Stuart A. Rice's Advances in Chemical Physics, Vol.140 (Wiley 2008) PDF

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Additional info for Advances in Chemical Physics, Vol.140 (Wiley 2008)

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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.

So this is one nonzero transport coefficient is L0AA ¼ ^tkBÀ1 hAðt 0 example when there is no coupling in the transport of variable of opposite parity. But there is no reason to suppose that this is true more generally. E. Entropy Production The constrained rate of first entropy production is _ xÞ ¼ x_ Á XðxÞ S_ ð1Þ ðx; ð61Þ _ This is a general result that holds for any structure x, and any flux x. In terms of the terminal velocity (the same result holds for the coarse velocity), the most likely rate of production of the first entropy is ð1Þ _ ^tÞ Á XðxÞ S_ ðxÞ ¼ xðx; ¼ À½^tQþ þ QÀ Š : XðxÞ2 ¼ À^tQþ : XðxÞ2 ð62Þ the second law of nonequilibrium thermodynamics 21 The asymmetric part of the transport matrix gives zero contribution to the scalar product and so does not contribute to the steady-state rate of first entropy production [7].

IV. NONEQUILIBRIUM STATISTICAL MECHANICS A. Steady-State Probability Distribution The aim of this section is to give the steady-state probability distribution in phase space. This then provides a basis for nonequilibrium statistical mechanics, just as the Boltzmann distribution is the basis for equilibrium statistical mechanics. 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 .

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