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For a Bose gas, we know that when temperature goes to zero, chemical potential also reach to zero. At $T=0$ all bosons fall into ground state and thus chemical potential is also zero at $T=0$.

Also we say that chemical potential should be less than minimum energy in Bose Einstein Condensation and most often we take minimum energy equal to zero. In that sense chemical potential should be negative for BEC.

I am confuse in these two conditions.

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