In this paper we have analyzed the connections between entropy, reversibility, irreversibility, the H theorem and transport equation of Boltzmann and the Poincaré's recurrence theorem. These topics are usually studied separatelly in many papers and books, but they are not analyzed globally in order to obtain the connections between them as we have done here. We have written the paper following a simple and didactic approach in order to have a readable text to undergraduate physics students.
reversibility; irreversibility; Boltzmann's H-theorem; Poincaré's recurrence theorem; transport equation
