  A dynamical system defined by a metriplectic structure is a dissipative model
characterized by a specific pair of tensors, which defines the Leibniz
brackets. Generally, these tensors are Poisson brackets tensor and a symmetric
metric tensor that models purely dissipative dynamics. In this paper, the
metriplectic system describing a simplified two-photon absorption by a
two-level atom is disclosed. The Hamiltonian component describes the free
electromagnetic radiation. The metric component encodes the radiation-matter
coupling, driving the system to an asymptotically stable state in which the
excited level of the atom is populated due to absorption. This work is intended
as a first result to pave the way to apply the metriplectic formalism to many
other irreversible processes in nonlinear optics.
