A statistical description for the Quasi-Stationary-States of the dipole-type Hamiltonian Mean Field Model based on a family of Vlasov solutions

For non-equilibrium quasi-stationary-states (QSS), we present a theoretical background based on a family of Vlasov equation solutions constructed by non-Gaussian distributions. Proposing a transformation, we connect the Vlasov stationary solutions to a non-standard theoretical perspective. Such one is suitable to describe the QSS involved in the d-HMF model, which occur while the system evolves towards equilibrium. Our results complement the notion of Tsallis formalism and represent input on a theoretical description of the systems behavior with long-range interactions out of equilibrium.