Abstract
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.
Similar content being viewed by others
References
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).
H. S. Leff and A. F. Rex, editors,Maxwell's Demon: Entropy, Information, Computing (Princeton University Press, Princeton, New Jersey, 1990).
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.
R. Landauer,Phys. Today 23 (May 1991).
L. Brillouin,Science and Information Theory, 2nd edn. (Academic Press, New York, 1962).
C. H. Bennett,Int. J. Theor. Phys. 21, 905 (1982).
C. H. Bennett,Sci. Am. 257, 108 (November 1987).
D. H. Wolpert,Phys. Today 98 (March 1992).
R. C. Tolman.The Principles of Statistical Mechanics (Dover, New York, 1938).
L. D. Landau and E. M. Lifshitz,Statistical Physics, 3rd edn. Vol. 5 ofCourse of Theoretical Physics (Pergamon, Oxford, 1980).
R. Landauer,IBM J. Res. Dee. 5, 183 (1961).
C. H. Bennett,Sci. Am. 258, 8 (February 1988).
R. Landauer, Information is physical, inWorkshop on Physics and Computation PhysComp '92 (IEEE Computer Society Press, Los Alamitos, California, 1993), pp. 1–4.
R. P. Feynman, R. B. Leighton, and M. Sands,The Feynman Lectures on Physics (Addison-Wesley, Reading, Massachusetts, 1965).
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.
H. S. Leff and A. F. Rex,Am. J. Phys. 62, 994 (1994).
W. H. Zurek and J. P. Paz,Phys. Rev. Lett. 72, 2508 (1994).
R. Landauer,Phys. Scr. 35, 88 (1987).
C. H. Bennett and R. Landauer,Sci. Am. 48 (July 1985).
D. H. Wolpert,Int. J. Theor. Phys. 31, 743 (1992).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Fahn, P.N. Maxwell's demon and the entropy cost of information. Found Phys 26, 71–93 (1996). https://doi.org/10.1007/BF02058888
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02058888