We link, by means of a semiclassical approach, the fractional statistics of particles obeying the Haldane exclusion principle to the Tsallis statistics and derive a generalized quantum entropy and its associated statistics.

Jan 1, 199611 citations

Physical Review Letters

von Neumann Entropy Associated with the Haldane Exclusion Statistics

A. K. Rajagopal

Published Sep 18, 1995• 4 citations

Publisher

DOI: 10.1103/physrevlett.75.2452.2

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von Neumann Entropy Associated with the Haldane Exclusion Statistics

A. K. Rajagopal

We obtain the von Neumann entropy per state of the Haldane exclusion statistics with parameter $g$ in terms of the mean occupation number $\overline{n}$ as ${S}_{H}=\ensuremath{-}\overline{n}{w\mathrm{ln}w\ensuremath{-}(1+w)\mathrm{ln}(1+w)}$, where $w=\frac{(1\ensuremath{-}\overline{n}g)}{\overline{n}}$. 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.We obtain the von Neumann entropy per state of the Haldane exclusion statistics with parameter $g$ in terms of the mean occupation number $\overline{n}$ as ${S}_{H}=\ensuremath{-}\overline{n}{w\mathrm{ln}w\ensuremath{-}(1+w)\mathrm{ln}(1+w)}$, where $w=\frac{(1\ensuremath{-}\overline{n}g)}{\overline{n}}$. 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.

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Haldane exclusion statistics and the Boltzmann equation

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Generalized fractional statistics

Kaniadakis, Giorgio, Lavagno, Andrea, P. Quarati

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We obtain the von Neumann entropy per state of the Haldane exclusion statistics with parameter

g

in terms of the mean occupation number

\overline{n}

as ${S}_{H}=\ensuremath{-}\overline{n}{w\mathrm{ln}w\ensuremath{-}(1+w)\mathrm{ln}(1+w)}$, where $w=\frac{(1\ensuremath{-}\overline{n}g)}{\overline{n}}$. 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.