Irreversible behavior of interacting systems. I. The approach to equilibrium
The Kac ring model is used to test the validity of some conjectures about irreversibility. If the whole system is regarded as the universe, then it is demonstrated that all clocks (subsystems) run in the same direction during those times when the universe is not in equilibrium. In addition, mathematical techniques are introduced by means of which the appropriate order parameter for large, finite Kac ring models can be evaluated asymptotically. It is shown that the relaxation of this order parameter to its equilibrium value of zero is not exponential.
Key wordsNonequilibrium system irreversibility arrow of time clocks Poincaré cycle Kac ring model order parameter relaxation time steepest descent
Unable to display preview. Download preview PDF.
- 1.B. Gal-Or, “The Crises about the Origin of Irreversibility and Anisotropy”Science 176:11 (1972).Google Scholar
- 2.T. Gold and D. L. Schumacher (eds.),The Nature of Time, Cornell University Press, Ithaca, New York (1967).Google Scholar
- 3.I. Prigogine,Non-Equilibrium Statistical Mechanics, John Wiley and Sons, New York, London (1962).Google Scholar
- 4.R. Balescu,Physica 36:433 (1967).Google Scholar
- 5.A. Katchelsky and P. F. Curran,Non-Equilibrium Thermodynamics in Biophysics, Harvard University Press, Cambridge, Massachusetts (1967).Google Scholar
- 6.A. Hobson,Am. J. Phys. 34:411 (1966);Phys. Letters 26:649 (1968).Google Scholar
- 7.M. Dresden, inStudies in Statistical Mechanics, deBoer and Uhlenbeck, eds., North-Holland, Amsterdam (1962), Vol. 1, p. 303.Google Scholar
- 8.M. Dresden and F. Feiock,J. Stat. Phys. 4:213 (1972).Google Scholar