  The correspondence between cosmological models powered by a decaying vacuum
energy density and gravitationally induced particle production is investigated.
Although being physically different in the physics behind them we show that
both classes of cosmologies under certain conditions can exhibit the same
dynamic and thermodynamic behavior. Our method is applied to obtain three
specific models that may be described either as Lambda(t)CDM or gravitationally
induced particle creation cosmologies. In the point of view of particle
production models, the later class of cosmologies can be interpreted as a kind
of one-component unification of the dark sector. By using current type Ia
supernovae data, recent estimates of the cosmic microwave background shift
parameter and baryon acoustic oscillations measurements we also perform a
statistical analysis to test the observational viability within the two
equivalent classes of models and we obtain the best-fit of the free parameters.
By adopting the Akaike information criterion we also determine the rank of the
models considered here. Finally, the particle production cosmologies (and the
associated decaying Lambda(t)-models) are modeled in the framework of field
theory by a phenomenological scalar field model.
