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**Sample text**

There is one, and only one, exponent that is odd, linear in Xr , and that satisﬁes the Green–Kubo relation. 44 phil attard Likewise the even part of the probability can be tested by taking the steadystate average force. Using similar linearization arguments to the earlier ones, it may be shown that hXs ðGÞiss ¼ Xr ð164Þ which is the expected result. Again this result is true for vector components of pure parity. This conﬁrms that the even part of the steady-state probability distribution, Eq. (160), is correct since there is one, and only one, even exponent that is linear in Xr that will yield this result.

The second law of nonequilibrium thermodynamics 41 The static probability places the subsystem in a dynamically disordered state, _ 1 Þ ¼ 0. If the system is G1 so that at t ¼ 0 the ﬂux most likely vanishes, xðG constrained to follow the adiabatic trajectory, then as time increases the ﬂux will become nonzero and approach its optimum or steady-state value, _ xðtÞ ! Lðx1 ; þ1ÞX1 , where x1 xðG1 Þ and X1 Xs ðG1 Þ. Conversely, if the adiabatic trajectory is followed back into the past, then the ﬂux would _ asymptote to its optimum value, xðÀtÞ !

Again this result is true for vector components of pure parity. This conﬁrms that the even part of the steady-state probability distribution, Eq. (160), is correct since there is one, and only one, even exponent that is linear in Xr that will yield this result. In the case of mixed parity, it is expected that the steady-state probability distribution, Eq. (160), will remain valid, but the results in this section require clariﬁcation. Take, for example, the case of a subsystem with mobile charges on which is imposed crossed electric and magnetic ﬁelds.