Entropy, observability and the generalised second law of thermodynamics

Abstract

We derive the Generalised Second Law (GSL) of Thermodynamics, pertaining to processes in which observable systems exchange matter with unobservable regions of space-time, i.e. Black Holes. Our derivation of this Law is based exclusively on a treatment of observable quanties, and thus avoids Bekenstein's [1] assumption that a Black Hole has an entropy, proportional to its surface area. In fact, we demonstrate that it follows from simple statistical thermodynamic and general relativistic properties of the open system comprising the matter and fields in the region outside a Black Hole that, in suitable units, the sum of the entropy of that region and the surface area of the Hole never decreases. This is formally equivalent to the GSL of Ref. [1], though in our scheme, the area term represents mechanical work done by the exterior system, not entropy. Since our derivation of the GSL depends on the Hawking thermalisation effect [2], we devote the Appendix to a sketch of our earlier model-independent treatment [3] of quantum fields on manifolds, which covers this effect.