  We give an alternative method to that of Hardy-Ramanujan-Rademacher to derive
the leading exponential term in the asymptotic approximation to the partition
function p(n,a), defined as the number of decompositions of a positive integer
'n' into integer summands, with each summand appearing at most 'a' times in a
given decomposition. The derivation involves mapping to an equivalent physical
problem concerning the quantum entropy and energy currents of particles flowing
in a one-dimensional channel connecting thermal reservoirs, and which obey
Gentile's intermediate statistics with statistical parameter 'a'. The method is
also applied to partitions associated with Haldane's fractional exclusion
statistics.
