Limita Bekenstein: Diferență între versiuni

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Versiunea de la 30 aprilie 2012 19:35

În fizică, limita Bekenstein este limita superioară a entropiei S (ori a informației I) care poate fi conținută într-o regiune finită dată a spațiului care are o cantitate finită de energie; sau invers, valoarea maximă a informațiilor necesare pentru a descrie perfect un anumit sistem fizic până la nivelul său cuantic.^[1] Acest lucru implică faptul că informația unui sistem fizic, sau informația necesară pentru a descrie perfect acest sistem, trebuie să fie finită dacă regiunea de spațiu și energia sunt finite. În informatică, acest lucru implică faptul că există o rată maximă de procesare a informațiilor pentru un sistem fizic care are o dimensiune și energie finită, și că o mașină Turing cu memorie nelimitată este fizic imposibilă.

Ecuații

Forma universală a acestei limite a fost formulată de Jacob Bekenstein ca o inegalitate: ^[1]^[2]^[3]

S\leq {\frac {2\pi kRE}{\hbar c}}

în care S este entropia, k este constanta Boltzmann, R este raza sferei în care se află un sistem dat, E este echivalentul masă-energie care conține masele de repaus, ħ este constanta Planck redusă, iar c este viteza luminii. De remarcat că în timp ce gravitația joacă un rol important în ecuație, expresia limitei nu conține constanta lui Newton G.

În termeni informatici, limita este dată de

I\leq {\frac {2\pi RE}{\hbar c\ln 2}}

în care I este informația 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.^[4] The right-hand side of the foregoing relation is approximately equal to 2.5769087×10⁴³×(mass in kilograms)×(radius in meters).

Bibliografie suplimentară

J. D. Bekenstein, "Black Holes and the Second Law", Lettere al Nuovo Cimento, Vol. 4, No 15 (August 12, 1972), pp. 737-740, doi:10.1007/BF02757029, Bibcode: 1972NCimL...4..737B. Mirror link.
Jacob D. Bekenstein, "Black Holes and Entropy", Physical Review D, Vol. 7, No. 8 (April 15, 1973), pp. 2333-2346, doi:10.1103/PhysRevD.7.2333, Bibcode: 1973PhRvD...7.2333B. Mirror link.
Jacob D. Bekenstein, "Generalized second law of thermodynamics in black-hole physics", Physical Review D, Vol. 9, No. 12 (June 15, 1974), pp. 3292-3300, doi:10.1103/PhysRevD.9.3292, Bibcode: 1974PhRvD...9.3292B. Mirror link.
Jacob D. Bekenstein, "Statistical black-hole thermodynamics", Physical Review D, Vol. 12, No. 10 (November 15, 1975), pp. 3077-3085, doi:10.1103/PhysRevD.12.3077, Bibcode: 1975PhRvD..12.3077B. Mirror link.
Jacob D. Bekenstein, "Black-hole thermodynamics", Physics Today, Vol. 33, Issue 1 (January 1980), pp. 24-31, doi:10.1063/1.2913906, Bibcode: 1980PhT....33a..24B. Mirror link.
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, doi:10.1103/PhysRevD.23.287, Bibcode: 1981PhRvD..23..287B. Mirror link.
Jacob D. Bekenstein, "Energy Cost of Information Transfer", Physical Review Letters, Vol. 46, No. 10 (March 9, 1981), pp. 623-626, doi:10.1103/PhysRevLett.46.623, Bibcode: 1981PhRvL..46..623B. Mirror link.
Jacob D. Bekenstein, "Specific entropy and the sign of the energy", Physical Review D, Vol. 26, No. 4 (August 15, 1982), pp. 950-953, doi:10.1103/PhysRevD.26.950, Bibcode: 1982PhRvD..26..950B.
Jacob D. Bekenstein, "Entropy content and information flow in systems with limited energy", Physical Review D, Vol. 30, No. 8, (October 15, 1984), pp. 1669-1679, doi:10.1103/PhysRevD.30.1669, Bibcode: 1984PhRvD..30.1669B. Mirror link.
Jacob D. Bekenstein, "Communication and energy", Physical Review A, Vol. 37, Issue 9 (May 1988), pp. 3437-3449, doi:10.1103/PhysRevA.37.3437, Bibcode: 1988PhRvA..37.3437B. Mirror link.
Marcelo Schiffer and Jacob D. Bekenstein, "Proof of the quantum bound on specific entropy for free fields", Physical Review D, Vol. 39, Issue 4 (February 15, 1989), pp. 1109-1115, doi:10.1103/PhysRevD.39.1109 PMID 9959747, Bibcode: 1989PhRvD..39.1109S.
Jacob D. Bekenstein, "Is the Cosmological Singularity Thermodynamically Possible?", International Journal of Theoretical Physics, Vol. 28, Issue 9 (September 1989), pp. 967-981, doi:10.1007/BF00670342, Bibcode: 1989IJTP...28..967B.
Jacob D. Bekenstein, "Entropy bounds and black hole remnants", Physical Review D, Vol. 49, Issue 4 (February 15, 1994), pp. 1912-1921, doi:10.1103/PhysRevD.49.1912, Bibcode: 1994PhRvD..49.1912B. Also at arΧiv:gr-qc/9307035, July 25, 1993.
Oleg B. Zaslavskii, "Generalized second law and the Bekenstein entropy bound in Gedankenexperiments with black holes", Classical and Quantum Gravity, Vol. 13, No. 1 (January 1996), pp. L7-L11, doi:10.1088/0264-9381/13/1/002, Bibcode: 1996CQGra..13L...7Z. See also O. B. Zaslavskii, "Corrigendum to 'Generalized second law and the Bekenstein entropy bound in Gedankenexperiments with black holes'", Classical and Quantum Gravity, Vol. 13, No. 9 (September 1996), p. 2607, doi:10.1088/0264-9381/13/9/024, Bibcode: 1996CQGra..13.2607Z.
Jacob D. Bekenstein, "Non-Archimedean character of quantum buoyancy and the generalized second law of thermodynamics", Physical Review D, Vol. 60, Issue 12 (December 15, 1999), Art. No. 124010, 9 pages, doi:10.1103/PhysRevD.60.124010, Bibcode: 1999PhRvD..60l4010B. Also at arΧiv:gr-qc/9906058, June 16, 1999.

