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Thermodynamic cost of computation, algorithmic complexity and the information metric

Nature volume 341, pages 119–124 (1989)Cite this article

Abstract

Algorithmic complexity is a measure of randomness. In contrast to Shannon's entropy it is defined without a recourse to probabilities; for a binary string s it is given by the size, in bits, of the shortest computer program with the output s. I show that algorithmic complexity sets limits on the thermodynamic cost of computations, casts a new light on the limitations of Maxwell's demon and can be used to define distance between binary strings.

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References

  1. Bennett, C. H. IBM J. Res. Dev. 17, 525–532 (1973).

    Article  Google Scholar 

  2. Bennett, C. H. Int. J. theor. Phys. 21, 305–340 (1982).

    Article  Google Scholar 

  3. Bennett, C. H. IBM J. Res. Dev. 32, 16–25 (1988).

    Article  Google Scholar 

  4. Landauer, R. IBM J. Res. Dev. 3, 113–131 (1961).

    Google Scholar 

  5. Landauer, R. in Signal Processing (ed. Haykin, S.) 18–47 (Prentice-Hall, New York, 1989).

    Google Scholar 

  6. Bennett, C. H. & Landauer, R. Scient. Am. 253, 48–56 (1985).

    Article  Google Scholar 

  7. Fredkin, E. & Toffoli, T. Int. J. theor. Phys. 21, 219–253 (1982).

    Article  Google Scholar 

  8. Zurek, W. H. Phys. Rev. Lett. 53, 391–394 (1984).

    Article  ADS  Google Scholar 

  9. Bennett, C. H. SIAM J. Comput. 18, 766–776 (1989).

    Article  MathSciNet  Google Scholar 

  10. Zurek, W. H. Phys. Rev. A (in the press).

  11. Solomonoff, R. J. Inf. Control 7, 1–22 (1964).

    Article  MathSciNet  Google Scholar 

  12. Kolmogorov, A. N. Inf. Transmission 1, 3–11 (1965).

    Google Scholar 

  13. Kolmogorov, A. N. IEEE Trans Inf. Theory 14, 662–664 (1968).

    Article  Google Scholar 

  14. Kolmogorov, A. N. Usp. mat. Nauk 25, 602–613 (1970).

    Google Scholar 

  15. Chaitin, G. J. J. Ass. Comput. Mach. 13, 547–569 (1966).

    Article  Google Scholar 

  16. Chaitin, G. J. Scient. Am. 232(5), 47–52 (1975).

    Article  Google Scholar 

  17. Chaitin, G. J. IBM J. Res. Dev. 21, 350–359 (1977).

    Article  Google Scholar 

  18. Chaitin, G. J. Algorithmic Information Theory (Cambridge University Press, 1987).

    Book  Google Scholar 

  19. Gacs, P. Soviet Math. Dokl. 15, 1477–1478 (1974).

    Google Scholar 

  20. Chaitin, G. J. J. Ass. Comput. Mach. 22, 245–268 (1975).

    Article  Google Scholar 

  21. Levin, L. A. Soviet Math. Dokl 17, 522–526 (1976).

    Google Scholar 

  22. Stewart, I. Nature 332, 115–116 (1988).

    Article  ADS  Google Scholar 

  23. Davies, M. Computability and Undecidability (McGraw-Hill, 1958).

    Google Scholar 

  24. Hofstadter, D. Gödel, Escher, Bach (Random House, New York, 1979).

    MATH  Google Scholar 

  25. Turing, A. M. Proc. Lond. math Soc. 42, 230–265 (1936).

    Google Scholar 

  26. Press, W. H., Flannery, B. P., Teukolsky, S. A. & Vetterling, W. T. Numerical Recipes Section 13.6 (Cambridge University Press, 1987).

    MATH  Google Scholar 

  27. Bennett, C. H. Scient. Am. 255(11), 108–117 (1987).

    Article  Google Scholar 

  28. Szilard, L. Z. Phys. 53, 840–856 (1929).

    Article  ADS  CAS  Google Scholar 

  29. Zurek, W. H. in Frontiers of Nonequilibrium Statistical Mechanics, (eds More, T. G. & Scully, M. O.) 151–161 (Plenum, New York, 1986).

    Book  Google Scholar 

  30. Shannon, C. E. & Weaver, W. The Mathematical Theory of Communication (University of Illinois Press, 1949).

    MATH  Google Scholar 

  31. Hamming, R. W. Coding and Information Theory (Prentice-Hall, Englewood Cliffs, 1987).

    MATH  Google Scholar 

  32. Lloyd, S. & Pagels, H. Ann. Phys. 188, 186–213 (1988).

    Article  ADS  Google Scholar 

  33. (ed. Zurek, W. H.) Proc. Santa Fe Inst. Workshop “Complexity, Entropy, and Physics of Information” (Addison-Wesley, in the press).

  34. Smoluchowski, M. in Vortgäge über die Kinetische Theorie der matene und der Elektnzität (Teubner, Leipzig, 1914).

    Google Scholar 

Download references

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  1. Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico, 87545, USA

    W. H. Zurek

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Zurek, W. Thermodynamic cost of computation, algorithmic complexity and the information metric. Nature 341, 119–124 (1989). https://doi.org/10.1038/341119a0

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