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A non-equilibrium statistical-thermodynamic approach to the study of aFr\"ohlich-Bose-Einstein condensation of magnons under radio-frequencyradiation pumping is presented. Such a system displays a complex behaviorconsisting in steady-state conditions to the emergence of a synergeticdissipative structure resembling the Bose-Einstein condensation of systems inequilibium. A kind of "two fluid model" arises: the "normal" non-equilibriumstructure and Fr\"ohlich condensate or "non-equilibrium" one, which is shown tobe an attractor to the system. We analyze some aspects of the irreversiblethermodynamics of this dissipative complex system, namely, its informationalentropy, expressions for the fluctuations in non-equilibrium conditions, theassociated Maxwell relations and the formulation of a generalized$\mathscr{H}$-theorem. We also study the informational entropy production ofthe system, an order parameter is introduced and Glansdorff-Prigogine criteriafor evolution and (in)stability are verified.

Statistical Thermodynamics of the Fr\"ohlich-Bose-Einstein Condensation of Magnons out of Equilibrium