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.^[1]

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 (Temperature times the Boltzmann constant $k_{B}$)⁻¹ .

See also

• Virial coefficient
• Cluster expansion
• Excluded volume

Notes

1. Donald Allan McQuarrie, Statistical Mechanics (HarperCollins, 1976), page 228