Based on prior research indicating a decrease in the spectral slope of electroencephalogram (EEG) during anesthesia induction and an increase during recovery, we propose Slope Entropy (SlopEn), which uniquely emphasizes variations in signal slope, as a new index for monitoring the depth of anesthesia (DoA). The performance of SlopEn is investigated on just a single frontal EEG channel and is compared against other well-known entropy metrics utilized in the field. After filtering the EEG signal, four types of entropy, including SlopEn, are derived from all EEG sub-bands and separately inputted to a regressor for estimating DoA index values. Comparing the results obtained using SlopEn with those from the Sample entropy demonstrates the superiority of the former, achieving a higher correlation coefficient (0.75 vs. 0.63) and a lower median absolute error (4.2 vs. 6.2) between the estimated and reference DoA index values. These findings establish that the SlopEn has the potential to become a valuable index for DoA monitoring using single frontal channel EEG systems.