We study thermodynamics properties of a one dimensional gas of hard elongated particles. Their centers are restricted to a line, while they can rotate in two-dimensional space.  The particles are shaped like needles, rectangles, ellipses, and ``metronomes" [1-2]. (In each system all particles are identical.) Hard particles lack energy scale, and the temperature appears only as a prefactor in the expression for the free energy. The physical properties of such a system have a non-trivial dependence on the density and on the shape of the particles. We use both Monte Carlo methods and transfer matrix approach to study the systems.

There exists a formalism [3] that relates the elastic properties of hard potentials to the probabilities of contacts between particles. We use Monte Carlo methods to estimate those probabilities and calculate the pressure and elasticity coefficient of the hard-needle gas as a function of its density, and compare the results with the same quantities obtained analytically from a transfer matrix approach [1].

Correlations between orientations of the objects are studied (by transfer matrix method) as a function of density and aspect ratio. The behavior in the extreme high-density (jamming) limit is described by a few universality classes depending on the object's shape. In particular, there is a diverging correlation length when the contact point  of  adjacent objects is far from the line along which their centers move, as for needles and rectangles [2].

[1] Y. Kantor and M. Kardar, Phys. Rev. E 79, 041109 (2009).

[2] Y. Kantor and M. Kardar, Europhys. Lett. 87, 60002 (2009).

[3] M. Murat and Y. Kantor, Phys. Rev. E 74, 031124 (2006).