Foundations of Physics

, Volume 40, Issue 2, pp 205–238 | Cite as

Does a Computer Have an Arrow of Time?

  • Owen J. E. MaroneyEmail author


Schulman (Entropy 7(4):221–233, 2005) has argued that Boltzmann’s intuition, that the psychological arrow of time is necessarily aligned with the thermodynamic arrow, is correct. Schulman gives an explicit physical mechanism for this connection, based on the brain being representable as a computer, together with certain thermodynamic properties of computational processes. Hawking (Physical Origins of Time Asymmetry, Cambridge University Press, Cambridge, 1994) presents similar, if briefer, arguments. The purpose of this paper is to critically examine the support for the link between thermodynamics and an arrow of time for computers. The principal arguments put forward by Schulman and Hawking will be shown to fail. It will be shown that any computational process that can take place in an entropy increasing universe, can equally take place in an entropy decreasing universe. This conclusion does not automatically imply a psychological arrow can run counter to the thermodynamic arrow. Some alternative possible explanations for the alignment of the two arrows will be briefly discussed.

Landauer’s principle Arrow of time Causality Computers 


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  1. 1.
    Schulman, L.S.: A computer’s arrow of time. Entropy 7(4), 221–233 (2005). zbMATHCrossRefMathSciNetADSGoogle Scholar
  2. 2.
    Hawking, S.W.: The no boundary condition and the arrow of time. In: Halliwell, J.J., Perez-Mercader, J., Zurek, W.H. (eds.) Physical Origins of Time Asymmetry. Cambridge University Press, Cambridge (1994) Google Scholar
  3. 3.
    Boltzmann, L.: Lectures on Gas Theory, 1896–1898. Dover, New York (1995) Google Scholar
  4. 4.
    Reichenbach, H.: The Direction of Time. University of California Press, Berkeley (1956) (NB. My copy is a Dover, New York, reprint from 1999) Google Scholar
  5. 5.
    Horwich, P.: Asymmetries in Time. MIT, Cambridge (1987) Google Scholar
  6. 6.
    Sklar, L.: Physics and Chance: Philosophical Issues in the Foundations of Statistical Mechanics. Cambridge University Press, Cambridge (1993) Google Scholar
  7. 7.
    Earman, J.: The “Past Hypothesis”: Not even false. Stud. Hist. Philos. Mod. Phys. 37(3), 399–430 (2006) CrossRefMathSciNetGoogle Scholar
  8. 8.
    Maudlin, T.: Remarks on the passing of time. Proc. Aristot. Soc. 102(3), 237–252 (2002) CrossRefGoogle Scholar
  9. 9.
    Sklar, L.: Philosophy and Spacetime Physics. University of California, Cambridge (1985) Google Scholar
  10. 10.
    Landauer, R.: Irreversibility and heat generation in the computing process. IBM J. Res. Dev. 5, 183–191 (1961). Reprinted in [24, 36] zbMATHMathSciNetCrossRefGoogle Scholar
  11. 11.
    Hawking, S.W.: Arrow of time in cosmology. Phys. Rev. D 32(10), 2489–2495 (1985) CrossRefMathSciNetADSGoogle Scholar
  12. 12.
    Hawking, S.W.: The direction of time. New Sci. 115, 46–49 (1987) ADSGoogle Scholar
  13. 13.
    Albert, D.Z.: Time and Chance. Harvard University Press, Cambridge (2001) Google Scholar
  14. 14.
    Schulman, L.S.: Time’s Arrow and Quantum Measurement. CUP, Cambridge (1997) Google Scholar
  15. 15.
    Zeh, H.D.: Remarks on the compatibility of opposite arrows of time. Entropy 7(4), 199–207 (2005). zbMATHCrossRefMathSciNetADSGoogle Scholar
  16. 16.
    Schulman, L.S.: Two-way thermodynamics: could it really happen? Entropy 7(4), 208–220 (2005). zbMATHCrossRefMathSciNetADSGoogle Scholar
  17. 17.
