  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 a special 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 environment, the state of the
system may go towards a situation of lower probability to increase observer's
information in environment. This is a kind of an information-based interaction
in which the total entropy is not constrained by the second law.
