  A non-equilibrium statistical-thermodynamic approach to the study of a
Fr\"ohlich-Bose-Einstein condensation of magnons under radio-frequency
radiation pumping is presented. Such a system displays a complex behavior
consisting in steady-state conditions to the emergence of a synergetic
dissipative structure resembling the Bose-Einstein condensation of systems in
equilibium. A kind of "two fluid model" arises: the "normal" non-equilibrium
structure and Fr\"ohlich condensate or "non-equilibrium" one, which is shown to
be an attractor to the system. We analyze some aspects of the irreversible
thermodynamics of this dissipative complex system, namely, its informational
entropy, expressions for the fluctuations in non-equilibrium conditions, the
associated Maxwell relations and the formulation of a generalized
$\mathscr{H}$-theorem. We also study the informational entropy production of
the system, an order parameter is introduced and Glansdorff-Prigogine criteria
for evolution and (in)stability are verified.
