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We report the properties of more than 800 bursts detected from the repeatingfast radio burst (FRB) source FRB 20201124A with the Five-hundred-meterAperture Spherical radio Telescope (FAST) during an extremely active episode onUTC September 25-28, 2021 in a series of four papers. In this second paper ofthe series, we mainly focus on the energy distribution of the detected bursts.The event rate initially increased exponentially but the source activitystopped within 24 hours after the 4th day. The detection of 542 bursts in onehour during the fourth day marked the highest event rate detected from onesingle FRB source so far. The bursts have complex structures in thetime-frequency space. We find a double-peak distribution of the waiting time,which can be modeled with two log-normal functions peaking at 51.22 ms and10.05 s, respectively. Compared with the emission from a previous activeepisode of the source detected with FAST, the second distribution peak time issmaller, suggesting that this peak is defined by the activity level of thesource. We calculate the isotropic energy of the bursts using both a partialbandwidth and a full bandwidth and find that the energy distribution is notsignificantly changed. We find that an exponentially connected broken-power-lawfunction can fit the cumulative burst energy distribution well, with the lowerand higher-energy indices being $-1.22\pm0.01$ and $-4.27\pm0.23$,respectively. Assuming a radio radiative efficiency of $\eta_r = 10^{-4}$, thetotal isotropic energy of the bursts released during the four days when thesource was active is already $3.9\times10^{46}$ erg, exceeding $\sim 23\%$ ofthe available magnetar dipolar magnetic energy. This challenges the magnetarmodels invoking an inefficient radio emission (e.g. synchrotron maser models).

FAST observations of an extremely active episode of FRB 20201124A: II. Energy Distribution