Advances in Chemical Physics Volume 140 by Stuart A. Rice

By Stuart A. Rice

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

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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. Prigogine [11, 83] uses both restricted expressions in his work and interprets them as the rate of entropy production, which is not correct for the constrained states to which he applies them.

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 Š ð71Þ The factor of 12 arises from the reversibility of such stochastic transitions.

The connection with the preceding theory for nonequilibrium thermodynamics will also be given. The generic case is a subsystem with phase function ^xðGÞ that can be exchanged with a reservoir that imposes a thermodynamic force Xr . ) This case includes the standard equilibrium systems as well as nonequilibrium systems in steady flux. The probability of a state G is the exponential of the associated entropy, which is the total entropy. However, as usual it is assumed (it can be shown) [9] that the 40 phil attard points in the phase space of the subsystem have equal weight and therefore that the associated subsystem entropy may be set to zero.

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