Partition asymptotics from 1D quantum entropy and energy currents

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, d), defined as the number of decompositions of N into integer summands, with each summand appearing at most d times in a given decomposition. The derivation involves mapping to an equivalent physical problem concerning the averaged quantum entropy and energy currents of particles flowing in a one-dimensional (1D) channel connecting heat reservoirs, and which obey Gentile’s intermediate statistics with statistical parameter d. The method is also applied to partitions associated with Haldane’s fractional exclusion statistics.