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Comparing black hole thermodynamics with the axiomatic formulation ofthermodynamics for laboratory systems, it is found that some basic assumptions(required by experimental facts) in laboratory thermodynamics do not hold forblack hole thermodynamics. Hence, at present, it is not obvious whether blackhole thermodynamics retains some crucial theorems of laboratory thermodynamics(e.g. Carnot's theorem, increase of entropy by arbitrary adiabatic process, anduniqueness of entropy) whose proofs use the basic assumptions which do not holdfor black holes. This paper aims to clarify such nontriviality in black holethermodynamics, and propose a suitable set of basic assumptions in black holethermodynamics, which are regarded as the rigorous foundation of black holethermodynamics as phenomenology.

Nontriviality in Black Hole Thermodynamics: towards physically and mathematically rigorous foundation as phenomenology