On the relationship between entropy and information

In this paper, we analyze the relationship between entropy and information in the context of the mixing process of two identical ideal gases. We will argue that entropy has an information-based feature that is enfolded in the statistical entropy, but the second law does not include it directly. Therefore, in some given processes in thermodynamics where there is no matter and energy interaction between the system and the environment, the state of the system may goes towards a situation of lower probability to increase observer's information in the environment. This is a kind of an information-based interaction in which the total entropy is not constrained by the second law