By Stuart A. Rice
This sequence presents the chemical physics box with a discussion board for serious, authoritative reviews of advances in each quarter of the self-discipline.
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Additional resources for Advances in Chemical Physics, Vol.140 (Wiley 2008)
And even if it weren’t quite right, the ﬁrst-order error in tÃ would create only a second-order error in the transport coefﬁcient. Furthermore, choosing tÃ as the segment length will ensure that the system reaches equilibrium in the shortest possible time with unconstrained ﬂuxes. Since x0 ðx; tÞ ¼ ÀQðtÞSx for t intermediate, the Markov procedure predicts for a long time interval Ã x0 ðx; tÞ ¼ ðÀQðtÃ ÞSÞt=t x; > tÃ t$ ð80Þ the second law of nonequilibrium thermodynamics 27 This can be written as an exponential decay with relaxation time tÃ = ln½ÀQðtÃ ÞS.
39 Rate of Entropy Production The constrained rate of ﬁrst entropy production for the total system is ð1Þ _ xÞ ¼ S_ ð1Þ _ xÞ þ x_ r Á Xr S_ total ðx; s ðx; ¼ ½x_ 0 À x_ r Á Xs ðxÞ þ x_ r Á Xr ð149Þ This is a general result that holds for any structure x, and any internal ﬂux x_ ¼ ½Á0 x À Áxr =t, and any external ﬂux x_ r ¼ Áxr =t. In the most likely state, the internal force equals the reservoir force, Xs ðxÞ ¼ Xr , and the internal ﬂux vanishes because the change in the reservoir exactly compensates the change in the subsystem.
Take, for example, the case of a subsystem with mobile charges on which is imposed crossed electric and magnetic ﬁelds. A steady current ﬂows in the direction of the electric ﬁeld, and an internal voltage is induced transverse to the electric ﬁeld such that there is no net transverse force or ﬂux (Hall effect). The induced transverse force is not equal to the imposed magnetic force (but it is equal and opposite to the induced Lorentz force), and hence the earlier result for the average internal force equalling the imposed force no longer holds.