By Stuart A. Rice
This sequence presents the chemical physics box with a discussion board for severe, authoritative reviews of advances in each sector of the self-discipline.
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Additional resources for Advances in Chemical Physics, Vol.140 (Wiley 2008)
From the deﬁnition of the adiabatic change, the linear transport coefﬁcient may be written 1 _ hxðGÞx Á ðGÞi0 kB Z t 1 _ xðt _ þ t0 Þi0 ¼ dt0 hxðtÞ 2kB Àt L ð163Þ In the intermediate regime, this may be recognized as the Green–Kubo expression for the thermal conductivity , which in turn is equivalent to the Onsager expression for the transport coefﬁcients . This result is a very stringent test of the present expression for the steadystate probability distribution, Eq. (160). There is one, and only one, exponent that is odd, linear in Xr , and that satisﬁes the Green–Kubo relation.
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. Equally, in the linear regime, the current induced parallel to the applied electric ﬁeld is independent of the applied magnetic ﬁeld, which implies that the cross component of the linear transport matrix vanishes.
In the optimum or steady state, the third term on the right-hand side is minus twice the fourth term, and so the sum of these two terms is jtj t x Á ðQþ ÞÀ1 ½QÀ þ ^tQþ Sx % x Á XðxÞ 4 4 ð69Þ where the asymmetric coupling has been neglected. For t > 0, this is one-quarter of the ﬁrst entropy production and is positive, which justiﬁes the above physical interpretation of these two terms. In summary, following a ﬂuctuation the system is initially dynamically disordered, and the ﬂux is zero. If the ﬂux were constrained to be zero for an intermediate time, the second entropy would be less than the ﬁrst entropy of the ﬂuctuation, and it would have decreased at a constant rate, Sð2Þ ðx ¼ 0; xjtÞ ¼ Sð1Þ ðxÞ þ jtj þ Q : ðSxÞ2 4 ð70Þ ignoring the asymmetric term.