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Hawking radiation and Bekenstein--Hawking entropy are the two robustpredictions of a yet unknown quantum theory of gravity. Any theory which failsto reproduce these predictions is certainly incorrect. While several approacheslead to Bekenstein--Hawking entropy, they all lead to different sub-leadingcorrections. In this article, we ask a question that is relevant for anyapproach: Using simple techniques, can we know whether an approach containsquantum or semi-classical degrees of freedom? Using naive dimensional analysis,we show that the semi-classical black-hole entropy has the same dimensionaldependence as the gravity action. Among others, this provides a plausibleexplanation for the connection between Einstein's equations and thermodynamicequation of state, and that the quantum corrections should have a differentscaling behavior.

Corrections to Bekenstein-Hawking entropy --- Quantum or not-so quantum?