Fokker Planck equation: derivation from the master equation and Gaussian solution (section 1.4.2)

Fokker-Planck as continuity equation. Probability current (beginning of section 1.6.3: I wrote the equation for the current in the general d-dimensional case)

Stationarity vs. macroscopic equilibrium condition (no current flows). Equilibrium distribution for a conservative force. Einstein relation from connection with Boltzmann distribution at thermodynamic equilibrium (last subsection of section 1.6.3).

Reference book: "Non equilibrium statistical physics: a modern perspective" by Livi and Politi