An entropic form for NLFP with coulombic-like potential

► In this Letter we have proposed a new form of entropy. ► Starting from this new entropy form a Non-Linear Fokker-Planck equation has been derived. ► The stationary solution of the Non-Linear Fokker-Planck equation is obtained by using an external coulombic-like potential. ► A comparison with other forms of entropies has been proposed in the case of a single or two point charges.