  We show by explicit computations that the product of all the horizon areas is
independent of the mass, regardless of the topology of the horizons. The
universal character of this relation holds for all known five dimensional
asymptotically flat black rings, and for black strings. This gives further
evidence for the crucial role that the thermodynamic properties at each horizon
play in understanding the entropy at the microscopic level. To this end we
propose a "first law" for the inner Cauchy horizons of black holes. The
validity of this formula, which seems to be universal, was explicitly checked
in all cases.
