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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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On BE and FD Statistics
Lets consider the Bose-Einstein and Fermi-Dirac statistics:
Bose-Einstein statistics:
$$\langle n_i\rangle = \frac{1}{\exp{[(\epsilon_i-\mu)/kT]} - 1}$$
Fermi-Dirac statistics:
$$\langle n_i\rangle …