The expression of the free energy of a liquid in terms of an explicit
decomposition of the particle configurations into local coordination clusters
is examined. We argue that the major contribution to the entropy associated
with structural fluctuations arises from the local athermal constraints imposed
by the overlap of adjacent coordination shells. In the context of the recently
developed Favoured Local Structure model [Soft Matt. 11, 3322 (2015)], we
derive explicit expressions for the structural energy and entropy in the high
temperature limit, compare this approximation with simulation data and consider
the extension of this free energy to the case of spatial inhomogeneity in the
distribution of local structures
