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 .

Notes

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

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Mayer f-function

Definition

See also

Notes