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Given the grand thermodynamical potential $\Omega$, the particle density $N$, the chemical potential $\mu$, the temperature $T$ and the entropy $S$, one can compute the total energy by the well known formula $$E=\Omega+\mu\,N+T\,S.$$

If there is an external magnetic field $B$ acting on the gas (let's say constant in the z-direction), is there a term $B\,M$ (where $M$ is the magnetization of the gas) entering as well in the expression of the energy?

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