VON-NEUMANN ENTROPY ASSOCIATED WITH THE HALDANE EXCLUSION STATISTICS

We obtain the von Neumann entropy per state of the Haldane exclusion statistics with parameter g in terms of the mean occupation number n̄ as SH=-n̄{w lnw-(1+w)ln(1+w)}, where w=(1-n̄g)n̄. This reduces correctly to the well known expressions in the limiting cases of Bose (g=0) and Fermi (g=1) statistics. We have derived the second and third order fluctuations in the occupation numbers for arbitrary g. An elegant general duality relationship between the w factor associated with the particle and that associated with the hole at the reciprocal g is deduced along with the attendant relationship between the two respective entropies. © 1995 The American Physical Society.