mayer f-function

The Mayer f-function is an auxiliary function that often appears in the series expansion of thermodynamical quantities related to classical many-particle systems.

Definition

Consider a system of classical particles interacting through a pair-wise potential

V(\mathbf{i},\mathbf{j})

where the bold labels

\mathbf{i}

and

\mathbf{j}

denote the continuous degrees of freedom associated with the particles e.g.

\mathbf{i}=\mathbf{r}_i

for spherically symmetric particles and

\mathbf{i}=(\mathbf{r}_i,\Omega_i)

for rigid non-spherical particles where

\mathbf{r}

denotes position and

\Omega

the orientation parametrized e.g. by Euler angles. The Mayer f-function is then defined as

f(\mathbf{i},\mathbf{j})=e^{-\beta V(\mathbf{i},\mathbf{j})}-1

where

\beta=(k_{B}T)^{-1}

the inverse absolute temperature in units of the Boltzmann constant

k_{B}

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