In this paper, we introduce the dynamic cumulative residual interval Tsallis entropy (DCRITE) of order a, an information measure that generalizes both cumulative residual Tsallis entropy and interval (doubly truncated) entropies to quantify uncertainty for a lifetime (or loss) known to fall inside \( (t_1, t_2) \) . We provide its formal definition and show how DCRITE reduces to known measures. Several equivalent representations and probabilistic interpretations are derived, linking DCRITE to doubly truncated mean residual lifetimes and to normalized versions useful for comparisons across intervals. We also derive analytical bounds and monotonicity results, and characterize distributions by functional relations of DCRITE. Actuarial applications to loss data are provided to demonstrate model fitting and the practical computation of DCRITE for a range of parameter choices. A simulation study investigates the sampling properties of the DCRITE estimator and compares its performance with a competing entropy measure. Finally, we introduce the dynamic cumulative residual interval entropy generating function and present its basic properties and connections with DCRITE.
