Abstract: This paper first introduces the establishment process of the concepts of thermodynamic entropy and information entropy. Based on the application example of entropy in information theory，the correlation between thermodynamic entropy and information entropy is found. Finally，the relationship between information and energy， information entropy and thermodynamic entropy is discussed through Maxwell’s demon solved by Szilard，Landauer and modern experiments.

Key words: theory of entropy, thermal entropy, Maxwell’s demon, Landauer’s eraser