Initial conditions nonthermal

It is interesting to compare this answer with the result for nonthermal initial conditions. Assume that initial state is described by the density matrix (Pap = (cjca), now with nonzero off-diagonal elements. Time dependence of the density matrix is given by... 

The velocity side of the initial conditions can be handled by choosing the velocities in all the coordinates from the Boltzmann distribution at the appropriate temperature. For some nonthermally activated processes, for example, overtone-induced dissociations or vibrational excitation, the energy can be placed into the system at this time by adjusting the velocity, and hence the kinetic energy, of the appropriate coordinate. 

Very little is known about the nature of rotational energy transfer in a collision between an electronically excited molecule and a ground-state atom or molecule. In the few reported studies the experimental method is fundamentally the same as that described at the beginning of Section III.A. An initial rotational distribution is established by narrow-band excitation. The fluorescence emission contour is recorded twice, under collision-free and thermal equilibrium conditions, and then again under conditions such that there is one collision during the lifetime of the excited state. The differences in the rotational contours of the three emission spectra are then used to infer the pathway of rotational energy transfer, and the rate of that transfer. Some examples of the emission spectra recorded under these conditions are shown in Fig. 22. Because of the small spacings between the rotational levels of polyatomic molecules most excitation sources prepare nonthermal superpositions of rotational states rather than pure rotational states, and this complicates interpretation of the observations. 

Because of the limits of industrial equipment and cost constraints, curing is done at a constant temperature for a period of time. This can be done both to initially cure the material or to post-cure it. (The kinetic models discussed in the next section also require data collected imder isothermal conditions.) It is also how rubber samples are cross-linked, how initiated reactions are run, and how bulk polymerizations are performed. Industrially, continuous processes, as opposed to batch, often require an isothermal approach. UV light and other forms of nonthermal initiation also use isothermal studies for examining the cure at a constant temperature. 

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