Phys. Rev. D 23, 287–298 (1981)

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

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Jacob D. Bekenstein^*
Institute for Theoretical Physics, University of California, Santa Barbara, California 93106

Received 7 July 1980; revised 25 August 1980; published in the issue dated 15 January 1981

We present evidence for the existence of a universal upper bound of magnitude 2πR/ℏc 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.

URL:

http://link.aps.org/doi/10.1103/PhysRevD.23.287

DOI:

10.1103/PhysRevD.23.287

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^*On sabbatical leave from Physics Department, Ben Gurion University, Beer Sheva, Israel.

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Phys. Rev. D 23, 287–298 (1981)

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

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