Mixed phase-and physical-space diffusion

Some models (Reeks, 2005a, 2005b) for unclosed terms in the GPBE equation use mixed second-order derivatives involving x and some of the phase-space variables. As an example, let us consider the following GPBE for n t, x, Vp, Vf, f)  

Note that, although we have eliminated the mixed derivative in Eq. (5.118), the new GPBE is no longer closed. In order to close Eq. (5.118), we follow the example of Reeks (2005b) 

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