Laplace transform of the grand canonical partition function

[evilcman]

Does anyone recognize this expression for the pressure: p(T,\mu) = T s^*(T,\mu)
where s^* is the extreme right singularity in the Laplace transform of the grand canonical partion function. If someone knows this, I am curious in the derivation, and in what cases it is applicable. (In the publication where I found this, they use it in an infinite volume limit, but I don't know if that is important or not. )

Thanks in advance.

 

[DrDu]

There has been a very important article by Lee and Yang who consider the poles of the grand canonical partition function to prove some general properties of phase transitions:

@article{yang1952statistical,
title={{Statistical theory of equations of state and phase transitions. I. Theory of condensation}},
author={Yang, CN and Lee, TD},
journal={Physical Review},
volume={87},
number={3},
pages={404--409},
issn={0031-899X},
year={1952},
publisher={APS}
}