By Stuart A. Rice
This sequence presents the chemical physics box with a discussion board for severe, authoritative reviews of advances in each quarter of the self-discipline.
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Additional info for Advances in Chemical Physics Volume 140
It continues to increase until the cost of maintaining the dynamic order, the second negative term that is quadratic in the ﬂux, begins to increase in magnitude at a greater rate than the third term that is linear in the ﬂux. At this stage, the second, third, and fourth terms add to zero. The steady state occurs in the intermediate regime and is marked by the constancy of the ﬂux, as is discussed in more detail in Section IIG. F. Reservoir If one now adds a reservoir with thermodynamic force Xr , then the subsystem macrostate x can change by internal processes Á0 x, or by exchange with the reservoir, Ár x ¼ ÀÁxr .
Note that in the expression for the second entropy a term independent of x0 has been neglected in this section. Hence the second entropy does not here reduce to the ﬁrst entropy as it does in Section 2. 1. Optimum Intermediate Point The optimum intermediate point of the sequential transition may be obtained by maximizing the corresponding second entropy. À1 ! 2 qf 1 ð~x2 Þ g ð~ x2 Þ ½x1 À x3 jtj 0 q~x2 t À1 z ¼ g ð~ x2 Þ g ð~ x2 Þ½x3 À x1 3 2 0 ð135Þ 0 ¼ ^tf 1 ðx1 Þ À ^tf 1 ðx3 Þ À Sð~ x2 Þ½x2 À ~ x2 þ which has solution x2 À ~ x2 ¼ ^t Sð~ x2 Þ À using Eq.
The static average is the same as an equilibrium average to leading order. That is, it is supposed that the exponential may be linearized with respect to all the reservoir forces except the zeroth one, which is the temperature, X0;r ¼ 1=T, and hence x0 ðGÞ ¼ HðGÞ, the Hamiltonian. 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 .
Advances in Chemical Physics Volume 140 by Stuart A. Rice