As the percentage of renewable energy in the Energy Internet (EI) gradually increases, how to deal with the uncertainty of renewable energy in the economic dispatch problem (EDP) becomes an important issue. This paper proposes a digital twin (DT) assisted economic dispatch strategy for EI with information entropy. First, we leverage the storage capacity of the DT and an extensive historical data set to provide a theoretical framework for quantifying uncertainty of renewable energy. Second, a renewable energy cost function based on the maximum entropy principle, confidence interval, and penalty factor is proposed to model the renewable energy resources considering the uncertainty. Further, we design a fully distributed Newton-surplus-based optimization algorithm. This algorithm achieves fast second-order convergence to ensure the real-time performance of the DT-assisted economic dispatch framework and overcome the asymmetry caused by the directed communication network. In addition, we give theoretical proof that the Newton-surplus-based algorithm can converge to the global optimal point. Finally, simulations validate the effectiveness of the proposed algorithm. Note to Practitioners—The essence of EDP is to minimize the total costs through optimal resource allocation while ensuring compliance with all operational constraints. With the increasing penetration of renewable energy resources, their strong stochasticity and uncertainty pose challenges to achieve reliable dispatch strategy. To address this issue, this paper presents the DT-assisted economic dispatch framework, model, and method to quantify the uncertainty of renewable energy resources and achieve distributed economic dispatch with fast convergence speed for EI. Our research is beneficial for practitioners to understand how to use the DT and information entropy to deal with the uncertain of renewable energy resources. The theory and simulation results demonstrate the correctness and effectiveness of the proposed method.