Rotating black strings beyond Maxwell's electrodynamics

In this paper, we investigate the asymptotically Anti de Sitter solutions of rotating black strings coupled to Born-Infeld and Modified Maxwell non-linear electrodynamics in the context of Einsteinian, Einsteinian cubic and Einsteinian quartic gravity. By studying the near-horizon behavior of solutions, we find the mass parameter, surface gravity and accordingly the Hawking temperature. We also compute the entropy, mass, angular momentum, electric charge, and the electrostatic potential of solutions to show that, in the context of above theories and in the presence of two mentioned non-linear electrodynamics, the first law of thermodynamics for rotating black strings is also exactly hold. We also investigate extremality, thermal stability and phase transition of solutions.