  We investigate the robustness of topological superconductors under the
perturbing influence of a finite charge current. To this aim, we introduce a
modified Kitaev Hamiltonian parametrically dependent on the quasiparticle
momentum induced by the current. Using different quantifiers of the topological
phase, such as the Majorana polarization and the edge state quantum conditional
mutual information, we prove the existence of a finite critical value of the
quasiparticle momentum below which edge modes and topological superconductivity
survive. We also discuss how a finite current breaks time reversal symmetry and
changes the topological class in the Altland-Zirnbauer classification scheme
compared to the case of isolated systems. Our findings provide a nontrivial
example of the interplay between topology and the nonequilibrium physics of
open quantum systems, a relation of crucial importance in the quest to a viable
topological quantum electronics.
