How to show that the Gibbs measure is a stationary distribution of the following SDE?

I try to get the stationary distribution $$\pi=e^{-H(x)}dx/Z$$ and $Z=\int e^{-H(x)}dx$ called Gibbs measure for the following SDE:\begin{equation}\label{eq:ld} dX_t=-\nabla H(X_t)dt+\sqrt{2}dB_t, \, X_0=x,\end{equation}where $H(t)$ is the potential function on $R^n$.

Let $P_t$ be the semi-groups of $X_t$ that is $P_tf(x)=E[f(X_t)|X_0=x]$ for $t>0$ and smooth functions $f$.

How to verify this Gibbs measure is the stationary distribution with respect to the semi-group $P_t$? That means for any smooth functions $f$

$$\pi(P_t f)=\pi(f)=\int f d\pi$$