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Title: Thermodynamics of computation and information distance

Abstract

Applying the tools of algorithmic information theory, we compare several candidates for an asymptotically machine-independent. absolute measure of the informational or cognitive'' distance between discrete objects x and y. The maximum of the conditional Kolmogorov complexities max[l brace]K(y[vert bar]z) K(m[vert bar]y)[r brace], is shown to be optimal, in the sense of being minimal within an additive constant among semicomputable, symmetric, positive semidefinite functions of z and y satisfying a reasonable normalization condition and obeying the triangle intequality. The optimal metric, in turn, differs by at most an additive logarithmic term from the size of the smallest program for a universal reversible computer to transform x into y. This program functions in a 'catalytic'' capacity, being retained in the computer before, during, and after the computation. Similarly, the sum of the conditional complexities. K(y[vert bar]x) + K(x[vert bar]y), is shown to be equal within a logarithmic term to the minimal amount Of information flowing out and in during a reversible computation in which the program is not retained. Finally. using the physical theory of reversible computation, it is shown that the simple difference K(x) - K(y) is an appropriate (ie universal, antisymmetric, and transitive) measure of the amount of thermodynamic workmore » required to transform string x into string y by the most efficient process.« less

Authors:
; ; ; ;
Publication Date:
Research Org.:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE; USDOE, Washington, DC (United States)
OSTI Identifier:
6230593
Report Number(s):
LA-UR-93-1569; CONF-9306155-1
ON: DE93012730
DOE Contract Number:  
W-7405-ENG-36
Resource Type:
Conference
Resource Relation:
Conference: Symposium on theory of computation (STOC), San Diego, CA (United States), 7-11 Jun 1993
Country of Publication:
United States
Language:
English
Subject:
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMPUTER CALCULATIONS; ALGORITHMS; THERMODYNAMICS; ENTROPY; MATHEMATICAL MODELS; MEMORY MANAGEMENT; MATHEMATICAL LOGIC; PHYSICAL PROPERTIES; THERMODYNAMIC PROPERTIES; 990200* - Mathematics & Computers; 661300 - Other Aspects of Physical Science- (1992-)

Citation Formats

Bennett, C H, Gacs, P, Li, M, Vitanyi, P M.B., and Zurek, W H. Thermodynamics of computation and information distance. United States: N. p., 1993. Web. doi:10.1145/167088.167098.
Bennett, C H, Gacs, P, Li, M, Vitanyi, P M.B., & Zurek, W H. Thermodynamics of computation and information distance. United States. https://doi.org/10.1145/167088.167098
Bennett, C H, Gacs, P, Li, M, Vitanyi, P M.B., and Zurek, W H. 1993. "Thermodynamics of computation and information distance". United States. https://doi.org/10.1145/167088.167098. https://www.osti.gov/servlets/purl/6230593.
@article{osti_6230593,
title = {Thermodynamics of computation and information distance},
author = {Bennett, C H and Gacs, P and Li, M and Vitanyi, P M.B. and Zurek, W H},
abstractNote = {Applying the tools of algorithmic information theory, we compare several candidates for an asymptotically machine-independent. absolute measure of the informational or cognitive'' distance between discrete objects x and y. The maximum of the conditional Kolmogorov complexities max[l brace]K(y[vert bar]z) K(m[vert bar]y)[r brace], is shown to be optimal, in the sense of being minimal within an additive constant among semicomputable, symmetric, positive semidefinite functions of z and y satisfying a reasonable normalization condition and obeying the triangle intequality. The optimal metric, in turn, differs by at most an additive logarithmic term from the size of the smallest program for a universal reversible computer to transform x into y. This program functions in a 'catalytic'' capacity, being retained in the computer before, during, and after the computation. Similarly, the sum of the conditional complexities. K(y[vert bar]x) + K(x[vert bar]y), is shown to be equal within a logarithmic term to the minimal amount Of information flowing out and in during a reversible computation in which the program is not retained. Finally. using the physical theory of reversible computation, it is shown that the simple difference K(x) - K(y) is an appropriate (ie universal, antisymmetric, and transitive) measure of the amount of thermodynamic work required to transform string x into string y by the most efficient process.},
doi = {10.1145/167088.167098},
url = {https://www.osti.gov/biblio/6230593}, journal = {},
number = ,
volume = ,
place = {United States},
year = {Fri Mar 12 00:00:00 EST 1993},
month = {Fri Mar 12 00:00:00 EST 1993}
}

Conference:
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