  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 $\nu$. 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.
