This work presents a nonequilibrium statistical-thermodynamic approach to the study of a Fröhlich-Bose-Einstein condensation of magnons under radio-frequency radiation pumping. Fröhlich-Bose-Einstein condensates display a complex behavior consisting in steady-state conditions to the emergence of a synergetic dissipative structure resembling the Bose-Einstein condensation of systems in equilibrium. Then a kind of "two-fluid model" arises: the "normal" nonequilibrium structure and the Fröhlich condensate, which is shown to be an attractor to the system. In this study we analyze some aspects of the irreversible thermodynamics of this dissipative complex system. We obtained the expression for the informational entropy of the two-fluid condensate and introduced an order parameter to characterize the role of the Fröhlich interaction in ordering the system. The analysis highlights the order increase due to the Fröhlich interaction. We also study the informational entropy production of the system, considering its internal and external parts. Finally, the Glansdorff-Prigogine criteria for evolution and (in)stability are verified.