Virial expansion and condensation with a new generating function

TL;DR

This paper introduces a new generating function for the canonical partition function that directly involves irreducible cluster integrals, leading to new insights into virial expansion and condensation phenomena.

Contribution

It develops a novel generating function that simplifies and generalizes Mayer's approach, enabling derivation of virial and condensation criteria from a different mathematical perspective.

Findings

Derived virial expansion criteria

Established condensation criteria

Unified previous results under a new framework

Abstract

Mayer's convergence method for virial expansion and condensation is studied using a new generating function for canonical partition function, which directly depends on irreducible cluster integral, $\beta_k$, unlike Mayer's work where it depends on reducible cluster integral, $b_l$. The virial expansion, criteria for it's validity and criteria for condensation, etc. are derived from our generating function. All earlier Mayer's results are obtained from this new generating function.