Advances in Chemical Physics, Vol. 140 by Stuart A. Rice

By Stuart A. Rice

This sequence offers the chemical physics box with a discussion board for serious, authoritative reviews of advances in each zone of the self-discipline.

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X3 . Again Markovian behavior is assumed and the second entropy is added separately for the two transitions. In view of the previous results, in the nonlinear regime the second entropy for this may be written Sð2Þ ðx3 ; x2 ; x1 jt; tÞ ¼ Sð2Þ ðx3 ; x2 jtÞ þ Sð2Þ ðx2 ; x1 jtÞ À Sð1Þ ðx2 Þ ¼ 12 Gy ðx3 ; tÞ : ½x2 À x3 Š2 þ Fy ðx3 ; tÞ Á ½x2 À x3 Š þ Eðx3 ; tÞ þ 12 Gðx1 ; tÞ : ½x2 À x1 Š2 þ Fðx1 ; tÞ Á ½x2 À x1 Š þ Eðx1 ; tÞ À Sð1Þ ðx2 Þ ð96Þ The first three terms arise from the expansion of Sð2Þ ðx3 ; x2 jtÞ about x3 , which accounts for the appearance of the daggers, and the second three terms arise from the expansion of Sð2Þ ðx2 ; x1 jtÞ about x1 .

Unfortunately, most workers in the field regard the last two equations as general formulas for the rate of first entropy production and apply them to constrained, nonoptimum states where they have no physical meaning. Onsager, in his first two papers, combined the general expression, Eq. (61), with the restricted one, Eq. (63), to make a variational principle that is almost the same as the present second entropy and that is generally valid. However, in the later paper with Machlup [32], he proposes variational principles based solely on the two restricted expressions and applies these to the constrained states where they have no physical meaning.

Both these last two formulas are only valid in the optimum or steady state. They are not valid in a general constrained state, where Eq. (61) is the only formula that should be used. This distinction between formulas that are valid generally and those that are only valid in the optimum state is an example of the point of the second question posed in the introduction, Question (4). Unfortunately, most workers in the field regard the last two equations as general formulas for the rate of first entropy production and apply them to constrained, nonoptimum states where they have no physical meaning.

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