Skip to main content
Log in

Classical and quantum limitations on energy consumption in computation

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript


Fundamental limitations on the energy dissipated during one elementary logical operation are discussed. A model of a real physical device (parametric quantron) based on the Josephson effect in superconductors is used throughout the discussion. This device is shown to be physically reversible, and moreover it can serve as the clementary cell of a logically reversible computer, both these properties being necessary to achieve the fundamental limits of energy dissipation. These limits due to classical and quantum statistics are shown to lie well below the earlier estimates,k B T and ηϑ, respectively.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others


  • Bennett, C. H. (1973).IBM Journal of Research and Development,17, 525.

    Google Scholar 

  • Bledsoe, W. W. (1961).IRE Transactions,EC-10, 530.

    Google Scholar 

  • Bohm, D. (1951).Quantum Theory, Prentice Hall, Englewood-Cliffs, New Jersey, Chap. 22.

    Google Scholar 

  • Brillouin, L. (1956).Science and Information Theory, Academic Press, New York Chaps. 14 and 18.

    Google Scholar 

  • Keyes, R. W. (1975).Proceedings of IEEE,63, 740.

    Google Scholar 

  • Keyes, R. W. (1981).Proceedings of IEEE,69, 267.

    Google Scholar 

  • Keyes, R. W., and Landauer, R. W. (1970).IBM Journal of Research and Development,14, 152.

    Google Scholar 

  • Kulik, I. O., and Yanson, I. K. (1970).Josephson Effect in Superconducting Tunnel Structures, Kefer Press, Jerusalem Chapters 1–3.

    Google Scholar 

  • Landau, L. D., and Lifshitz, E. M. (1958).Quantum Mechanics, Pergamon, London, Chaps. 3 and 7.

    Google Scholar 

  • Landauer, R. W. (1961).IBM Journal of Research and Development.,5, 183.

    Google Scholar 

  • Landauer, R. W. (1976).Berichte der Bunsengesellschaft, Phys.-Chem.,80, 1048.

    Google Scholar 

  • Likharev, K. K. (1975).Radio Engineering and Electronic Physics.,19, 109.

    Google Scholar 

  • Likharev, K. K. (1977).IEEE Transactions. MAG-15, 240.

    Google Scholar 

  • Likharev, K. K. (1981).Macroscopic Quantum Tunneling and Dissipation in Josephson Junctions and SQUIDs. Submitted to the 16th Int. Conf. on Low Temperature Physics, Los Angeles, California, August 1981.

  • Likharev, K. K., and Ulrich, B. T. (1978).Systems with Josephson Junctions. Basic Theory, Moscow Univ. Publ., Moscow (in Russian), Chaps. 1 and 2.

    Google Scholar 

  • Louisell, W. (1973).Quantum Statistical Properties of Radiation. Wiley, New York, Chaps. 6, 7.

    Google Scholar 

  • Marko, H. (1965).Kybernetik,2, 274.

    Google Scholar 

  • Solimar, L. (1974).Superconducting Tunneling and Applications, Chapman and Hall, London, Chaps. 12–14.

    Google Scholar 

  • von Neumann, J. (1966).Theory of Self-Reproducing Automata, Univ. Illinois Press, Urbana, p. 66.

    Google Scholar 

  • Vorontsov, Yu. I. (1980).Soviet Physics—Doklady,251, 1110.

    Google Scholar 

Download references

Author information

Authors and Affiliations


Rights and permissions

Reprints and permissions

About this article

Cite this article

Likharev, K.K. Classical and quantum limitations on energy consumption in computation. Int J Theor Phys 21, 311–326 (1982).

Download citation

  • Received:

  • Issue Date:

  • DOI: