Universal upper bound on the entropy-to-energy ratio for bounded systems

Journal Article · Thu Jan 15 00:00:00 EST 1981 · Phys. Rev., D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.23.287· OSTI ID:6978647

Bekenstein, J D

We present evidence for the existence of a universal upper bound of magnitude 2..pi..R/hc to the entropy-to-energy ratio S/E of an arbitrary system of effective radius R. For systems with negligible self-gravity, 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.

• Research Organization: Institute for Theoretical Physics, University of California, Santa Barbara, California 93106
• OSTI ID: 6978647
• Journal Information: Phys. Rev., D; (United States), Vol. 23:2
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BLACK HOLES
ENTROPY
GENERAL RELATIVITY THEORY
LIMITING VALUES
QUANTUM FIELD THEORY
QUANTUM GRAVITY
STATISTICAL MODELS
UNIVERSE
FIELD THEORIES
MATHEMATICAL MODELS
PHYSICAL PROPERTIES
THERMODYNAMIC PROPERTIES
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