The s=3/2 Ising 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=1/2 Ising
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 endproduct, 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.Comment: 12 pages, 7 figures, 6 table
