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It seems to be a common understanding at present that, once event horizonsare in thermal equilibrium, the entropy-area law holds inevitably. However norigorous verification is given to such a very strong universality of the law inmulti-horizon spacetimes. Then, based on thermodynamically consistent andrigorous discussion, this paper suggests an evidence of breakdown ofentropy-area law for horizons in Schwarzschild-de Sitter spacetime, in whichthe temperatures of the horizons are different. The outline is as follows: Weconstruct carefully "two thermal equilibrium systems" individually for blackhole event horizon (BEH) and cosmological event horizon (CEH), for which theEuclidean action method is applicable. The integration constant (subtractionterm) in Euclidean action is determined with referring to Schwarzschild and deSitter canonical ensembles. The free energies of the two thermal systems arefunctions of three independent state variables, and we find a similarity of ourtwo thermal systems with the magnetized gas in laboratory, which gives us aphysical understanding of the necessity of three independent state variables.Then, via the thermodynamic consistency with three independent state variables,the breakdown of entropy-area law for CEH is suggested. The validity of the lawfor BEH can not be judged, but we clarify the key issue for BEH's entropy.Finally we make comments which may suggest the breakdown of entropy-area lawfor BEH, and also propose two discussions; one of them is on the quantumstatistics of underlying quantum gravity, and another is on the SdS black holeevaporation from the point of view of non-equilibrium thermodynamics.

To what extent is the entropy-area law universal ? -- Multi-horizon and multi-temperature spacetime may break the entropy-area law --