Recognition of emotions is still an unresolved challenge, which could be helpful to improve current human-machine interfaces. Recently, nonlinear analysis of some physiological signals has shown to play a more relevant role in this context than their traditional linear exploration. Thus, the present work introduces for the first time the application of three recent entropy-based metrics: sample entropy (SE), quadratic SE (QSE) and distribution entropy (DE) to discern between emotional states of calm and negative stress (also called distress). In the last few years, distress has received growing attention because it is a common negative factor in the modern lifestyle of people from developed countries and, moreover, it may lead to serious mental and physical health problems. Precisely, 279 segments of 32-channel electroencephalographic (EEG) recordings from 32 subjects elicited to be calm or negatively stressed have been analyzed. Results provide that QSE is the first single metric presented to date with the ability to identify negative stress. Indeed, this metric has reported a discriminant ability of around 70%, which is only slightly lower than the one obtained by some previous works. Nonetheless, discriminant models from dozens or even hundreds of features have been previously obtained by using advanced classifiers to yield diagnostic accuracies about 80%. Moreover, in agreement with previous neuroanatomy findings, QSE has also revealed notable differences for all the brain regions in the neural activation triggered by the two considered emotions. Consequently, given these results, as well as easy interpretation of QSE, this work opens a new standpoint in the detection of emotional distress, which may gain new insights about the brain's behavior under this negative emotion.