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A dynamical system defined by a metriplectic structure is a dissipative modelcharacterized by a specific pair of tensors, which defines the Leibnizbrackets. Generally, these tensors are Poisson brackets tensor and a symmetricmetric tensor that models purely dissipative dynamics. In this paper, themetriplectic system describing a simplified two-photon absorption by atwo-level atom is disclosed. The Hamiltonian component describes the freeelectromagnetic radiation. The metric component encodes the radiation-mattercoupling, driving the system to an asymptotically stable state in which theexcited level of the atom is populated due to absorption. This work is intendedas a first result to pave the way to apply the metriplectic formalism to manyother irreversible processes in nonlinear optics.

Metriplectic Structure of a Radiation-Matter Interaction Toy Model