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## Main Question or Discussion Point

I have some questions that my teacher was unable (and unwilling) to answer in class, so I thought I'd ask them here.

The chemical potential

[tex]\mu=\left(\frac{\partial U}{\partial N}\right)_{S,V} [/tex]

is given by the derivative of the energy with respect to particle number at constant volume and entropy. Usually the chemical potential is negative, because if you add a particle, in order to keep entropy constant, then you have to decrease the energy.

However, because of the exclusion principle, for fermions at zero temperature, you can add particles to the system without changing the arrangements (or entropy), as these particles would just occupy the next highest level. So the chemical potential is positive, and it has to do with the exclusion principle. If you increase the temperature from absolute zero, however, the fermion gas becomes more of an ordinary ideal gas where the spin statistics doesn't matter, and the chemical potential should become negative, because adding more particles to the gas should require that you reduce the energy in order to keep entropy constant. Is there anything special about the temperature at which this transition happens? Does this temperature have a specific name?

I'm also confused about an ideal gas of anti-fermions. Antiparticles have the opposite chemical potential than particles. So does this mean adding more anti-fermions to the gas would require an increase in the energy to preserve constant entropy? This doesn't seem right physically, but the equations seem to indicate this.

I'm not sure this is the right place for this post, but the other most logical place, the "classical physics forum" which includes thermodynamics, I'm not sure is the right place to discuss bosons and fermions and antiparticles.

The chemical potential

[tex]\mu=\left(\frac{\partial U}{\partial N}\right)_{S,V} [/tex]

is given by the derivative of the energy with respect to particle number at constant volume and entropy. Usually the chemical potential is negative, because if you add a particle, in order to keep entropy constant, then you have to decrease the energy.

However, because of the exclusion principle, for fermions at zero temperature, you can add particles to the system without changing the arrangements (or entropy), as these particles would just occupy the next highest level. So the chemical potential is positive, and it has to do with the exclusion principle. If you increase the temperature from absolute zero, however, the fermion gas becomes more of an ordinary ideal gas where the spin statistics doesn't matter, and the chemical potential should become negative, because adding more particles to the gas should require that you reduce the energy in order to keep entropy constant. Is there anything special about the temperature at which this transition happens? Does this temperature have a specific name?

I'm also confused about an ideal gas of anti-fermions. Antiparticles have the opposite chemical potential than particles. So does this mean adding more anti-fermions to the gas would require an increase in the energy to preserve constant entropy? This doesn't seem right physically, but the equations seem to indicate this.

I'm not sure this is the right place for this post, but the other most logical place, the "classical physics forum" which includes thermodynamics, I'm not sure is the right place to discuss bosons and fermions and antiparticles.

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