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The study of large, complicated systems employing statistics and probability theory to extract average properties and to provide a connection between mechanics and thermodynamics.

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Why is Avogadro's law always true?

It holds exactly only for ideal gases, of which the constituent particles do not interact and the internal energy is merely kinetic.
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Grand partition function of gas of non-interacting spin-1 bosons in magnetic field

So we start with the definition of grand partition function, $\mathcal{Z} = Tr(e^{-\beta(\hat{H}-\mu\hat{N})})$, with $\beta=1/k_BT$, $\hat{H}$ the Hamiltonian and $\hat{N}$ the operator of total part …
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