Scaling of hysteresis loop of interacting polymers under a periodic force

Using Langevin Dynamics simulations, we study a simple model of interacting-polymer under a periodic force. The force-extension curve strongly depends on the magnitude of the amplitude $(F)$ and the frequency ($\nu$) of the applied force. In low frequency limit, the system retraces the thermodynamic path. At higher frequencies, response time is greater than the external time scale for change of force, which restrict the biomolecule to explore a smaller region of phase space that results in hysteresis of different shapes and sizes. We show the existence of dynamical transition, where area of hysteresis loop approaches to a large value from nearly zero area with decreasing frequency. The area of hysteresis loop is found to scale as $F^{\alpha} \nu^{\beta}$ for the fixed length. These exponents are found to be the same as of the mean field values for a time dependent hysteretic response to periodic force in case of the isotropic spin.