A measure of correlations for statistical systems is advanced, called correlation index. The measure is general, being applicable to quantum and classical, equilibrium and nonequilibrium statistical systems. After formulating the general notion of correlation indices for arbitrary trace-class operators, the calculation of the correlation indices are illustrated by several examples of density operators and reduced density matrices. The computation of the correlation indices for equilibrium systems is exemplified for bosonic systems with the Bose-Einstein condensate, superconducting systems, and for spin systems. Correlation indices for nonequilibrium systems are considered for nonlinear dynamics of spin and pseudospin systems.A measure of correlations for statistical systems is advanced, called correlation index. The measure is general, being applicable to quantum and classical, equilibrium and nonequilibrium statistical systems. After formulating the general notion of correlation indices for arbitrary trace-class operators, the calculation of the correlation indices are illustrated by several examples of density operators and reduced density matrices. The computation of the correlation indices for equilibrium systems is exemplified for bosonic systems with the Bose-Einstein condensate, superconducting systems, and for spin systems. Correlation indices for nonequilibrium systems are considered for nonlinear dynamics of spin and pseudospin systems.

quant-pharXiv:2609.34859Journal of Statistical PhysicsSep 29, 20261 citation

A nonstandard statistics for strongly correlated systems: Two simple examples

Józef Spałek, Piotr Kuterba, Mateusz Wójcik +4 more

We discuss two different cases of strongly correlated fermions statistics. The first of them called that of the non-Fermi liquid (NFL), i.e., that of fermions with exclusion of doubly occupancies of quasimomentum states $\{\bf k\}$ and opposite spins ( $\uparrow\downarrow$ ). The second is that of statistical spin liquid (SSL), in which the fermion spins hop around and mix with the holes (unoccupied) states. For both cases we calculate the system entropy and the corresponding statistical distribution function, analyzed for a two-dimensional square-lattice filling $n\in [0,1]$ and relative temperature $k_B T/|t|$ , where $t<0$ is the nearest neighbor hopping integral. We are particularly interested in the situation when the system of itinerant fermions reduce to the Mott-insulator state for the half-filled band ( $n\to1$ ). Thislimiting situation signals a qualitative difference between the present SSL statistics and that of uncorrelated fermions representing normal Fermi-liquid state.We discuss two different cases of strongly correlated fermions statistics. The first of them called that of the non-Fermi liquid (NFL), i.e., that of fermions with exclusion of doubly occupancies of quasimomentum states $\{\bf k\}$ and opposite spins ($\uparrow\downarrow$). The second is that of statistical spin liquid (SSL), in which the fermion spins hop around and mix with the holes (unoccupied) states. For both cases we calculate the system entropy and the corresponding statistical distribution function, analyzed for a two-dimensional square-lattice filling $n\in [0,1]$ and relative temperature $k_B T/|t|$, where $t<0$ is the nearest neighbor hopping integral. We are particularly interested in the situation when the system of itinerant fermions reduce to the Mott-insulator state for the half-filled band ($n\to1$). Thislimiting situation signals a qualitative difference between the present SSL statistics and that of uncorrelated fermions representing normal Fermi-liquid state.

Apr 23, 20260 citations

Spin and Statistics

IMPERIAL COLLEGE PRESS eBooksOct 1, 20100 citations

The spin-statistics theorem

Robert H. Romer

American Journal of PhysicsJul 12, 200214 citations

A Nonstandard Statistics for Strongly Correlated Systems: Two Simple Examples

Józef Spałek, Piotr Kuterba, M. Wójcik +4 more

We discuss two different cases of strongly correlated fermions statistics. The first of them is the non-Fermi liquid (NFL) case, i.e. , that of fermions with exclusion of doubly occupancy of quasimomentum states $\{\mb k\}$ with opposite spins ( $\uparrow \downarrow$ ). The second is the statistical spin liquid (SSL) case, in which the fermion spins hop around and mix with the holes (unoccupied) states. For both cases, we calculate the system entropy and the corresponding statistical distribution function, analyzed for a two-dimensional square-lattice filling $n\in [0,1]$ and relative temperature $k_\mathrm {B} T/|t|$ , where $t\lt 0$ is the nearest neighbor hopping integral. We are particularly interested in the situation when the system of itinerant fermions reduce to the Mott-insulator state for the half-filled band ( $n\to 1$ ). This limiting situation signals a qualitative difference between the present SSL statistics and that of uncorrelated fermions representing a normal Fermi-liquid state. Abstract Published by the Jagiellonian University 2026 authorsWe discuss two different cases of strongly correlated fermions statistics. The first of them is the non-Fermi liquid (NFL) case, i.e. , that of fermions with exclusion of doubly occupancy of quasimomentum states $\{\mb k\}$ with opposite spins ($\uparrow \downarrow $). The second is the statistical spin liquid (SSL) case, in which the fermion spins hop around and mix with the holes (unoccupied) states. For both cases, we calculate the system entropy and the corresponding statistical distribution function, analyzed for a two-dimensional square-lattice filling $n\in [0,1]$ and relative temperature $k_\mathrm {B} T/|t|$, where $t\lt 0$ is the nearest neighbor hopping integral. We are particularly interested in the situation when the system of itinerant fermions reduce to the Mott-insulator state for the half-filled band ($n\to 1$). This limiting situation signals a qualitative difference between the present SSL statistics and that of uncorrelated fermions representing a normal Fermi-liquid state. Abstract Published by the Jagiellonian University 2026 authors

arXiv:2607.09542Acta Physica Polonica BMay 15, 20260 citations

\{\bf k\}

and opposite spins (

\uparrow\downarrow

). The second is that of statistical spin liquid (SSL), in which the fermion spins hop around and mix with the holes (unoccupied) states. For both cases we calculate the system entropy and the corresponding statistical distribution function, analyzed for a two-dimensional square-lattice filling

n\in [0,1]

and relative temperature

k_B T/|t|

, where

t<0

is the nearest neighbor hopping integral. We are particularly interested in the situation when the system of itinerant fermions reduce to the Mott-insulator state for the half-filled band (

n\to1

). Thislimiting situation signals a qualitative difference between the present SSL statistics and that of uncorrelated fermions representing normal Fermi-liquid state.

\uparrow \downarrow

). The second is the statistical spin liquid (SSL) case, in which the fermion spins hop around and mix with the holes (unoccupied) states. For both cases, we calculate the system entropy and the corresponding statistical distribution function, analyzed for a two-dimensional square-lattice filling

n\in [0,1]

and relative temperature

k_\mathrm {B} T/|t|

, where

t\lt 0

is the nearest neighbor hopping integral. We are particularly interested in the situation when the system of itinerant fermions reduce to the Mott-insulator state for the half-filled band (

n\to 1

). This limiting situation signals a qualitative difference between the present SSL statistics and that of uncorrelated fermions representing a normal Fermi-liquid state. Abstract Published by the Jagiellonian University 2026 authors