{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T15:11:34Z","timestamp":1774624294470,"version":"3.50.1"},"reference-count":48,"publisher":"Springer Science and Business Media LLC","issue":"3-4","license":[{"start":{"date-parts":[[1982,4,1]],"date-time":"1982-04-01T00:00:00Z","timestamp":386467200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int J Theor Phys"],"published-print":{"date-parts":[[1982,4]]},"DOI":"10.1007\/bf01857726","type":"journal-article","created":{"date-parts":[[2005,6,30]],"date-time":"2005-06-30T22:14:11Z","timestamp":1120169651000},"page":"203-217","source":"Crossref","is-referenced-by-count":49,"title":["Minimum energy requirements of information transfer and computing"],"prefix":"10.1007","volume":"21","author":[{"given":"Hans J.","family":"Bremermann","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"BF01857726_CR1","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1016\/0003-4916(69)90251-6","volume":"53","author":"G. R. Allcock","year":"1969","unstructured":"Allcock, G. R. (1969). \u201cThe time of arrival in quantum mechanics. I. Formal considerations,Annals of Physics,53, 253\u2013285; \u201cII. The individual measurement,\u201dAnnals of Physics,53, pp. 286\u2013310; III. \u201cThe measurement ensemble,\u201dAnnals of Physics.53, pp. 311\u2013348.","journal-title":"Annals of Physics"},{"key":"BF01857726_CR2","volume-title":"Brains, Machines, and Mathematics","author":"M. A. Arbib","year":"1964","unstructured":"Arbib, M. A. (1964).Brains, Machines, and Mathematics. McGraw-Hill, New York."},{"key":"BF01857726_CR3","first-page":"95","volume":"1","author":"R. Ashby","year":"1967","unstructured":"Ashby, R. (1967). \u201cThe place of the brain in the natural world,\u201dCurrents in Modern Biology,1, 95\u2013104.","journal-title":"Currents in Modern Biology"},{"key":"BF01857726_CR4","series-title":"Bionics Symposium","volume-title":"Cybernetic Problems in Bionics","author":"R. Ashby","year":"1968","unstructured":"Ashby, R. (1968). \u201cSome consequences of Bremermann's limit for information processing systems\u201d inCybernetic Problems in Bionics (Bionics Symposium. 1966), H. L. Oestreicher and D. R. Moore, eds. Gordon & Breach, New York."},{"key":"BF01857726_CR5","first-page":"2","volume":"18","author":"R. Ashby","year":"1973","unstructured":"Ashby, R. (1973). Editorial,Behavioral Science,18, 2\u20136.","journal-title":"Behavioral Science"},{"key":"BF01857726_CR6","doi-asserted-by":"crossref","first-page":"2333","DOI":"10.1103\/PhysRevD.7.2333","volume":"7","author":"J. D. Bekenstein","year":"1973","unstructured":"Bekenstein J. D. (1973). \u201cBlack holes and entropy.\u201dPhysical Review D,7, 2333.","journal-title":"Physical Review D"},{"key":"BF01857726_CR7","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1063\/1.2913906","volume":"Jan.","author":"J. D. Bekenstein","year":"1980","unstructured":"Bekenstein, J. D. (1980). \u201cBlack-hole thermodynamics.\u201dPhysics Today, Jan., 24\u201331.","journal-title":"Physics Today"},{"key":"BF01857726_CR8","doi-asserted-by":"crossref","first-page":"623","DOI":"10.1103\/PhysRevLett.46.623","volume":"46","author":"J. D. Bekenstein","year":"1981","unstructured":"Bekenstein, J. D. (1981a). \u201cThe energy cost of information transfer.\u201dPhysical Review Letters,46, 623.","journal-title":"Physical Review Letters"},{"key":"BF01857726_CR9","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1103\/PhysRevD.23.287","volume":"23","author":"J. D. Bekenstein","year":"1981","unstructured":"Bekenstein, J. D. (1981b) Universal Upper Bound to Entropy-to-Energy Ratio for Bounded Systems.Physical Review D,23, 287.","journal-title":"Physical Review D"},{"key":"BF01857726_CR10","doi-asserted-by":"crossref","first-page":"525","DOI":"10.1147\/rd.176.0525","volume":"17","author":"C. H. Bennett","year":"1973","unstructured":"Bennett, C. H. (1973). \u201cLogical reversibility of computation.\u201dIBM Journal of Research and Development,17, 525\u2013532.","journal-title":"IBM Journal of Research and Development"},{"key":"BF01857726_CR11","series-title":"Course of Theoretical Physics, Part I","volume-title":"Relativistic Quantum Theory","author":"V. B. Berestetskii","year":"1971","unstructured":"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."