In the context of energy transition and "dual carbon" goal, active distribution networks in the new power system can achieve scalable energy conservation and emissions reduction by increasing the penetration of renewable energy and leveraging demand-side management. To this end, a two-stage low-carbon energy management strategy based on dynamic carbon entropy theory is proposed. Carbon pricing serves as the price signal to encourage flexible loads to participate in low-carbon demand response. Firstly, the carbon entropy model is analyzed and an carbon entropy model considering energy storage is proposed, refining the carbon emission characteristics of the demand side. Building on this foundation, the evaluation index of node carbon potential is put forward to evaluate the cleanliness of carbon emission of the system. Secondly, a two-stage low-carbon optimization scheduling model is developed for active distribution networks based on the dynamic carbon entropy. The proposed model utilizes the guidance of time-of-use electricity prices and node carbon prices to promote the integration of new energy sources, reduce system carbon emissions, and play a role in peak shaving and valley filling. Finally, the proposed model's effectiveness is validated using an IEEE 33-node system, demonstrating the feasibility and advantages of the proposed low-carbon energy management method through case studies in active distribution networks.