    Short, T., Ladyman, J., Groisman, B., Presnell, S.: The connections between logical and thermodynamical irreversibility. Stud. Hist. Philos. Mod. Phys. 38(1), 58–79 (2007). CrossRefMathSciNetGoogle Scholar
  18. 18.
    Maroney, O.J.E.: The (absence of a) relationship between thermodynamic and logical reversibility. Stud. Hist. Philos. Mod. Phys. 36, 355–374 (2005). physics/0406137 CrossRefMathSciNetGoogle Scholar
  19. 19.
    Maroney, O.J.E.: Generalising Landauer’s Principle. Phys. Rev. E 79, 031105-1 (2009). quant-ph/0702094 CrossRefMathSciNetADSGoogle Scholar
  20. 20.
    Caves, C.M.: Quantitative limits on the ability of a Maxwell demon to extract work from heat. Phys. Rev. Lett. 64(18), 2111–2114 (1990) zbMATHCrossRefMathSciNetADSGoogle Scholar
  21. 21.
    Caves, C.M.: Information and entropy. Phys. Rev. E 47(6), 4010–4017 (1993). Reprinted in [24] CrossRefMathSciNetADSGoogle Scholar
  22. 22.
    Piechocinska, B.: Information erasure. Phys. Rev. A 61, 062314 (2000). Reprinted in [24] CrossRefMathSciNetADSGoogle Scholar
  23. 23.
    Bub, J.: Maxwell’s demon and the thermodynamics of computation. Stud. Hist. Philos. Mod. Phys. 32, 569–579 (2001). quant-ph/0203017 CrossRefMathSciNetGoogle Scholar
  24. 24.
    Leff, H.S., Rex, A.F. (eds.): Maxwell’s Demon 2: Entropy, Classical and Quantum Information, Computing. IoP, Bristol (2003). ISBN 0750307595 Google Scholar
  25. 25.
    Bennett, C.H.: Notes on Landauer’s principle, reversible computation, and Maxwell’s demon. Stud. Hist. Philos. Mod. Phys. 34, 501–510 (2003). physics/0210005 CrossRefGoogle Scholar
  26. 26.
    Earman, J., Norton, J.D.: Exorcist XIV: The wrath of Maxwell’s demon. Part II: From Szilard to Landauer and beyond. Stud. Hist. Philos. Mod. Phys. 30(1), 1–40 (1999) CrossRefMathSciNetGoogle Scholar
  27. 27.
    Maroney, O.J.E.: Information and Entropy in Quantum Theory. Ph.D. Thesis, Birkbeck College, University of London (2002). quant-ph/0411172
  28. 28.
    Norton, J.D.: Eaters of the lotus: Landauer’s principle and the return of Maxwell’s demon. Stud. Hist. Philos. Mod. Phys. 36, 375–411 (2005). CrossRefMathSciNetGoogle Scholar
  29. 29.
    Turgut, S.: Relations between entropies produced in non-deterministic processes. Phys. Rev. E 79, 041102 (2009) CrossRefADSGoogle Scholar
  30. 30.
    Gibbs, J.W.: Elementary Principles in Statistical Mechanics. New York-London (1902) (NB. My copy is an Ox Bow Press, Woodbridge, Connecticut, reprint from 1981) Google Scholar
  31. 31.
    Tolman, R.C.: The Principles of Statistical Mechanics. Oxford University Press, Oxford (1938) (NB. My copy is a Dover, New York, reprint from 1979) Google Scholar
  32. 32.
    Partovi, M.H.: Irreversibility, reduction and entropy increase in quantum measurements. Phys. Lett. A 137(9), 445–450 (1989) CrossRefMathSciNetADSGoogle Scholar
  33. 33.
    Loewer, B.: Counterfactuals and the second law. In: Price, H., Corry, R. (eds.) Causality, Physics, and the Constitution of Reality: Russell’s Republic Revisited. Oxford University Press, Oxford (2007) Google Scholar
  34. 34.
    Price, H.: Time’s Arrow and Archimedes’ Point. Oxford University Press, Oxford (1996) Google Scholar
  35. 35.
    Frisch, M.: Does a low-entropy constraint prevent us from influencing the past? Philosophy of Science e-print Service (2007).
  36. 36.
    Leff, H.S., Rex, A.F. (eds.): Maxwell’s Demon. Entropy, Information, Computing. Adam Hilger, Bristol (1990). ISBN 0-7503-0057-4 Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Centre for Time, SOPHIUniversity of SydneySydneyAustralia
  2. 2.Perimeter Institute for Theoretical PhysicsWaterlooCanada

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