},{"key":"BF01857726_CR12","doi-asserted-by":"crossref","first-page":"530","DOI":"10.1109\/TEC.1961.5219243","volume":"10","author":"W. W. Bledsoe","year":"1961","unstructured":"Bledsoe, W. W. (1961). \u201cA basic limitation of the speed of digital computers.\u201dIRE Transactions Electronic Computers,EC-10, 530.","journal-title":"IRE Transactions Electronic Computers"},{"key":"BF01857726_CR13","series-title":"Technical Report","volume-title":"On finite renormalization constants and the multiplication of causal functions in perturbation theory","author":"H. J. Bremermann","year":"1959","unstructured":"Bremermann, H. J. (1959). \u201cOn finite renormalization constants and the multiplication of causal functions in perturbation theory,\u201d Technical Report, Department of Mathematics, University of California, Berkeley, California."},{"key":"BF01857726_CR14","series-title":"Self-organizing Systems","volume-title":"Optimization through evolution and recombination","author":"H. J. Bremermann","year":"1962","unstructured":"Bremermann, H. J. (1962a). \u201cPart I: Limitations on data processing arising from quantum theory,\u201d in Optimization through evolution and recombination\u201d inSelf-organizing Systems, M. C. Yovits, G. T. Jacobi, and G. D. Goldstein, eds. Spartan Books. Washington, D.C."},{"key":"BF01857726_CR15","unstructured":"Bremermann., H. J. (1962b). Quantum-theoretical Limitations of Data Processing.Abstracts of Short Communications. International Congress of Mathematics, Stockholm."},{"key":"BF01857726_CR16","doi-asserted-by":"crossref","first-page":"200","DOI":"10.1109\/TME.1963.4323073","volume":"7","author":"H. J. Bremermann","year":"1963","unstructured":"Bremermann, H. J. (1963). \u201cLimits of genetic control,\u201dIEEE Transactions on Military Electronics,7, 200.","journal-title":"IEEE Transactions on Military Electronics"},{"key":"BF01857726_CR17","volume-title":"Distributions, Complex Variables, and Fourier Transforms","author":"H. J. Bremermann","year":"1965","unstructured":"Bremermann, H. J. (1965).Distributions, Complex Variables, and Fourier Transforms. Addison-Wesley, Reading, Massachusetts."},{"key":"BF01857726_CR18","volume-title":"Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Problability","author":"H. J. Bremermann","year":"1967","unstructured":"Bremermann, H. J. (1967a). \u201cQuantum Noise and Information,\u201d inProceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Problability. University of California Press, Berkeley, California."},{"key":"BF01857726_CR19","doi-asserted-by":"crossref","first-page":"929","DOI":"10.1137\/0115083","volume":"15","author":"H. J. Bremermann","year":"1967","unstructured":"Bremermann, H. J. (1967b). \u201cSome remarks on analytic representation and products of distributions.SIAM Journal Applied Mathematics,15, 929.","journal-title":"SIAM Journal Applied Mathematics"},{"key":"BF01857726_CR20","volume-title":"Cybernetics and Bionics","author":"H. J. Bremermann","year":"1974","unstructured":"Bremermann, H. J. (1974a). \u201cAlgorithms, complexity, transcomputability, and the analysis of systems,\u201d inCybernetics and Bionics, W. D. Keidel, W. Handler, and M. Spreng, eds. Oldenbourg, Munich."},{"key":"BF01857726_CR21","series-title":"Biomathematics Lecture Notes","volume-title":"Physics and Mathematics of the Nervous System","author":"H. J. Bremermann","year":"1974","unstructured":"Bremermann, H. J. (1974b). \u201cComplexity of automata, brains and behavior.\u201d inPhysics and Mathematics of the Nervous System, M. Conrad, W. G\u00fcttinger, and M. Dal Cin, eds.,Biomathematics Lecture Notes, Vol. 4. Springer, Heidelberg."},{"key":"BF01857726_CR22","volume-title":"the Encyclopaedia of Ignorance","author":"H. J. Bremermann","year":"1977","unstructured":"Bremermann H. J. (1977). \u201cComplexity and transcomputability,\u201d inthe Encyclopaedia of Ignorance, M. Duncan, ed. Pergamon Press, Oxford."},{"key":"BF01857726_CR23","volume-title":"Science and Information Theory","author":"L. Brillouin","year":"1956","unstructured":"Brillouin, L. (1956).Science and Information Theory, Academic Press, London: second ed., 1962.","edition":"second ed."