This Note lays out the specialization of the two-potential constitutive framework — also known as the “generalized standard materials” framework — to rubber viscoelasticity. Inter alia, it is shown that a number of popular rubber viscoelasticity formulations, introduced over the years following different approaches, are special cases of this framework. As a first application of practical relevance, the framework is utilized to put forth a new objective and thermodynamically consistent rubber viscoelastic model for incompressible isotropic elastomers. The model accounts for the non-Gaussian elasticity of elastomers, as well as for the deformation-enhanced shear thinning of their viscous dissipation governed by reptation dynamics. The descriptive and predictive capabilities of the model are illustrated via comparisons with experimental data available from the literature for two commercially significant elastomers.