  This study investigates the (longitudinal) thermodynamic and structural
characteristics of single-file confined square-well and square-shoulder disks
by employing a mapping technique that transforms the original system into a
one-dimensional polydisperse mixture of nonadditive rods. Leveraging standard
statistical-mechanical techniques, exact results are derived for key
properties, including the equation of state, internal energy, radial
distribution function, and structure factor. The asymptotic behavior of the
radial distribution function is explored, revealing structural changes in the
spatial correlations. Additionally, exact analytical expressions for the second
virial coefficient are presented. Comparisons with Monte Carlo simulations
demonstrate an excellent agreement with theory.