},{"key":"BF01857726_CR24","doi-asserted-by":"crossref","unstructured":"Csanky, L. (1976). \u201cFast parallel matrix inversion algorithms.\u201dSIAM Journal of Computing,5.","DOI":"10.1137\/0205040"},{"issue":"No. 8","key":"BF01857726_CR25","first-page":"31","volume":"9","author":"L. Csanky","year":"1976","unstructured":"Csanky, L. and Bremermann, H. J. (1976). Complexity of Parallel Computation. Arbeitsberichte IMMD, University of Erlangen\u2014N\u00fcrnberg, Vol.9, No. 8, 31.","journal-title":"Arbeitsberichte IMMD, University of Erlangen\u2014N\u00fcrnberg"},{"key":"BF01857726_CR26","volume-title":"The Feynman Lectures on Physics","author":"R. P. Feynman","year":"1963","unstructured":"Feynman, R. P., Leighton, R. B., and Sands, M. (1963).The Feynman Lectures on Physics. Addison-Wesley, Reading, Massachusetts."},{"key":"BF01857726_CR27","unstructured":"Fredkin, E., and Toffoli, T. (1981). Conservative logic, Technical Memo, MIT\/LCS\/TM-197 (April 29)."},{"key":"BF01857726_CR28","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1038\/248030a0","volume":"248","author":"S. W. Hawking","year":"1974","unstructured":"Hawking, S. W. (1974). \u201cBlack hole explosions?\u201dNature,248, 30.","journal-title":"Nature"},{"key":"BF01857726_CR29","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1007\/BF02345020","volume":"43","author":"S. W. Hawking","year":"1975","unstructured":"Hawking, S. W. (1975). \u201cParticle creation by black holes.\u201dCommunications in Mathematical Physics,43, 199.","journal-title":"Communications in Mathematical Physics"},{"key":"BF01857726_CR30","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1103\/PhysRevD.13.191","volume":"13","author":"S. W. Hawking","year":"1976","unstructured":"Hawking, S. W. (1976). \u201cBlack holes and thermodynamics.\u201d Physical Review. D.13, 191.","journal-title":"Physical Review. D."},{"key":"BF01857726_CR31","volume-title":"Topics in Mathematical Systems Theory","author":"R. E. Kalman","year":"1969","unstructured":"Kalman, R. E., Falb, P. L., and Arbib, M. A. (1969).Topics in Mathematical Systems Theory. McGraw-Hill, New York."},{"key":"BF01857726_CR32","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1007\/BF01857729","volume":"21","author":"R. W. Keyes","year":"1982","unstructured":"Keyes, R. W. (1982).International Journal of Theoretical Physics,21, 263 (this issue).","journal-title":"International Journal of Theoretical Physics"},{"key":"BF01857726_CR33","doi-asserted-by":"crossref","first-page":"1235","DOI":"10.1126\/science.194.4271.1235","volume":"194","author":"D. E. Knuth","year":"1976","unstructured":"Knuth, D. E. (1976). \u201cMathematics and computer science: Coping with finiteness.\u201dScience,194, 1235\u20131242.","journal-title":"Science"},{"key":"BF01857726_CR34","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1147\/rd.53.0183","volume":"5","author":"R. Landauer","year":"1961","unstructured":"Landauer, R. (1961). \u201cIrreversibility and heat generation in the computing process.\u201dIBM Journal of Research and Development,5, 183\u2013191.","journal-title":"IBM Journal of Research and Development"},{"key":"BF01857726_CR35","doi-asserted-by":"crossref","first-page":"1048","DOI":"10.1002\/bbpc.19760801105","volume":"80","author":"R. Landauer","year":"1976","unstructured":"Landauer R. (1976). \u201cFundamental limitations in the computational process.\u201dBerichte der Bunsengesellschaft f\u00fcr Physikalische Chemie,80, 1048\u20131059.","journal-title":"Berichte der Bunsengesellschaft f\u00fcr Physikalische Chemie"},{"key":"BF01857726_CR36","volume-title":"Synergetics","author":"R. Landauer","year":"1973","unstructured":"Landauer, R., and Woo, J. W. F. (1973). \u201cCooperative phenomena in data processing,\u201d inSynergetics H. Haken, ed. B. G. Teubner, Stuttgart."