Credit: Alan Stonebraker; Data shown in (c) are courtesy of K. M. Daily, Washington State University

Figure 1: (a),(b) Schematic illustrations of one of many possible configurations of the three-body cluster at low and high temperature, respectively. At low $T$, only a few configurations with small energy contribute to a given virial coefficient $bn$. At high temperature, many configurations with small and large energy contribute. (c) Shows the cluster expansion parameter, or fugacity, $z=exp[μ/(kBT$)], where $μ$ denotes the chemical potential and $kB$ the Boltzmann constant, as a function of $T/TF$ for the example of infinitely strong interactions. The thermodynamic potential $Ω$, which determines the energy and entropy, can be written as $Ω∝Σnbnzn$, where $bn$ is determined by the energy spectrum of the $n$th cluster. The contribution of the $n$th cluster is suppressed by a factor of $z$ compared to that of the ($n-1$)th cluster. The suppression is very effective for $T/TF>1$ (i.e., only terms with $n=1,2,$ and $3$ are needed), but higher-order clusters are needed for $T/TF≤0.75$.