Biomedical systems produce biosignals that arise from interaction mechanisms. In a general form, those mechanisms occur across multiple scales, both spatial and temporal, and contain linear and non-linear information. In this framework, entropy measures are good candidates in order provide useful evidence about disorder in the system, lack of information in time-series and/or irregularity of the signals. The most common movement disorder is essential tremor (ET), which occurs 20 times more than Parkinson's disease. Interestingly, about 50%-70% of the cases of ET have a genetic origin. One of the most used standard tests for clinical diagnosis of ET is Archimedes' spiral drawing. This work focuses on the selection of non-linear biomarkers from such drawings and handwriting, and it is part of a wider cross study on the diagnosis of essential tremor, where our piece of research presents the selection of entropy features for early ET diagnosis. Classic entropy features are compared with features based on permutation entropy. Automatic analysis system settled on several Machine Learning paradigms is performed, while automatic features selection is implemented by means of ANOVA (analysis of variance) test. The obtained results for early detection are promising and appear applicable to real environments.