  The aim of the present paper is to provide a preliminary investigation of the
thermodynamics of particles obeying monotone statistics. To render the
potential physical applications realistic, we propose a modified scheme called
block-monotone, based on a partial order arising from the natural one on the
spectrum of a positive Hamiltonian with compact resolvent. The block-monotone
scheme is never comparable with the weak monotone one and is reduced to the
usual monotone scheme whenever all the eigenvalues of the involved Hamiltonian
are non-degenerate. Through a detailed analysis of a model based on the quantum
harmonic oscillator, we can see that: (a) the computation of the
grand-partition function does not require the Gibbs correction factor $n!$
(connected with the indistinguishability of particles) in the various terms of
its expansion with respect to the activity; and (b) the decimation of terms
contributing to the grand-partition function leads to a kind of "exclusion
principle" analogous to the Pauli exclusion principle enjoined by Fermi
particles, which is more relevant in the high-density regime and becomes
negligible in the low-density regime, as expected.
