The entropy change during spin relaxation for a realistic model system is studied, whose spin dynamics can be handled with the Boltzmann equation. The time evolution of the von Neumann entropy is monitored during the process and is compared with the recently introduced concept of the Loschmidt echo envelope. The time evolution of the two quantities is remarkably similar which helps to distinguish reversible and irreversible changes to the ensemble spin state. The method is also demonstrated for a toy model of nuclear magnetic resonance, where the usual pi spin echo is performed numerically, and the echo envelope also follows the time evolution of the von Neumann entropy. The numerical approach highlights the utility of the entropy concept in analyzing various processes which occur during spin relaxation.