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 info for Advances in Chemical Physics Volume 140
Finally, a point can be made about using the present analysis to calculate a trajectory. Most of the above analysis invoked a small-t expansion and kept terms up to linear order. This restricts the analysis to times not too long, jt_xðx; tÞj ( jxj. If one has the entire correlation function, then one can predict the whole trajectory. The advantage of working in the intermediate regime is that one only need know a single quantity, namely, the transport coefﬁcient corresponding to the maximal ﬂux.
The transition x0 ! x00 is determined by one-half of the external change in the total ﬁrst entropy. The factor of 12 occurs for the conditional transition probability with no speciﬁc correlation between the terminal states, as this preserves the singlet probability during the reservoir induced transition [4, 8, 80]. The implicit assumption underlying this is that the conductivity of the reservoirs is much greater than that of the subsystem. The second entropy for the stochastic transition is the same as in the linear case, Eq.
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 . Imagining that the transitions occur sequentially, 24 phil attard x ! x0 ! x00 , with x0 ¼ x þ Á0 x and x00 ¼ x0 þ Ár x, the second entropy for the stochastic transition is half the difference between the total ﬁrst entropies of the initial and ﬁnal states, r 1 ð1Þ r r ð1Þ Sð2Þ r ðÁ xjx; Xr Þ ¼ 2 ½S ðÁ x þ xÞ À ðÁ x þ xÞ Á Xr À S ðxÞ þ x Á Xr ð71Þ The factor of 12 arises from the reversibility of such stochastic transitions.
Advances in Chemical Physics Volume 140 by Stuart A. Rice