequence of the hidden
$E_{8(+8)}$ symmetry in this sector of the solution space, and are distinct
from the usual "Smarr-type" formulas that can be derived from the first law of
black hole mechanics. We also derive the "physical process" version of this
first law applicable to a general stationary black hole spacetime without any
symmetry assumptions other than stationarity, allowing in particular arbitrary
horizon topologies. The work terms in the first law exhibit the topology of the
horizon via the intersection numbers between cycles of various dimensions.
