FIG. 4: Unlooped lifetime τ$_{u}$ as a function of a constant applied force. The solid line is the theoretical fit, given by the Kramers relation of Eq. (8) to the data points (squares). The coefficients of the potential U ( x ; h ) are a = 4 . 64 × 10 − 5 N / m and b = 739 N / m $^{2}$. to our constant force (zero fluctuation) data, the result of which is shown in Fig. 4. We have found the difference in the resulting fit parameters to be negligible between the exact, Eq. (6), and approximate Kramers relation, Eq. (8). Moreover, the zero tension ( h = 0) energy barrier Δ U = a $^{3}$/ 6 b 2 = 7 . 4 k$_{B}$T , from this fit, is in remarkable agreement with the energy cost for loop formation predicted by an elastic rod model of DNA, Δ U = 7 . 7 k$_{B}$T [11]. Since we add noise to the system by linearly modulating the tension applied to the DNA, we may incorporate this additional noise by modifying the correlations of the stochastic source ξ ( t ) such that λ = γk$_{B}$T$_{E}$ , where we have introduced the effective temperature With the replacement T → T$_{E}$ in Eq. (8) we are able to account for the effects of noise on the unlooped lifetimes τ$_{u}$ ( h ; T$_{α}$/T ) at a mean tension h . This model gives excellent agreement with our experimental measurements of the looping lifetime τ$_{u}$ ( h ; T$_{α}$/T ) as a function of noise (see Fig. 2). Furthermore, it predicts a robustness to noise similar to what we observe experimentally (see Fig. 2). The theory predicts a fairly constant ratio τ$_{u}$ ( h ; 0 . 05) /τ$_{u}$ ( h ; 0) = 0 . 65 , 0 . 63 , and 0 . 62 at a mean tension h = 123 , 153 , and 175 fN, respectively. 8 T$_{E}$ = T (1 + T$_{α}$/T ) . (9)