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Using a Markov chain approach we rederive the exact density functional forhard rod mixtures on a one-dimensional lattice, which forms the basis of thelattice fundamental measure theory. The transition probability in the Markovchain depends on a set of occupation numbers, which reflects the property of azero-dimensional cavity to hold at most one particle. For given mean occupationnumbers (density profile), an exact expression for the equilibrium distributionof microstates is obtained, that means an expression for the unique externalpotential that generates the density profile in equilibrium. By considering therod ends to fall onto lattice sites, the mixture is always additive.

Exact density functional for hard rod mixtures derived from Markov chain approach