  The phase behavior and structural properties of hard anisotropic particles
(prisms and dumbbells) are examined in one-dimensional channels using the
Parsons--Lee (PL) theory, and the transfer-matrix and neighbor-distribution
methods. The particles are allowed to move freely along the channel, while
their orientations are constrained such that one particle can occupy only two
or three different lengths along the channel. In this confinement setting, hard
prisms behave as an additive mixture, while hard dumbbells behave as a
non-additive one. We prove that all methods provide exact results for the phase
properties of hard prisms, while only the neighbor-distribution and
transfer-matrix methods are exact for hard dumbbells. This shows that
non-additive effects are incorrectly included into the PL theory, which is a
successful theory of the isotropic-nematic phase transition of rod-like
particles in higher dimensions. In the one-dimensional channel, the
orientational ordering develops continuously with increasing density, i.e., the
system is isotropic only at zero density, while it becomes perfectly ordered at
the close-packing density. We show that there is no orientational correlation
in the hard prism system, while the hard dumbbells are orientationally
correlated with diverging correlation length at close packing. On the other
hand, positional correlations are present for all the systems, the associated
correlation length diverging at close packing.
