Universal upper bound on the entropytoenergy ratio for bounded systems
Abstract
We present evidence for the existence of a universal upper bound of magnitude 2πRℏc to the entropytoenergy ratio SE of an arbitrary system of effective radius R. For systems with negligible selfgravity, the bound follows from application of the second law of thermodynamics to a gedanken experiment involving a black hole. Direct statistical arguments are also discussed. A microcanonical approach of Gibbons illustrates for simple systems (gravitating and not) the reason behind the bound, and the connection of R with the longest dimension of the system. A more general approach establishes the bound for a relativistic field system contained in a cavity of arbitrary shape, or in a closed universe. Black holes also comply with the bound; in fact they actually attain it. Thus, as long suspected, black holes have the maximum entropy for given mass and size which is allowed by quantum theory and general relativity.
 Publication:

Physical Review D
 Pub Date:
 January 1981
 DOI:
 10.1103/PhysRevD.23.287
 Bibcode:
 1981PhRvD..23..287B