The significance of the persistence length:

At zero temperature, the shape of the filament is such that its energy is minimized. In other word, it then corresponds to a straight rod. At a non-zero temperature, it exchanges energy with its surroundings, so that it fluctuates its shape. With increase in bending energy, its shape turns more contorted and the local curvature grows. Thus the shapes of filaments have increasing energy from left to right. In any case, the probability of finding a filament at a particular conformation depends upon the energy of the conformation and is determined by the Boltzman’s law

where

(34.1)

Equation 34.1 suggests that conformations with large energy are less probable.