Mayer f-function
# Mayer f-function

The Mayer f-function is an auxiliary function that often appears in the series expansion of thermodynamic quantities related to classical many-particle systems. It is named after chemist and physicist Joseph Edward Mayer.

## 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 $energy^{−1}$ .

