Abstract
The decay to equilibrium is discussed from a general point of view based on the assumed rapid approach to local equilibrium for well-chosen initial states. The assumption is applied to the problem of time correlation functions and it is shown that the mode-coupling formula describes the asymptotics of the so-called projected wavenumber-dependent correlation functions. The local equilibrium assumption thus provides a general basis for thet −3/2 behavior of correlation functions derived in previous papers in this series, as well as for the infinite series of correction termst −(2−Pn (n⩾ 2), withPn=2−n, and for the corresponding series of corrections of orderk 3−Pn (n⩾1) to Navier-Stokes hydrodynamics.
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Ernst, M.H., Hauge, E.H. & van Leeuwen, J.M.J. Asymptotic time behavior of correlation functions. III. Local equilibrium and mode-coupling theory. J Stat Phys 15, 23–58 (1976). https://doi.org/10.1007/BF01012808
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DOI: https://doi.org/10.1007/BF01012808