Facing the goal of "carbon peaking and carbon neutralization", the energy system presents many new characteristics, such as high proportion of renewable energy access, various forms of electrical cold and hot energy, frequent interaction between source network and storage, and deep coupling of information energy. Integrated energy system is faced with the energy trilemma problem that the three goals of “environmental sustainability-energy security-economy” cannot be met at the same time. In the integrated energy system with deep coupling of information, the impossible triangle problem will change from the traditional pure energy characteristic research to the dual characteristic research of information and energy. Entropy has the dual characteristics of information and energy. This paper summarizes the research of entropy theory in integrated energy system for the first time. Firstly, the basic theory of entropy is introduced and introduced into the impossible triangle problem as a quantitative tool. Then, based on the characteristics of energy impossibility triangle, the application of entropy theory in environmental protection, security and economy is introduced, the new problems in the operation of integrated energy system are summarized and refined, and the advantages of entropy theory in dealing with the impossibility triangle under the existing research results are analyzed. Finally, the main challenges and possible future research directions of the impossible triangle of integrated energy system based on entropy theory are summarized and prospected.