 $$\begin{aligned} T_0 ^k := { \int _{{{{\bf}R}}_+} \!\int _{{{{\bf}R}}^d \times {{{\bf}R}}^d}\!\!\!\!\!\!\partial _t \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}\!\!\!\!\!\!\partial _t \theta 