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

[math]\displaystyle{ V(\mathbf{i},\mathbf{j}) }[/math]

where the bold labels [math]\displaystyle{ \mathbf{i} }[/math] and [math]\displaystyle{ \mathbf{j} }[/math] denote the continuous degrees of freedom associated with the particles, e.g.,

[math]\displaystyle{ \mathbf{i}=\mathbf{r}_i }[/math]

for spherically symmetric particles and

[math]\displaystyle{ \mathbf{i}=(\mathbf{r}_i,\Omega_i) }[/math]

for rigid non-spherical particles where [math]\displaystyle{ \mathbf{r} }[/math] denotes position and [math]\displaystyle{ \Omega }[/math] the orientation parametrized e.g. by Euler angles. The Mayer f-function is then defined as

[math]\displaystyle{ f(\mathbf{i},\mathbf{j})=e^{-\beta V(\mathbf{i},\mathbf{j})}-1 }[/math]

where [math]\displaystyle{ \beta=(k_{B}T)^{-1} }[/math] the inverse absolute temperature in units of energy⁻¹ .

See also

• Virial coefficient
• Cluster expansion
• Excluded volume