Thermodynamic Time

  • C. K. Raju
Part of the Fundamental Theories of Physics book series (FTPH, volume 65)


In the previous chapters we saw how relativity resolves the problem of time measurement, and reduces all measurement to time measurement. Relativity, though, abolishes the intuitive notion of `becoming’. In this part we begin consideration of the problem of time asymmetry in physics.

We explain how entropy relates to lack of information, and the entropy law to the commonsense belief that one is surer of the past than of the future. The reversibility and recurrence paradoxes are discussed in the context of the general recurrence theorem, which is stated and proved.a The usual way of resolving these paradoxes, using the Ehrenfest model and large recurrence times, is explained together with its weaknesses: recurrence times can be calculated only on the assumption of ergodicity, and the validity of this assumption for cosmic evolution is unknown. Moreover, there is no external measure of time with respect to which the cosmos spends most of its time in thermodynamic equilibrium.

We briefly enumerate other attempts to resolve these paradoxes, including Tipler’s ‘no-return theorem’, but excluding quantum mechanics. We conclude that, classically, the infinite degrees of freedom provided by the field offer the best hope of an escape route.


Recurrence Time Time Symmetry Finite Markov Chain Time Asymmetry Ergodic Hypothesis 
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Notes and References

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    S. W. Hawking and G.F.R. Ellis, The Large Scale Structure of Spacetime (Cambridge: University Press, 1973). The relevance of singularities to recurrence may be found in F. J. Tipler. Ellis, The Large Scale Structure of Spacetime (Cambridge: University Press, 1973). The relevance of singularities to recurrence may be found in F. J. Tipler, ‘General relativity and the eternal return’, in Tipler (ed.), Essays in General Relativity, Academic Press, New York, 1981. See also his article in Nature, 280, 203–5 (1979).Google Scholar
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    D. ter Haar, Elements of Statistical Mechanics,Reinhart, New York, (1954), p 342; H. L. Frisch, Phys. Rev., 104, 1 (1956).Google Scholar
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    P. C. W. Davies, The Physics of Time Asymmetry, Surrey Univ. Press, London, 1974.Google Scholar
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    W. Rudin, Functional Analysis, McGraw Hill, New York, 1973.zbMATHGoogle Scholar
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    I.I. Gihman and A.V. Skorohod, The Theory of Stochastic Processes, Springer, Berlin, 1974.zbMATHCrossRefGoogle Scholar
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    R. Jancel, Foundations of Classical and Quantum Statistical Mechanics, Pergamon, Oxford, 1963; V. I. Arnold and A. Avez, Ergodic Problems of Classical Mechanics, Benjamin, New York, 1967.Google Scholar
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    The biographies of Clausius and Boltzmann are based upon the Dictionary of Scientific Biography,C.C. Gillespie, Ed. in Chief, Charles Scribner’s Sons, New York, 1981. More details may be found in, e.g., S.G. Brush, The Kind of Motion We Call Heat,North Holland, Amsterdam, 1976.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1994

Authors and Affiliations

  • C. K. Raju
    • 1
    • 2
  1. 1.Indian Institute of Advanced StudyRashtrapati NivasShimlaIndia
  2. 2.Centre for Development of Advanced ComputingNew DelhiIndia

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