The relationship between information and matter is not trivial, and may be more like the relationship between energy and matter, forming something like a triangle of influence in space-time. Information and energy both dissipate entropically through agglomerations of particles such that matter is, on average, stable in appearance. Appearance, though, is a function of information. Perhaps because information takes on a life of its own in human communication and has so many trivial uses for social organisms, we think of it as independent from matter and energy. Note, however, that we also think of energy as independent of matter.
The myth of Sisyphus shows how deeply entropy is engrained in the psyche and mythology of human history. The essential difference between gods and humans is that gods do not suffer entropy. Superheroes also live beyond the effects of entropy. Magic shows work by concealing the entropy of the reactions, whether spacial (disappearing and reappearing), informational (which card did you pick?), or chemical (spontaneous flame and reorganisation). Entropy is the difference between science and science fiction.