Gibbs ensemble

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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


Ref. 1 Eq. 2.70

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


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