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 ) {\displaystyle V(\mathbf {i} ,\mathbf {j} )}
where the bold labels i {\displaystyle \mathbf {i} } and j {\displaystyle \mathbf {j} } denote the continuous degrees of freedom associated with the particles, e.g.,
i = r i {\displaystyle \mathbf {i} =\mathbf {r} _{i}}
for spherically symmetric particles and
i = ( r i , Ω i ) {\displaystyle \mathbf {i} =(\mathbf {r} _{i},\Omega _{i})}
for rigid non-spherical particles where r {\displaystyle \mathbf {r} } denotes position and Ω {\displaystyle \Omega } the orientation parametrized e.g. by Euler angles. The Mayer f-function is then defined as
f ( i , j ) = e − β V ( i , j ) − 1 {\displaystyle f(\mathbf {i} ,\mathbf {j} )=e^{-\beta V(\mathbf {i} ,\mathbf {j} )}-1}
where β = ( k B T ) − 1 {\displaystyle \beta =(k_{B}T)^{-1}} the inverse absolute temperature in units of energy−1 .
See also Virial coefficient Cluster expansion Excluded volume
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