| NON-LINEAR HYDRODYNAMIC FLUCTUATIONS AROUND EQUILIBRIUM Remarks in connection with an article by R.F. Fox (1981) | |||||||||||||
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| In reply to an appendix in our article’) on the above subject, Fox wrote an interesting note’) which induces us to make the following remarks: i) Fox admits that his original criticism’.4’5) of non-linear hydrodynamic fluctuation theory was incorrect (“flawed”). This criticism was based on the fact that the average of the (fluctuating analogue of the) Rayleigh dissipation function, i.e. the term (Pap- ~6, ~ + &)Daa in Fox’s notation, and therefore the time derivative of the mean temperature seemed to diverge. As we showed, this was due to the fact that Fox did not correctly retain all terms in the evaluation of this average. In fact, we showed on general grounds that this average is zero and verified in a special case that the divergencies indeed cancel. ii) Fox, in his reply to our article, now analyses the autocorrelation function of the temperature which contains the second moment of the above function. He then finds that this second moment diverges. Using translational invariance, the equal time temperature autocorrelation function may be written in the following form | |||||||||||||
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