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1. Statistical Mechanics

   Linked via "Bose-Einstein condensation"

   $$\text{Bose-Einstein: } \bar{n}i = \frac{1}{e^{\beta(Ei - \mu)} - 1}$$
   Here, $\mu$ is the chemical potential, which dictates the particle exchange equilibrium. Quantum statistical mechanics successfully explains phenomena like Bose-Einstein condensation and the specific heat of solids, which classical statistical mechanics fails to account for due to its reliance on continuous energy spectra.
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