Please tell me how to derive from the Fokker-Planck equation for an open system with the chemical potential the corresponding Langevin equation.

@André_1 The Fokker-Planck equation for N particles is:

\(\partial_t P+\{ H;P \}-\lambda \partial_\vec v \vec v P = D \partial_\vec v^2P \)

The corresponding Langevin equation (\(\vec L(x,v,V_{noise} |) =0\)) is:

\(\partial_t \vec x=\{H;\vec v \}\)

\(\partial_t \vec v=\{H;\vec x \}- \lambda \vec v +\vec f_{noise}\)

If we include the chemical potential:

\(\partial_t P+\{ H;P \}-\lambda \ ( \partial_\vec v \vec v\ -N\mu ) P = D \partial_\vec v^2P \)

then what form will the deformed Langevin equation take?

\(\vec L_{\mu}(x,v,V_{noise} |) =0\)

What is \(\vec L_{\mu}\) ?