Classification of human activities performed sequentially and with unconstrained durations using radar sensors has been studied in this work. A novel processing pipeline comprising a sequence segmentation stage, a segment processing stage, and a classification stage has been proposed to address this challenge. Specifically, the segmentation stage has been implemented by monitoring Rényi entropy for fluctuations in the radar data, with the entropy, derived from micro-Doppler spectrograms, functioning as a descriptive quantity of the activity being performed. The method has been experimentally verified on a challenging, publicly available dataset collected with a network of five simultaneously operating pulsed ultrawideband radars. Classification performance has been compared to reference works in the literature on the same dataset, and a test accuracy and macro F1-score of 89.3% and 82.0% have been, respectively, demonstrated.