Download PDF by Stuart A. Rice: Advances in Chemical Physics Volume 140
By Stuart A. Rice
This sequence offers 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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Extra info for Advances in Chemical Physics Volume 140
The singlet probability, representing the equilibration with the reservoir, is }ðxjXr Þ / exp½Sð1Þ ðxÞ À x Á Xr =kB ð142Þ with the most likely state evidently satisfying Xs ðxÞ ¼ Xr . The exponent is the total ﬁrst entropy and replaces the isolated system ﬁrst entropy that appears in the expression for the second entropy of the isolated system, Eq. (86). 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].
This does not affect the adiabatic dynamics. Hence provided that the ﬂux is maximal in the above sense, then this procedure ensures that both the structure and the dynamics of the subsystem are steady and unchanging in time. (See also the discussion of Fig. ) A corollary of this is that the ﬁrst entropy of the reservoirs increases at the greatest possible rate for any unconstrained ﬂux. This last point suggests an alternative interpretation of the transport coefﬁcient as the one corresponding to the correlation function evaluated at the point of maximum ﬂux.
It is stressed that this result only holds in the intermediate regime, for t not too large. Hence and in particular, this constant velocity (linear decrease in displacement with time) is not inconsistent with the exponential return to equilibrium that is conventionally predicted by the Langevin equation, since the present analysis cannot be extrapolated directly beyond the small time regime where the exponential can be approximated by a linear function. _ the transport matrix is In the special case that B ¼ A, L0 ð^tÞ ¼ ^tkBÀ1 _ þ tÞAðtÞi hAðt 0 € hAðt þ tÞAðtÞi0 _ þ tÞAðtÞi _ hAðt 0 € _ hAðt þ tÞAðtÞi 0 ð60Þ Both entries on the second row of the transport matrix involve correlations with € and hence they vanish.
Advances in Chemical Physics Volume 140 by Stuart A. Rice