VONNEUMANN AND TSALLIS ENTROPIES ASSOCIATED WITH THE GENTILE INTERPOLATIVE QUANTUM STATISTICS

We obtain the von Neumann entropy per state of the Gentile interpolati ve statistics in terms of the mean occupation number (n) over bar, as S-G = -{(n) over bar In omega + In[(1 - omega)/(1 - omega(d+1))]}, whe re omega is obtained by solving the equation (n) over bar = omega/(1 omega) - (d + 1)omega(d+1)/(1 - omega(d+1)). These go over to the fam iliar expressions for the cases of Fermi (d = 1) and Bose (d = infinit y) statistics. The second order fluctuation from the mean is found to be mu(2) = R[omega/(1 - omega)2 - (d + 1)(2) omega(d+1)/(1 - omega(d+1 ))(2)]. For nonextensive systems, corresponding results are also deriv ed by employing the T sallis entropy which includes the von Neumann en tropy valid for extensive systems only. A discussion of these with the other interpolative statistics of Haldane is also given.