Foundations of Physics

, Volume 26, Issue 1, pp 71–93 | Cite as

Maxwell's demon and the entropy cost of information

  • Paul N. Fahn


We present an analysis of Szilard's one-molecule Maxwell's demon, including a detailed entropy accounting, that suggests a general theory of the entropy cost of information. It is shown that the entropy of the demon increases during the expansion step, due to the decoupling of the molecule from the measurement information. It is also shown that there is an entropy symmetry between the measurement and erasure steps, whereby the two steps additivelv share a constant entropy change, but the proportion that occurs during each of the two steps is arbitrary. Therefore the measurement step may be accompanied by an entropy increase, a decrease, or no change at all, and likewise for the erasure step. Generalizing beyond the demon, decorrelation between a physical system and information about that system always causes an entropy increase in the joint system comprised of both the original system and the information. Decorrelation causes a net entropy increase in the universe unless, as in the Szilard demon, the information is used to decrease entropy elsewhere before the correlation is lost. Thus, information is thermodynamically costly precisely to the extent that it is not used to obtain work from the measured system.


Entropy General Theory Measured System Physical System Original System 
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  1. 1.
    L. Szilard,Behav. Sci. 9, 301 (1964), originally published as “Über die Entropieverminderung in einem thermodynamischen System bei Eingriffen intelligenter Wesen.”Z. Phys. 53, 840–856 (1929).Google Scholar
  2. 2.
    H. S. Leff and A. F. Rex, editors,Maxwell's Demon: Entropy, Information, Computing (Princeton University Press, Princeton, New Jersey, 1990).Google Scholar
  3. 3.
    R. C. Merkle. Towards practical reversible logic, inWorkshop on Physics and Computation—PhysComp '92 (IEEE Computer Society Press, Los Alamitos, California, 1993), pp. 227–228.Google Scholar
  4. 4.
    R. Landauer,Phys. Today 23 (May 1991).Google Scholar
  5. 5.
    L. Brillouin,Science and Information Theory, 2nd edn. (Academic Press, New York, 1962).Google Scholar
  6. 6.
    C. H. Bennett,Int. J. Theor. Phys. 21, 905 (1982).Google Scholar
  7. 7.
    C. H. Bennett,Sci. Am. 257, 108 (November 1987).Google Scholar
  8. 8.
    D. H. Wolpert,Phys. Today 98 (March 1992).Google Scholar
  9. 9.
    R. C. Tolman.The Principles of Statistical Mechanics (Dover, New York, 1938).Google Scholar
  10. 10.
    L. D. Landau and E. M. Lifshitz,Statistical Physics, 3rd edn. Vol. 5 ofCourse of Theoretical Physics (Pergamon, Oxford, 1980).Google Scholar
  11. 11.
    R. Landauer,IBM J. Res. Dee. 5, 183 (1961).Google Scholar
  12. 12.
    C. H. Bennett,Sci. Am. 258, 8 (February 1988).Google Scholar
  13. 13.
    R. Landauer, Information is physical, inWorkshop on Physics and Computation PhysComp '92 (IEEE Computer Society Press, Los Alamitos, California, 1993), pp. 1–4.Google Scholar
  14. 14.
    R. P. Feynman, R. B. Leighton, and M. Sands,The Feynman Lectures on Physics (Addison-Wesley, Reading, Massachusetts, 1965).Google Scholar
  15. 15.
    P. Gács, The Boltzmann entropy and randomness tests, inProceedings of the Workshop on Physics and Computation—PhysComp '94 (IEEE Computer Society Press, Los Alamitos, California, 1994), pp. 209–216.Google Scholar
  16. 16.
    H. S. Leff and A. F. Rex,Am. J. Phys. 62, 994 (1994).Google Scholar
  17. 17.
    W. H. Zurek and J. P. Paz,Phys. Rev. Lett. 72, 2508 (1994).Google Scholar
  18. 18.
    R. Landauer,Phys. Scr. 35, 88 (1987).Google Scholar
  19. 19.
    C. H. Bennett and R. Landauer,Sci. Am. 48 (July 1985).Google Scholar
  20. 20.
    D. H. Wolpert,Int. J. Theor. Phys. 31, 743 (1992).Google Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • Paul N. Fahn
    • 1
  1. 1.Information Systems LaboratoryStanford UniversityStanford

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