This paper proposes a novel lightweight method using the multitaper power spectrum to estimate arousal levels at wearable devices. We show that the spectral slope (1/f) of the electrophysiological power spectrum reflects the scale-free neural activity. To evaluate the proposed feature's performance, we used scalp EEG recorded during anesthesia and sleep with technician-scored Hypnogram annotations. It is shown that the proposed methodology discriminates wakefulness from reduced arousal solely based on the neurophysiological brain state with more than 80% accuracy. Therefore, our findings describe a common electrophysiological marker that tracks reduced arousal states, which can be applied to different applications (e.g., emotion detection, driver drowsiness). Evaluation on hardware shows that the proposed methodology can be implemented for devices with a minimum RAM of 512 KB with 55 mJ average energy consumption.