Date of Original Version
We derive exact density functionals for systems of hard rods with rst-neighbor interactions of arbitrary shape but limited range on a one-dimensional lattice. The size of all rods is the same integer unit of the lattice constant. The derivation, constructed from conditional probabilities in a Markov chain approach, yields the exact joint probability distribution for the positions of the rods as a functional of their density prole. For contact interaction (\sticky core model") between rods we give a lattice fundamental measure form of the density functional and present explicit results for contact correlators, entropy, free energy, and chemical potential. Our treatment includes inhomogeneous couplings and external potentials.
Bakhti, B., G. Muller and P. Maass. "Interacting hard rods on a lattice: Distribution of microstates and density functionals." J. Chem. Phys. 139, 054113 (2013), http://dx.doi.org/10.1063/1.4816379.