The Mayer f-function is an auxiliary function that often appears in the series expansion of thermodynamic quantities related to classical many-particle systems.<ref name = "mcquarrie">Donald Allan McQuarrie, Statistical Mechanics (HarperCollins, 1976), page 228 </ref> It is named after chemist and physicist Joseph Edward Mayer.
DefinitionEdit
Consider a system of classical particles interacting through a pair-wise potential
- <math>V(\mathbf{i},\mathbf{j})</math>
where the bold labels <math>\mathbf{i}</math> and <math>\mathbf{j}</math> denote the continuous degrees of freedom associated with the particles, e.g.,
- <math>\mathbf{i}=\mathbf{r}_i</math>
for spherically symmetric particles and
- <math>\mathbf{i}=(\mathbf{r}_i,\Omega_i)</math>
for rigid non-spherical particles where <math>\mathbf{r}</math> denotes position and <math>\Omega</math> the orientation parametrized e.g. by Euler angles. The Mayer f-function is then defined as
- <math>f(\mathbf{i},\mathbf{j})=e^{-\beta V(\mathbf{i},\mathbf{j})}-1</math>
where <math>\beta=(k_{B}T)^{-1}</math> the inverse absolute temperature in units of energy−1 .