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We show that the vacuum ground state energy for massive scalars on a 1-dimL-sites periodic lattice can be interpreted as the thermodynamic free energy ofparticles at temperature 1/L governed by the Arutyunov-Frolov mirrorHamiltonian. Although the obligatory zero-point sum-over-frequencies is finiteon the lattice, a renormalization prescription is necessary in order to obtaina physical sensible result for the lattice Casimir energy. The coefficients ofevery term in the large L expansion of the lattice Casimir energy are providedin terms of modified Bessel functions.

Finite-sites corrections to the Casimir energy on a periodic lattice