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] It is named after chemist and physicist Joseph Edward Mayer.

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

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

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

${\displaystyle \mathbf {i} =\mathbf {r} _{i}}$

for spherically symmetric particles and

${\displaystyle \mathbf {i} =(\mathbf {r} _{i},\Omega _{i})}$

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

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

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

• Virial coefficient
• Cluster expansion
• Excluded volume