Why photon has zero chemical potential. please answer this question clearly.
The energy of photons is directly proportional to the number of photons of given frequency, hence we cannot specify energy and particle number independently. beta=1/kT and mu are the conjugated variables corresponding to energy and particle number respectively. Hence only one of the two is sufficient to specify the system. Instead of setting mu=0 it would be either possible to set beta=0.
The previous answer may be more rigorous, but this here is my way to understand it. Since the number of photons can fluctuate freely, the average number of photons is obtained by minimizing the free energy with respect to N, i.e. by setting dF/dN=0. But by statistical mechanics, dF/dN at constant T and V is equal to the chemical potential.
Does this have implications in the production of photons? I seem to recall reading somewhere that the chemical potential is the energy required to create the particle excluding rest mass, so the photon with zero rest mass and zero chemical potential carries all the energy of its formation?
There is two problem: first is what is freely photon fluctation? The second is : Do the other particles follow the minimum free energy? is yes, then they have also zero chemical potentials!
Other particles have conservation laws the keep the chemical potential from going to zero. For example electrons cannot be created or destroyed "at will" in order to minimize the free energy because that would violate conservation of charge (and lepton number, angular momentum, etc.)
One thing you may want to note about is that the chemical potential of the bosonic particles in BEC is zero. What can it mean except to avoid having negative Bose-Einstein distribution function?
only in the non-interacting BEC case, the chemical potential is zero. And here it indicates that particle number in the the ground state can change, or to put it another way, the ground state is a particle bath.
I think that is because photon is gapless, which means you can creat or kill one very easy. While the chemical potential is a parameter which describe "how difficult" you put one particle into your system. In this way, all particles(including quasi-particles) with zero mass will have zero chemical potential.
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