Generalized Pauli principle for particles with distinguishable traits

Abstract

The s = 3 2Ising spin chain with uniform nearest-neighbor coupling, quadratic single-site potential, and magnetic field is shown to be equivalent to a system of 17 species of particles with internal structure. The same set of particles (with different energies) is shown to generate the spectrum of the s = 1 2Ising chain with dimerized nearest-neighbor coupling. The particles are free of interaction energies even at high densities. The mutual exclusion statistics of particles from all species is determined by their internal structure and encoded in a generalized Pauli principle. The exact statistical mechanical analysis can be performed for thermodynamically open or closed systems and with arbitrary energies assigned to all particle species. Special circumstances make it possible to merge two or more species into a single species. All traits that distinguish the original species become ignorable. The particles from the merged species are effectively indistinguishable and obey modified exclusion statistics. Different mergers may yield the same end product, implying that the inverse process (splitting any species into subspecies) is not unique. In a macroscopic system of two merged species at thermal equilibrium, the concentrations of the original species satisfy a functional relation governed by their mutual statistical interaction. That relation is derivable from an extremum principle. In the Ising context the system is open and the particle energies depend on the Hamiltonian parameters. Simple models of polymerization and solitonic paramagnetism each represent a closed system of two species that can transform into each other. Here they represent distinguishable traits with different energies of the same physical particle.

Jammed disks in a narrow channel: criticality and ordering tendencies

“…Here we adapt a method of statistical mechanical analysis based on fractional exclusion statistics to jammed states of granular matter. This approach was originally developed for quantum many-body systems [16,17,18,19] and was recently extended to classical particles with shapes [20,21,22,23]. Whereas microscopic degrees of freedom are subject to thermal fluctuations, the disks in the narrow channel need to be subjected to random agitations to produce a comparable effect.…”

Coil-helix transition of polypeptide at water-lipid interface

“…The methodology employed for its exact statistical mechanical analysis is built on the concept of fractional statistics, invented by Haldane [15], and developed by Wu [16], Isakov [17], Anghel [18], and others [19] in the context of quantum many-body systems. The adaptation of this approach to classical statistical mechanical systems of particles with shapes was developed in a recent series of studies with applications to Ising spins [20, 21, 22, 23], jammed granular matter [24, 25], lattice gases with long-range interactions [26], and DNA under tension [27]. The application to the coil-helix transition of a long polypeptide adsorbed to a water-lipid interface worked out in the following is conceptually simple but surprisingly rich in scope.…”

Equivalence between fractional exclusion statistics and self-consistent mean-field theory in interacting-particle systems in any number of dimensions

“…This has been a prolific concept and was applied to both quantum and classical systems (see e.g. [3,4,[6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]). …”