Minimum energy requirements of information transfer and computing

  • Hans J. Bremermann


The minimum energy requirements of information transfer and computing are estimated from the time-energy uncertainty relation.


Field Theory Elementary Particle Quantum Field Theory Minimum Energy Energy Requirement 
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  1. Allcock, G. R. (1969). “The time of arrival in quantum mechanics. I. Formal considerations,Annals of Physics,53, 253–285; “II. The individual measurement,”Annals of Physics,53, pp. 286–310; III. “The measurement ensemble,”Annals of Physics.53, pp. 311–348.Google Scholar
  2. Arbib, M. A. (1964).Brains, Machines, and Mathematics. McGraw-Hill, New York.Google Scholar
  3. Ashby, R. (1967). “The place of the brain in the natural world,”Currents in Modern Biology,1, 95–104.Google Scholar
  4. Ashby, R. (1968). “Some consequences of Bremermann's limit for information processing systems” inCybernetic Problems in Bionics (Bionics Symposium. 1966), H. L. Oestreicher and D. R. Moore, eds. Gordon & Breach, New York.Google Scholar
  5. Ashby, R. (1973). Editorial,Behavioral Science,18, 2–6.Google Scholar
  6. Bekenstein J. D. (1973). “Black holes and entropy.”Physical Review D,7, 2333.Google Scholar
  7. Bekenstein, J. D. (1980). “Black-hole thermodynamics.”Physics Today, Jan., 24–31.Google Scholar
  8. Bekenstein, J. D. (1981a). “The energy cost of information transfer.”Physical Review Letters,46, 623.Google Scholar
  9. Bekenstein, J. D. (1981b) Universal Upper Bound to Entropy-to-Energy Ratio for Bounded Systems.Physical Review D,23, 287.Google Scholar
  10. Bennett, C. H. (1973). “Logical reversibility of computation.”IBM Journal of Research and Development,17, 525–532.Google Scholar
  11. Berestetskii, V. B., Lifshitz, E. M., and Pitaevskii, L. P. (1971).Relativistic Quantum Theory, Vol. 4. Course of Theoretical Physics, Part I. Pergamon Press, Oxford.Google Scholar
  12. Bledsoe, W. W. (1961). “A basic limitation of the speed of digital computers.”IRE Transactions Electronic Computers,EC-10, 530.Google Scholar
  13. Bremermann, H. J. (1959). “On finite renormalization constants and the multiplication of causal functions in perturbation theory,” Technical Report, Department of Mathematics, University of California, Berkeley, California.Google Scholar
  14. Bremermann, H. J. (1962a). “Part I: Limitations on data processing arising from quantum theory,” in Optimization through evolution and recombination” inSelf-organizing Systems, M. C. Yovits, G. T. Jacobi, and G. D. Goldstein, eds. Spartan Books. Washington, D.C.Google Scholar
  15. Bremermann., H. J. (1962b). Quantum-theoretical Limitations of Data Processing.Abstracts of Short Communications. International Congress of Mathematics, Stockholm.Google Scholar
  16. Bremermann, H. J. (1963). “Limits of genetic control,”IEEE Transactions on Military Electronics,7, 200.Google Scholar
  17. Bremermann, H. J. (1965).Distributions, Complex Variables, and Fourier Transforms. Addison-Wesley, Reading, Massachusetts.Google Scholar
  18. Bremermann, H. J. (1967a). “Quantum Noise and Information,” inProceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Problability. University of California Press, Berkeley, California.Google Scholar
  19. Bremermann, H. J. (1967b). “Some remarks on analytic representation and products of distributions.SIAM Journal Applied Mathematics,15, 929.Google Scholar
  20. Bremermann, H. J. (1974a). “Algorithms, complexity, transcomputability, and the analysis of systems,” inCybernetics and Bionics, W. D. Keidel, W. Handler, and M. Spreng, eds. Oldenbourg, Munich.Google Scholar
  21. Bremermann, H. J. (1974b). “Complexity of automata, brains and behavior.” inPhysics and Mathematics of the Nervous System, M. Conrad, W. Güttinger, and M. Dal Cin, eds.,Biomathematics Lecture Notes, Vol. 4. Springer, Heidelberg.Google Scholar
