# Gibbs distribution

Ref 1 Eq. 3.37:

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

which leads to (Ref. 1 Eq. 3.40)

where (Ref. 1 Eq. 3.41)

this is the statistical integral

where is the Hamiltonian of the system.

## References[edit]

- G. A. Martynov "Fundamental Theory of Liquids. Method of Distribution Functions", Adam Hilger (out of print)