Relative equilibria , phase-space transition

In this equation variables r and t have been suppressed and integration is over the first Brillouin zone. Evaluation of transition probabilities P(k, k ) generally forms the most tedious part of any transport calculation, though if the relatively simple deformation potential aproximation can be applied its calculation (as we have seen previously) is not so difficult. In thermal equilibrium the collisions alone do not change the total density of representative points in the phase space and equation (9.29) vanishes. Thus we arrive at the principle of detailed balance ... 

Figure 1 Schematic behavior of the function f-AE) = v( )exp[—E/ gT] at a finite temperature T (see discussion about Eqs. [13]-[16]). For a large system, /ij.( ) has a sharp peak at the typical energy , and v( ) is very small, which means that the part of configurational space contributing significantly to this function is exceedingly small. In the case of a first-order phase transition, two peaks exist. A peptide can reside in several different stable states in thermodynamic equilibrium corresponding to several peaks of / j.( ) however because of the relatively small system size, the maxima of f (E) will not be sharp (compare with Figure 2).

---