We propose a generic model of driven DNA under the influence of an oscillatory force of amplitude F and frequency v and show the existence of a dynamical transition for a chain of finite length. We find that the area of the hysteresis loop, A_loop, scales with the same exponents as observed in a recent study based on a much more detailed model. However, towards the true thermodynamic limit, the high-frequency scaling regime extends to lower frequencies for larger chain length L and the system has only one scaling A_loop ~ ν^-1F². Expansion of an analytical expression for A_loop obtained for the model system in the low-force regime revealed that there is
a new scaling exponent associated with force A_loop ~ ν^-1F^2.5, which has been validated by high-precision numerical calculation. By a combination of analytical and numerical arguments, we also deduce that for large but finite L, the exponents are robust and independent of temperature and friction coefficient.

References:
1. Periodically driven DNA: Theory and Simulation
Sanjay Kumar, Ravinder Kumar and Wolfhard Janke Phys. Rev. E , 93, 010402 (R)(2016)
2. Statistical mechanics of DNA unzipping under periodic force: Scaling behavior of hysteresis loop
Sanjay Kumar and Garima Mishra Phys. Rev. Lett. 110, 258102
(2013)