  It may be a common understanding at present that, once event horizons are in
thermal equilibrium, the entropy-area law holds inevitably. However, no
rigorous verification is given to such a very strong universality of the law in
multi-horizon spacetimes. In this article, based on thermodynamically
consistent and rigorous discussion, we investigate thermodynamics of
Schwarzschild-deSitter spacetime in which the temperatures of two horizons are
different. We recognize that three independent state variables exist in
thermodynamics of the horizons. One of the three variables represents the
effect of "external gravity" acting on one horizon due to another one. Then we
find that thermodynamic formalism with three independent variables suggests the
breakdown of entropy-area law, and clarifies the necessary and sufficient
condition for the entropy-area law. As a by-product, the special role of
cosmological constant in thermodynamics of horizons is also revealed.
