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Thermodynamic behavior of polymer chains out of equilibrium is a fundamental problem in both polymer physics and biological physics. By using molecular dynamics simulation, we discover a general non-equilibrium mechanism that controls the conformation and dynamics of polar active polymer, i.e., head activity commands the overall chain activity, resulting in re-entrant swelling of active chains and non-monotonic variation of Flory exponent $ν$. These intriguing phenomena lie in the head-controlled railway motion of polar active polymer, from which two oppose non-equilibrium effects emerge, i.e., dynamic chain rigidity and the involution of chain conformation characterized by the negative bond vector correlation. The competition between these two effects determines the polymer configuration. Moreover, we identify several generic dynamic features of polar active polymers, i.e., linear decay of the end-to-end vector correlation function, polymer-size dependent crossover from ballistic to diffusive dynamics, and a polymer-length independent diffusion coefficient that is sensitive to head activity. A simple dynamic theory is proposed to faithfully explain these interesting dynamic phenomena. This sensitive structural and dynamical response of active polymer to its head activity provides us a practical way to control active-agents with applications in biomedical engineering.