Note

^ ^a ^b 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, doi:10.1103/PhysRevD.23.287, Bibcode: 1981PhRvD..23..287B. Mirror link.
^ Jacob D. Bekenstein, "How Does the Entropy/Information Bound Work?", Foundations of Physics, Vol. 35, No. 11 (November 2005), pp. 1805-1823, doi:10.1007/s10701-005-7350-7, Bibcode: 2005FoPh...35.1805B. Also at arΧiv:quant-ph/0404042, April 7, 2004.
^ Jacob D. Bekenstein, "Bekenstein bound", Scholarpedia, Vol. 3, No. 10 (October 31, 2008), p. 7374, doi:10.4249/scholarpedia.7374.
^ 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, doi:10.1088/0034-4885/68/4/R04, Bibcode: 2005RPPh...68..897T, p. 902. Mirror link. Also released as "Feynman-Weinberg Quantum Gravity and the Extended Standard Model as a Theory of Everything", arΧiv:0704.3276, April 24, 2007, p. 8.

Legături externe

Jacob D. Bekenstein, "Bekenstein bound", Scholarpedia, Vol. 3, No. 10 (2008), p. 7374, doi:10.4249/scholarpedia.7374.
Jacob D. Bekenstein, "Bekenstein-Hawking entropy", Scholarpedia, Vol. 3, No. 10 (2008), p. 7375, doi:10.4249/scholarpedia.7375.
Jacob D. Bekenstein's website at the Racah Institute of Physics, Hebrew University of Jerusalem, which contains a number of articles on the Bekenstein bound.

[Bekenstein1981-1-1] 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, doi:10.1103/PhysRevD.23.287, Bibcode: 1981PhRvD..23..287B. Mirror link.

[Bekenstein2005-2] Jacob D. Bekenstein, "How Does the Entropy/Information Bound Work?", Foundations of Physics, Vol. 35, No. 11 (November 2005), pp. 1805-1823, doi:10.1007/s10701-005-7350-7, Bibcode: 2005FoPh...35.1805B. Also at arΧiv:quant-ph/0404042, April 7, 2004.

[Bekenstein2008-3] Jacob D. Bekenstein, "Bekenstein bound", Scholarpedia, Vol. 3, No. 10 (October 31, 2008), p. 7374, doi:10.4249/scholarpedia.7374.

[Tipler2005b-4] 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, doi:10.1088/0034-4885/68/4/R04, Bibcode: 2005RPPh...68..897T, p. 902. Mirror link. Also released as "Feynman-Weinberg Quantum Gravity and the Extended Standard Model as a Theory of Everything", arΧiv:0704.3276, April 24, 2007, p. 8.

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