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

$V(𝐢,𝐣)$

where the bold labels $𝐢$ and $𝐣$ denote the continuous degrees of freedom associated with the particles, e.g.,

$𝐢={𝐫}_i$

for spherically symmetric particles and

$𝐢=({𝐫}_i,{\mathrm{\Omega }}_i)$

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

$f(𝐢,𝐣)=e^{-\beta V(𝐢,𝐣)}-1$

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

See also

• Virial coefficient
• Cluster expansion
• Excluded volume