  The recent experimental realization of exotic matter states in isolated
quantum systems and the ensuing controversy about the existence of negative
absolute temperatures demand a careful analysis of the conceptual foundations
underlying microcanonical thermostatistics. Here, we provide a detailed
comparison of the most commonly considered microcanonical entropy definitions,
focussing specifically on whether they satisfy or violate the zeroth, first and
second law of thermodynamics. Our analysis shows that, for a broad class of
systems that includes all standard classical Hamiltonian systems, only the
Gibbs volume entropy fulfills all three laws simultaneously. To avoid
ambiguities, the discussion is restricted to exact results and analytically
tractable examples.
