Thermodynamics of Computation

  • H. John Caulfield
  • Lei QianEmail author
Reference work entry
Part of the Encyclopedia of Complexity and Systems Science Series book series (ECSSS)


Analog computing

An analog computer is often negatively defined as a computer that is not digital. More properly, it is a computer that uses quantities that can be made proportional to the amount of signal detected. That analogy between a real number and a physical property gives the name “analog.” Many problems arise in analog computing, because it is so difficult to obtain a large number of distinguishable levels and because noise builds up in cascaded computations. But, being unencoded, it can always be run faster than its digital counterpart.


Any activity with input/output patterns mapped onto real problems to be solved.

Digital computing

The name derives from digits (the fingers). Digital computing works with discrete items like fingers. Most digital computing is binary – using 0 and 1. Because signals are restored to a 1 or a 0 after each operation, noise accumulation is not much of a problem. And, of course, digital computers are much more flexible than analog...


Primary Literature

  1. Benzi R, Parisi G, Sutera A, Vulpiani A (1983) A theory of stochastic resonance in climatic change. SIAM J Appl Math 43:565–578MathSciNetCrossRefGoogle Scholar
  2. Bouwmeester D, Ekert A, Zeilinger A (2001) The physics of quantum information. Springer, BerlinzbMATHGoogle Scholar
  3. Caulfield HJ (1992) Space – time complexity in optical computing. Multidim Syst Sig Process 2:373–378CrossRefGoogle Scholar
  4. Caulfield HJ, Qian L (2006) The other kind of quantum computing. Int J Unconv Comput 2(3):281–290Google Scholar
  5. Caulfield HJ, Brasher JD, Hester CF (1991) Complexity issues in optical computing. Opt Comput Process 1:109–113Google Scholar
  6. Caulfield HJ, Kukhtarev N, Kukhtareva T, Schamschula MP, Banarjee P (1999) One, two, and three-beam optical chaos and self organization effects in photorefractive materials. Mater Res Innov 3:194–199CrossRefGoogle Scholar
  7. Caulfield HJ, Vikram CS, Zavalin A (2006) Optical logic redux. Opt Int J Light Electron Opt 117:199–209CrossRefGoogle Scholar
  8. Caulfield HJ, Soref RA, Qian L, Zavalin A, Hardy J (2007a) Generalized optical logic elements – GOLEs. Opt Commun 271:365–376CrossRefGoogle Scholar
  9. Caulfield HJ, Soref RA, Vikram CS (2007b) Universal reconfigurable optical logic with silicon-on-insulator resonant structures. Photonics Nanostruct 5:14–20CrossRefGoogle Scholar
  10. Cerny V (1985) A thermodynamical approach to the travelling salesman problem: an efficient simulation algorithm. J Optim Theory Appl 45:41–51MathSciNetCrossRefGoogle Scholar
  11. Das A, Chakrabarti BK (eds) (2005) Quantum annealing and related optimization methods, vol 679, Lecture Notes in Physics. Springer, HeidelbergzbMATHGoogle Scholar
  12. Grantham W, Amitm A (1990) Discretization chaos – feedback control and transition to chaos. In: Control and dynamic systems, vol34. Advances in control mechanics. Pt. 1 (A91-50601 21–63). Academic, San Diego, pp 205–277Google Scholar
  13. Herbst BM, Ablowitz MJ (1989) Numerically induced chaos in the nonlinear Schrödinger equation. Phys Rev Lett 62:2065–2068MathSciNetCrossRefGoogle Scholar
  14. Hinton GE, Sejnowski TJ (1986) Learning and relearning in Boltzmann machines. In: Rumelhart DE, McClelland JL, the PDP Research Group (eds) Parallel distributed processing: explorations in the microstructure of cognition vol 1. Foundations. Cambridge MIT Press, Cambridge, pp 282–317Google Scholar
  15. Hopfield JJ (1982) Neural networks and physical systems with emergent collective computational abilities. Proc Natl Acad Sci U S A 79:2554–2558MathSciNetCrossRefGoogle Scholar
  16. Ilachinski A (2001) Cellular automata: a discrete Universe. World Scientific, SingaporeCrossRefGoogle Scholar
  17. Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220(4598):671–680MathSciNetCrossRefGoogle Scholar
  18. Kupiec SA, Caulfield HJ (1991) Massively parallel optical PLA. Int J Opt Comput 2:49–62Google Scholar
  19. Nicolis G, Prigogine I (1977) Self-organization in nonequilibrium systems. Wiley, New YorkzbMATHGoogle Scholar
  20. Nielsen MA, Chuang IL (2000) Quantum computation and quantum information. Cambridge University Press, New YorkzbMATHGoogle Scholar
  21. Nyce JM (1996) Guest editor’s introduction. IEEE Ann Hist Comput 18:3–4CrossRefGoogle Scholar
  22. Ogorzalek MJ (1997) Chaos and complexity in nonlinear electronic circuits. World Sci Ser Nonlinear Sci Ser A 22Google Scholar
  23. Orponen P (1997) A survey of continuous-time computation theory. In: Du DZ, Ko KI (eds) Advances in algorithms, languages, and complexity. Kluwer, Dordrecht, pp 209–224CrossRefGoogle Scholar
  24. Pour-El MB, Richards JI (1989) Computability in analysis and physics. Springer, BerlinCrossRefGoogle Scholar
  25. Prigogine I, Stengers I (1984) Order out of chaos. Bantam Books, New YorkGoogle Scholar
  26. Prigogine I, Stengers I, Toffler A (1986) Order out of chaos: man’s new dialogue with nature. Flamingo, LondonGoogle Scholar
  27. Shamir J, Caulfield HJ, Crowe DG (1991) Role of photon statistics in energy-efficient optical computers. Appl Opt 30:3697–3701CrossRefGoogle Scholar
  28. Weaver W (1948) Science and complexity. Am Sci 36:536–541Google Scholar
  29. Wolfram S (1983) Statistical mechanics of cellular automata. Rev Mod Phys 55:601–644MathSciNetCrossRefGoogle Scholar

Books and Reviews

  1. Bennett CH (1982) The thermodynamics of computation a review. Int J Theor Phys 21:905–940CrossRefGoogle Scholar
  2. Bernard W, Callen HB (1959) Irreversible thermodynamics of nonlinear processes and noise in driven systems. Rev Mod Phys 31:1017–1044MathSciNetCrossRefGoogle Scholar
  3. Bub J (2002) Maxwell’s Demon and the thermodynamics of computation. arXiv:quant-ph/0203017Google Scholar
  4. Casti JL (1992) Reality rules. Wiley, New YorkzbMATHGoogle Scholar
  5. Deutsch D (1985) Quantum theory, the Church-Turing principle and the universal quantum computer. Proc R Soc Lond Ser A Math Phys Sci 400:97–117MathSciNetCrossRefGoogle Scholar
  6. Karplus WJ, Soroka WW (1958) Analog methods: computation and simulation. McGraw Hill, New YorkzbMATHGoogle Scholar
  7. Leff HS, Rex AF (eds) (1990) Maxwell’s demon: entropy, information, computing. Princeton University Press, PrincetonGoogle Scholar
  8. Zurek WH (1989) Algorithmic randomness and physical entropy. Phys Rev Abstr 40:4731–4751MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Fisk UniversityNashvilleUSA

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