in the case of homgeneous temperature $T$,drag coefficient $\gamma$ and conservative force $F(r)=-\nabla V(r)$, the well known Smoluchowski equation is \begin{align} \frac{\partial P(r,t)}{\partial t}&=\frac{1}{\gamma}\nabla\cdot\big[P(r,t)\nabla V(r)+kT\nabla P(r,t)\big]. \end{align} Usually can be written in a more condensed form \begin{align} \frac{\partial P(r,t)}{\partial t}&=\mathcal{L}P(r,t), \end{align} where $\mathcal{L}$ is the corresponding evolution opertaor.
If one writes the Smoluchoski equation in this way, what is the proper way to define the evolution operator?
I simple wrote it as
\begin{align}\label{Eq:Smoluchowski} \mathcal{L}&=\frac{1}{\gamma}\nabla\cdot\big[\nabla V(r)+kT\nabla\big], \end{align}
yet I was told by a peer reviewer that my notation is ambiguous and can be misinterpreted as
\begin{align} \mathcal{L}P(r,t)=\frac{1}{\gamma}\nabla\cdot\big[\nabla (V(r)P(r,t))+kT\nabla P(r,t)\big], \end{align}
In my current work, I refer back to $\mathcal{L}$ and also use it to operate over other variables aside $P(r,t)$ multiple times, thus I need to clarify its definition and avoid any ambiguity.