Title: The Generalized Second Law; Part 2 of 2-part series titled "A Primer on Black Hole Entropy and the Generalized Second Law" (See part 1 here:    • BHI Foundations Seminar (02/05/24) "B...  )

Abstract: The Second Law in ordinary thermodynamics, properly speaking, takes the form of the Clausius or the Kelvin Postulate applied to ordinary matter, the two usually argued to be physically equivalent, even though the principle of entropy non-decrease is more often granted the honorific. It is now widely held that, in the framework of semi-classical gravity, we must generalize the principle of entropy non-decrease to include contributions from black hole entropy (and possibly contributions from other purely gravitational systems, such as cosmological horizons, but I will not treat that in this talk). That new statement is the Generalized Second Law (GSL): the total sum of the entropy of ordinary matter and the entropy of black holes does not decrease. In this talk, I give an exposition and analysis of a number of conceptual and foundational problems attending the assertion of the GSL. I introduce and briefly discuss, inter alia, questions about: what types of entropy are appropriate for its formulation; the cogency and status of various "proofs"; its relation to various classical and quantum energy conditions; its possible relation to holographic ideas; and the possibility of generalizing the Clausius and Kelvin Postulates in an analogous way. I conclude with speculative remarks on a few larger philosophical issues about how the assertion of the GSL may require modification to the plethora of established philosophical and foundational problems associated with the ordinary Second Law.

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