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Shannon entropy is a classical method to quantify data information. Here we associate Shannon entropy with the recurrence microstate probabilities to study dynamical systems, stochastic systems and experimental data. Additionally, the maximum entropy concept presents a specific recurrence threshold and turns the method almost free of parameter selection. This is also connected with data sampling and avoids under and oversampling. Finally, we show that this framework can be applied into discrete, continuous and real data and associated directly with machine learning techniques.