temporarily created by the probing electric field (see. Fig. \[fig:falling\]). Therefore the activation energy in this process shall be *negative*, i.e., $\chi\sim1/\left[1+A^{2}\omega^{2}\exp\left(-\frac{2\left|E_{a}\right|}{T}\right)\right]$, which is the form adopted in Eq. (\[eq:h1T\]).

We note that negative activation energy is known in some chemical reactions [@negativeActivation]. Negative activation energy appears here because when an *ac* electric field perturbs dipoles and tilts the relative energy of potential wells, dipoles outside potential wells will move towards the temporary potential minimum. However, the drifting to the potential minimum is hindered by thermal fluctuations of such dipoles. In fact, higher temperature (corresponding to larger kinetic energy) results in a slower relaxation to the energy minimum (corresponding to larger $\tau$), leading to negative activation energy. We also note that since the applied *ac* electric field is responsible for shifting the energy minimum and causing dipoles to drift, the change of its frequency may well alter the negative activation energy, explaining why $\theta$ in Eq. (\[eq:BZT-frequency\]) is dependent on the probing frequency. Similar arguments explains why $T_{O}$ also depends on the probing frequency.

In the above analysis, we focus on dipoles with kinetic energy higher than $E_{b}$. These dipoles are able to drift from one energy minimum to another 