Statistical mechanical systems with an exponential density of states are considered. The arithmetic analog of parafermions of arbitrary order is constructed and a formula for bosonāparafermion equivalence is obtained using properties of the Riemann zeta function. Interactions (nontrivial mixing) among arithmetic gases using the concept of twisted convolutions are also introduced. Examples of exactly solvable models are discussed in detail.

@article{Curiositiesofarithmeticgases,
title = {Curiosities of arithmetic gases},
author = {Ioannis Bakas and Mark J. Bowick},
url = {http://aip.scitation.org/doi/10.1063/1.529511 http://aip.scitation.org/doi/pdf/10.1063/1.529511},
urldate = {2017-10-16},
abstract = {Statistical mechanical systems with an exponential density of states are considered. The arithmetic analog of parafermions of arbitrary order is constructed and a formula for bosonāparafermion equivalence is obtained using properties of the Riemann zeta function. Interactions (nontrivial mixing) among arithmetic gases using the concept of twisted convolutions are also introduced. Examples of exactly solvable models are discussed in detail.},
comment = {},
year = 1991,
collections = {Unusual arithmetic}
}