Dynamics of the contour length fluctuation

Having studied the static distribution of the contour length, we now examine the dynamics of the contour length fluctuation. As before, we use the Rouse model for the dynamics (see Fig. 6.7). Let s be the curvilinear coordinate of the n-th Rouse segment measured from a 

The dynamics of are described by the Langevin equation for the Rouse model. 

Since eqn (6.77) is the same linear equation as appeared in the Rouse dynamics, analysis of this equation is straightforward. An important difference, however, must be mentioned. In the present case, the equilibrium average of the contour length is L  

If we take the average of both sides of eqn (6.77) for the equilibrium state, we have 

For this to be consistent with eqn (6.79), the boundary condition must be 

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