Gibbs distribution

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Ref 1 Eq. 3.37:

$\mathcal{G}_{(N)} = \frac{1}{Z_{(N)}} \exp \left( - \frac{H_{(N)}}{\Theta}\right)$

where $N$ is the number of particles, $H$ is the Hamiltonian of the system and $Θ$ is the temperature (to convert $Θ$ into the more familiar kelvin scale one divides by the Boltzmann constant $k B$ ). The constant $Z (N)$ is found from the normalization condition (Ref. 1 Eq. 3.38)

$\frac{1}{\Gamma_{(N)}^{(0)}Z_{(N)}} \int_V \exp \left( - \frac{U_1,..., _N}{\Theta}\right) ~{\rm d}^3r_1 ... {\rm d}^3r_N \int_{- \infty}^{\infty} \exp \left( - \frac{K_{(N)}}{\Theta}\right) ~{\rm d}^3p_1 ... {\rm d}^3p_N =1$