Multispecies Virial Expansions

Abstract

We study the virial expansion of mixtures of countably many different types of particles. The main tool is the Lagrange-Good inversion formula, which has other applications such as counting coloured trees or studying probability generating functions in multi-type branching processes. We prove that the virial expansion converges absolutely in a domain of small densities. In addition, we establish that the virial coefficients can be expressed in terms of two-connected graphs.

16 pages, 1 figure

References in corpus (5)

• Abstract cluster expansion with applications to statistical mechanical systems
• Cluster expansion in the canonical ensemble
• Mayer and virial series at low temperature
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Cited by in corpus (5)

• Cluster and virial expansions for the multi-species Tonks gas
• Onsager's missing steps retraced
• Thermodynamics of a hierarchical mixture of cubes
• Graph rules for the linked cluster expansion of the Legendre effective action
• Lagrange inversion and combinatorial species with uncountable color palette