},{"key":"BF01857726_CR37","first-page":"71","volume":"1","author":"L. B. Levitin","year":"1965","unstructured":"Levitin, L. B. (1965). \u201cTransmission of information by an ideal photon channel,\u201dInformation Transmission Problems 1, 71; \u201cIdeal physical transmission channel,\u201dInformation Transmission Problems,1, 122.","journal-title":"Information Transmission Problems"},{"key":"BF01857726_CR38","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1007\/BF01857732","volume":"21","author":"L. B. Levitin","year":"1982","unstructured":"Levitin, L. B. (1982).International Journal of Theoretical Physics,21, 299 (this issue).","journal-title":"International Journal of Theoretical Physics"},{"issue":"2","key":"BF01857726_CR39","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1109\/MSPEC.1967.5216205","volume":"4","author":"P. L. Ligomenides","year":"1967","unstructured":"Ligomenides, P. L. (1967). \u201cWave-mechanical uncertainty and speed limitations,\u201dIEEE Spectrum,4:2, 65\u201368.","journal-title":"IEEE Spectrum"},{"key":"BF01857726_CR40","volume-title":"Genes, Mind, and Culture: The Coevolutionary Process","author":"Ch. J. Lumsden","year":"1981","unstructured":"Lumsden, Ch. J., and Wilson, E. O. (1981).Genes, Mind, and Culture: The Coevolutionary Process, Harvard University Press, Cambridge, Massachusetts."},{"key":"BF01857726_CR41","volume-title":"Encyclopaedia of Ignorance","author":"J. Maynard Smith","year":"1979","unstructured":"Maynard Smith, J. (1979). \u201cThe limitations of evolution theory,\u201d inEncyclopaedia of Ignorance R. Duncan and M. Weston-Smith, eds. Pergamon Press, Oxford."},{"key":"BF01857726_CR42","volume-title":"Complexity of Computer Computations","year":"1972","unstructured":"Miller, R. E. and Thatcher, J. W. (eds.) (1972)Complexity of Computer Computations. Plenum Press, New York."},{"key":"BF01857726_CR43","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1017\/S0033583500000081","volume":"6","author":"G. Oster","year":"1973","unstructured":"Oster, G., Perelson, A. S., and Katchalsky, A. (1973). \u201cNetwork thermodynamics: Dynamic modelling of biophysical systems,\u201dQuarterly Review of Biophysics,6, 1.","journal-title":"Quarterly Review of Biophysics"},{"key":"BF01857726_CR44","volume-title":"the Fourier Integral and its Applications","author":"A. Papoulis","year":"1962","unstructured":"Papoulis, A. (1962).the Fourier Integral and its Applications. McGraw-Hill, New York."},{"key":"BF01857726_CR45","doi-asserted-by":"crossref","first-page":"667","DOI":"10.1016\/S0006-3495(75)85847-4","volume":"15","author":"A. S. Perelson","year":"1975","unstructured":"Perelson, A. S. (1975). \u201cNetwork thermodynamics, an overview,\u201dBiophysical Journal,15, 667\u2013685.","journal-title":"Biophysical Journal"},{"key":"BF01857726_CR46","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","volume":"27","author":"C. E. Shannon","year":"1948","unstructured":"Shannon, C. E. (1948). \u201cA mathematical theory of communication,\u201dBell System Technical Journal,27, pp. 379\u2013423, 623\u2013656.","journal-title":"Bell System Technical Journal"},{"issue":"5","key":"BF01857726_CR47","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1038\/scientificamerican0579-140","volume":"240","author":"L. J. Stockmeyer","year":"1979","unstructured":"Stockmeyer, L. J., and Chandra, A. K. (1979). \u201cIntrinsically difficult problems.\u201dScientific American,240, 5 (May), 140.","journal-title":"Scientific American"},{"key":"BF01857726_CR48","volume-title":"Aspects of Quantum Theory","author":"E. P. Wigner","year":"1972","unstructured":"Wigner, E. P. (1972). \u201cOn the time-energy uncertainty relation,\u201d inAspects of Quantum Theory, A. Salam, and E. P. Wigner, eds. Cambridge University Press, Cambridge."}],"container-title":["International Journal of Theoretical Physics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01857726.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF01857726\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01857726","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,10]],"date-time":"2019-05-10T14:25:23Z","timestamp":1557498323000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF01857726"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1982,4]]},"references-count":48,"journal-issue":{"issue":"3-4","published-print":{"date-parts":[[1982,4]]}},"alternative-id":["BF01857726"],"URL":"https:\/\/doi.org\/10.1007\/bf01857726","relation":{},"ISSN":["0020-7748","1572-9575"],"issn-type":[{"value":"0020-7748","type":"print"},{"value":"1572-9575","type":"electronic"}],"subject":[],"published":{"date-parts":[[1982,4]]}}}