  We use the anti-de Sitter (AdS) conformal field theory correspondence to
calculate the conserved charges and the Euclidean actions of the charged
rotating black string in four dimensions both in the canonical and the
grand-canonical ensemble. The four-dimensional solution of the Einstein-Maxwell
equations with a positive cosmological constant is introduced, and its
conserved quantities and actions for fixed charge and fixed electric potential
are calculated. We also study the thermodynamics of the asymptotically AdS
black strings and perform a stability analysis both in the canonical and the
grand-canonical ensembles. We find that the asymptotically AdS black string in
the canonical ensemble is locally stable, while in the grand-canonical ensemble
it is stable only for a part of the phase space.
