  The de Rham-Gabadadze-Tolley (dRGT) black string solution is a cylindrically
symmetric and static solution of the Einstein field equation with graviton mass
term. For the asymptotically de Sitter (dS) solution, it is possible to obtain
the black string with two event horizons corresponding to two thermodynamic
systems. The R\'enyi entropy is one of the entropic forms which is suitable to
deal with nonextensive properties of the black string. In this work, we
investigated the possibility to obtain a stable black string by using the
R\'enyi entropy in both separated and effective approaches. We found that the
nonextensivity provides the thermodynamically stable black string with moderate
size in both approaches. The transition from the hot gas phase to the
moderate-sized stable black string in the separated/effective description is a
first-order/zeroth-order phase transition. The significant ways to distinguish
the black string from both approaches are discussed.
