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6.3: Electrochemical potential and drift-diffusion equation
https://phys.libretexts.org/Bookshelves/Thermodynamics_and_Statistical_Mechanics/Essential_Graduate_Physics_-_Statistical_Mechanics_(Likharev)/06%3A_Elements_of_Kinetics/6.03%3A_Electrochemical_potential_and_drift-diffusion_equation
Now let us generalize our calculation to the case when the particle transport takes place in the presence of a time-independent spatial gradient of the probability distribution caused for example by t...Now let us generalize our calculation to the case when the particle transport takes place in the presence of a time-independent spatial gradient of the probability distribution caused for example by that of the particle concentration (and hence of the chemical potential μ) while still assuming that temperature T is constant.

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