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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Bekenstein bound ： ウィキペディア英語版 Bekenstein bound __NOTOC__ In physics, the Bekenstein bound is an upper limit on the entropy ''S'', or information ''I'', that can be contained within a given finite region of space which has a finite amount of energy—or conversely, the maximum amount of information required to perfectly describe a given physical system down to the quantum level.〔Jacob D. Bekenstein, ("Universal upper bound on the entropy-to-energy ratio for bounded systems" ), ''Physical Review D'', Vol. 23, No. 2, (January 15, 1981), pp. 287-298, , . (Mirror link ).〕 It implies that the information of a physical system, or the information necessary to perfectly describe that system, must be finite if the region of space and the energy is finite. In computer science, this implies that there is a maximum information-processing rate (Bremermann's limit) for a physical system that has a finite size and energy, and that a Turing machine with finite physical dimensions and unbounded memory is not physically possible. ==Equations== The universal form of the bound was originally found by Jacob Bekenstein as the inequality〔〔〔 :$S\; \backslash leq\; \backslash frac$ where ''S'' is the entropy, ''k'' is Boltzmann's constant, ''R'' is the radius of a sphere that can enclose the given system, ''E'' is the total mass–energy including any rest masses, ''ħ'' is the reduced Planck constant, and ''c'' is the speed of light. Note that while gravity plays a significant role in its enforcement, the expression for the bound does not contain Newton's Constant ''G''. In informational terms, the bound is given by :$I\; \backslash leq\; \backslash frac$ where ''I'' is the information expressed in number of bits contained in the quantum states in the sphere. The ln 2 factor comes from defining the information as the logarithm to the base 2 of the number of quantum states.〔Frank J. Tipler, ("The structure of the world from pure numbers" ), ''Reports on Progress in Physics'', Vol. 68, No. 4 (April 2005), pp. 897-964, , , p. 902. (Mirror link ). Also released as ("Feynman-Weinberg Quantum Gravity and the Extended Standard Model as a Theory of Everything" ), , April 24, 2007, p. 8.〕 Using mass energy equivalence, the informational limit may be reformulated as :$I\; \backslash leq\; \backslash frac\; \backslash approx\; 2.577\backslash times\; 10^\; m\; R$ where $m$ is the mass of the system in kilograms, and the radius $R$ is expressed in meters. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Bekenstein bound」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.