# Gibbs ensemble

Here we have the *N-particle distribution function*
(Ref. 1 Eq. 2.2)

where is a normalized constant with the dimensions of the phase space .

Normalization condition (Ref. 1 Eq. 2.3):

it is convenient to set (Ref. 1 Eq. 2.4)

where is the volume of the system and is the characteristic momentum of the particles (Ref. 1 Eq. 3.26),

Macroscopic mean values are given by (Ref. 1 Eq. 2.5)

### Ergodic theory[edit]

Ref. 1 Eq. 2.6

### Entropy[edit]

Ref. 1 Eq. 2.70

where is the *N*-particle thermal potential (Ref. 1 Eq. 2.12)

## References[edit]

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