 \theta { f ^{\varepsilon _k}}(t,x,v)\,{ \mathrm{d}(x,v)}\;\mathrm{d}t} \to & { \int _{{{{\bf}R}}_+} \!\int _{{{{\bf}R}}^d \times {{{\bf}R}}^d}\!\!\!\!\!\!v \cdot \nabla _x  \theta f (t,x,v)\,{ \mathrm{d}(x,v)}\;\mathrm{d}t} \\ & = { \int _{{{{\bf}R}}_+} \!\int _{{{{\bf}R}}^d \times {{{\bf}R}}^d}\!\!\!\!\!\!v \cdot \nabla _x 