Information is physical

MAY 01, 1991

There are no unavoidable energy consumption requirements per step in a computer. Related analysis has provided insights into the measurement process and the communications channel, and has prompted speculations about the nature of physical laws.

DOI: 10.1063/1.881299

Rolf Landauer

Thermodynamics arose in the 19th century out of the attempt to understand the performance limits of steam engines in a way that would anticipate all further inventions. Claude Shannon, after World War II, analyzed the limits of the communications channel. It is no surprise, then, that shortly after the emergence of modern digital computing, similar questions appeared in that field. It was not hard to associate a logic gate with a degree of freedom, then to associate kT with that, and presume that this energy has to be dissipated at every step. Similarly, it seemed obvious to many that the uncertainty principle, $ΔEΔt∼ℏ,$ could be used to calculate a required minimal energy involvement, and therefore energy loss, for very short $Δt.$

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References

1. C. E. Shannon, Bell Syst. Tech. J. 27, 379 (1948); https://doi.org/BSTJAN
ibid, p. 623.
2. T. Toffoli, N. Margolus, Cellular Automata Machines, MIT P., Cambridge, Mass. (1987).
3. K. Zuse, Int. J. Theor. Phys. 21, 589 (1982); https://doi.org/IJTPBM
Rechnender Raum, Friedrich Vieweg und Sohn, Braunschweig (1969).
4. R. Wright, Three Scientists and Their Gods, Times Books, New York (1988).
5. See The Economist, 22 April 1989, p. 81.
6. C. H. Bennett, IBM J. Res. Dev. 17, 525 (1973).https://doi.org/IBMJAE
7. E. Fredkin, T. Toffoli, Int. J. Theor. Phys. 21, 219 (1982).https://doi.org/IJTPBM
8. C. H. Bennett, Int. J. Theor. Phys. 21, 905 (1982).https://doi.org/IJTPBM
9. J. von Neumann, US Patent 2 815 488, filed 28 April 1954.
E. Goto, J. Electr. Commun. Eng., Japan, 38, 770 (1955).
10. K. K. Likharev, Int. J. Theor. Phys. 21, 311 (1982). https://doi.org/IJTPBM
K. K. Likharev, S. V. Rylov, V. K. Semenov, IEEE Trans. Magn. 21, 947 (1985).https://doi.org/IEMGAQ
11. C. H. Bennett, IBM J. Res. Dev. 32, 16 (1988).https://doi.org/IBMJAE
12. R. Landauer, in Selected Topics in Signal Processing, S. Haykin, ed., Prentice‐Hall, Englewood Cliffs, N.J. (1989), p. 18. (Printed version has some figures oriented incorrectly).
13. E. Biedermann, PHYSICS TODAY November 1990, p. 122.
14. E. Goto, N. Yoshida, K. F. Loe, W. Hioe, in Proc. 3rd Int. Symp. Foundations of Quantum Mechanics, Tokyo 1989, S. Kobayashi, H. Ezawa, Y. Murayama, S. Nomura, eds., Phys. Soc. Japan, Tokyo (1990) p. 412.
15. L. Szilard, Z. Phys. 53, 840 (1929); https://doi.org/ZEPYAA
English translation in J. A. Wheeler and W. H. Zurek, eds., Quantum Theory and Measurement, Princeton U.P., Princeton 1983, p. 539.
16. L. Brillouin in Science and Information Theory, Academic Press, New York (1956), p. 162.
D. Gabor, in Progress in Optics, vol. I, E. Wolf, ed. North‐Holland, Amsterdam (1961) p. 109.
17. C. H. Bennett, Sci. Am., November, 1987, p. 108.
18. O. Penrose, Foundations of Statistical Mechanics, Pergamon, Oxford (1970).
19. W. H. Zurek, Nature 341, 119 (1989). https://doi.org/NATUAS
See also C. M. Caves, W. G. Unruh, W. H. Zurek, Phys. Rev. Lett. 65, 1387 (1990).https://doi.org/PRLTAO
20. H. S. Leff and A. F. Rex, Maxwell’s Demon: Entropy, Information, Computing, Princeton U.P., Princeton (1990).
21. P. Benioff, J. Stat. Phys. 22, 563 (1980); https://doi.org/JSTPBS
P. Benioff, J. Stat. Phys. 29, 515 (1982);
P. Benioff, Phys. Rev. Lett. 48, 1581 (1982).https://doi.org/PRLTAO
22. D. Deutsch, Proc. R. Soc. London, Ser. A 425, 73 (1989). https://doi.org/PRLAAZ
P. Benioff, in New Techniques and Ideas in Quantum Measurement Theory, Ann. N. Y. Acad. Sci., vol. 480, D. M. Greenberger, ed., (1986) p. 475;
N. Margolus, ibid., p. 487.
A. Peres, Phys. Rev. A 32, 3266 (1985); https://doi.org/PLRAAN
W. H. Zurek, Phys. Rev. Lett. 53, 391 (1984).https://doi.org/PRLTAO
23. R. Feynman, Opt. News 11, 11 (1985);
reprinted in R. Feynman, Found. Phys. 16, 507 (1986).https://doi.org/FNDPA4
24. J. A. Wheeler in Proc. 3rd Int. Symp. Foundations of Quantum Mechanics, Tokyo 1989, S. Kobayashi, H. Ezawa, Y. Murayama, S. Nomura, eds., Phys. Soc. Japan, Tokyo, (1990), p. 354;
IBM J. Res. Dev. 32, 4 (1988).https://doi.org/IBMJAE

More about the Authors

Rolf Landauer. Thomas J. Watson Research Center, Yorktown Heights, New York.