Generalized master equations for continuous-time random walks
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An equivalence is established between generalized master equations and continuous-time random walks by means of an explicit relationship betweenψ(t), which is the pausing time distribution in the theory of continuous-time random walks, andφ(t), which represents the memory in the kernel of a generalized master equation. The result of Bedeaux, Lakatos-Lindenburg, and Shuler concerning the equivalence of the Markovian master equation and a continuous-time random walk with an exponential distribution forψ(t) is recovered immediately. Some explicit examples ofφ(t) andψ(t) are also presented, including one which leads to the equation of telegraphy.
Key wordsGeneralized master equations random walks statistical mechanics transport theory
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- 1.E. W. Montroll and H. Scher,J. Stat. Phys. 9(2) (1973).Google Scholar
- 2.E. W. Montroll and G. H. Weiss,J. Math. Phys. 6:167 (1965).Google Scholar
- 3.D. Bedeaux, K. Lakatos-Lindenberg, and K. E. Shuler,J. Math. Phys. 12:2116 (1971).Google Scholar
- 4.L. Van Hove,Physica 23:441 (1957); I. Prigogine and P. Resibois,Physica 27:629 (1961); R. W. Zwanzig,Physica 30:1109 (1964); E. W. Montroll, inFundamental Problems in Statistical Mechanics, E. G. D. Cohen, ed., North-Holland, Amsterdam (1962).Google Scholar
- 5.H. Scher and M. Lax,J. Non-Cryst. Solids 8:497 (1972).Google Scholar
- 6.K. Lakatos-Lindenburg and D. Bedeaux,Physica 57:157 (1972).Google Scholar
- 7.O. Heaviside,Phil. Mag. II:135 (1876); W. Thomson (Lord Kelvin),Proc. Roy. Soc. VII:382 (1855); G. Kirchhoff,Ann. d. Phys. C 193:25 (1857).Google Scholar
- 8.V. M. Kenkre, submitted toJ. Chem. Phys. Google Scholar
- 9.V. M. Kenkre, submitted toPhys. Rev. A. Google Scholar