  22. Bremermann H. J. (1977). “Complexity and transcomputability,” inthe Encyclopaedia of Ignorance, M. Duncan, ed. Pergamon Press, Oxford.Google Scholar
  23. Brillouin, L. (1956).Science and Information Theory, Academic Press, London: second ed., 1962.Google Scholar
  24. Csanky, L. (1976). “Fast parallel matrix inversion algorithms.”SIAM Journal of Computing,5.Google Scholar
  25. Csanky, L. and Bremermann, H. J. (1976). Complexity of Parallel Computation. Arbeitsberichte IMMD, University of Erlangen—Nürnberg, Vol.9, No. 8, 31.Google Scholar
  26. Feynman, R. P., Leighton, R. B., and Sands, M. (1963).The Feynman Lectures on Physics. Addison-Wesley, Reading, Massachusetts.Google Scholar
  27. Fredkin, E., and Toffoli, T. (1981). Conservative logic, Technical Memo, MIT/LCS/TM-197 (April 29).Google Scholar
  28. Hawking, S. W. (1974). “Black hole explosions?”Nature,248, 30.Google Scholar
  29. Hawking, S. W. (1975). “Particle creation by black holes.”Communications in Mathematical Physics,43, 199.Google Scholar
  30. Hawking, S. W. (1976). “Black holes and thermodynamics.” Physical Review. D.13, 191.Google Scholar
  31. Kalman, R. E., Falb, P. L., and Arbib, M. A. (1969).Topics in Mathematical Systems Theory. McGraw-Hill, New York.Google Scholar
  32. Keyes, R. W. (1982).International Journal of Theoretical Physics,21, 263 (this issue).Google Scholar
  33. Knuth, D. E. (1976). “Mathematics and computer science: Coping with finiteness.”Science,194, 1235–1242.Google Scholar
  34. Landauer, R. (1961). “Irreversibility and heat generation in the computing process.”IBM Journal of Research and Development,5, 183–191.Google Scholar
  35. Landauer R. (1976). “Fundamental limitations in the computational process.”Berichte der Bunsengesellschaft für Physikalische Chemie,80, 1048–1059.Google Scholar
  36. Landauer, R., and Woo, J. W. F. (1973). “Cooperative phenomena in data processing,” inSynergetics H. Haken, ed. B. G. Teubner, Stuttgart.Google Scholar
  37. Levitin, L. B. (1965). “Transmission of information by an ideal photon channel,”Information Transmission Problems 1, 71; “Ideal physical transmission channel,”Information Transmission Problems,1, 122.Google Scholar
  38. Levitin, L. B. (1982).International Journal of Theoretical Physics,21, 299 (this issue).Google Scholar
  39. Ligomenides, P. L. (1967). “Wave-mechanical uncertainty and speed limitations,”IEEE Spectrum,4:2, 65–68.Google Scholar
  40. Lumsden, Ch. J., and Wilson, E. O. (1981).Genes, Mind, and Culture: The Coevolutionary Process, Harvard University Press, Cambridge, Massachusetts.Google Scholar
  41. Maynard Smith, J. (1979). “The limitations of evolution theory,” inEncyclopaedia of Ignorance R. Duncan and M. Weston-Smith, eds. Pergamon Press, Oxford.Google Scholar
  42. Miller, R. E. and Thatcher, J. W. (eds.) (1972)Complexity of Computer Computations. Plenum Press, New York.Google Scholar
  43. Oster, G., Perelson, A. S., and Katchalsky, A. (1973). “Network thermodynamics: Dynamic modelling of biophysical systems,”Quarterly Review of Biophysics,6, 1.Google Scholar
  44. Papoulis, A. (1962).the Fourier Integral and its Applications. McGraw-Hill, New York.Google Scholar
  45. Perelson, A. S. (1975). “Network thermodynamics, an overview,”Biophysical Journal,15, 667–685.Google Scholar
  46. Shannon, C. E. (1948). “A mathematical theory of communication,”Bell System Technical Journal,27, pp. 379–423, 623–656.Google Scholar
  47. Stockmeyer, L. J., and Chandra, A. K. (1979). “Intrinsically difficult problems.”Scientific American,240, 5 (May), 140.Google Scholar
  48. Wigner, E. P. (1972). “On the time-energy uncertainty relation,” inAspects of Quantum Theory, A. Salam, and E. P. Wigner, eds. Cambridge University Press, Cambridge.Google Scholar

Copyright information

© Plenum Publishing Corporation 1982

Authors and Affiliations

  • Hans J. Bremermann
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeley

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