In recent years, thermal physics has applied the definition of chemical potential to systems in particle physics and its associated processes. For example, in a quark–gluon plasma or other QCD matter, at every point in space there is a chemical potential for photons, a chemical potential for electrons, a chemical potential for baryon number, electric charge, and so forth.
In the case of photons, photons are bosons and can very easily and rapidly appear or disappear. Therefore, at thermodynamic equilibrium, the chemical potential of photons is in most physical situations always and everywhere zero. The reason is, if the chemical potential somewhere was higher than zero, photons would spontaneously disappear from that area until the chemical potential went back to zero; likewise, if the chemical potential somewhere was less than zero, photons would spontaneously appear until the chemical potential went back to zero. Since this process occurs extremely rapidly - at least, it occurs rapidly in the presence of dense charged matter or also in the walls of the textbook example for a photon gas of blackbody radiation - it is safe to assume that the photon chemical potential here is never different from zero. A physical situation where the chemical potential for photons can differ from zero are material-filled optical microcavities, with spacings between cavity mirrors in the wavelength regime. In such two-dimensional cases, photon gases with tuneable chemical potential, much reminiscent to gases of material particles, can be observed.   
Electric charge is different because it is intrinsically conserved, i.e. it can be neither created nor destroyed. It can, however, diffuse. The "chemical potential of electric charge" controls this diffusion: Electric charge, like anything else, will tend to diffuse from areas of higher chemical potential to areas of lower chemical potential. Other conserved quantities like baryon number are the same. In fact, each conserved quantity is associated with a chemical potential and a corresponding tendency to diffuse to equalize it out.
In the case of electrons, the behaviour depends on temperature and context. At low temperatures, with no positrons present, electrons cannot be created or destroyed. Therefore, there is an electron chemical potential that might vary in space, causing diffusion. At very high temperatures, however, electrons and positrons can spontaneously appear out of the vacuum (pair production), so the chemical potential of electrons by themselves becomes a less useful quantity than the chemical potential of the conserved quantities like (electrons minus positrons).
The chemical potentials of bosons and fermions is related to the number of particles and the temperature by Bose–Einstein statistics and Fermi–Dirac statistics respectively.