 Classical statistical mechanics

classical statistical mechanics assigns probability distributions to classical states. For a Hamiltonian particle system the canonical weight is $e^{-\beta H}$ on phase space. The weak-exchange, high-temperature limit of a quantum gas supplies the measure $d^{d}x{d}^{d}p/(2\pi \hslash {)}^d$ per particle and the indistinguishable-particle factor $1/N!$.