Information generation has no intrinsic mathematical or scientific relationship to biology any more than there is a theoretical model for gravitation in a ham sandwich. To assert otherwise is sheer cluelessness. Therefore, I will attempt to narrow down exactly what you mean by "informational generation".
It is questionable what you mean by "information generation" since "information" is a suitcase term that has very specific mathematical definitions that are quite different than many common definitions. If we were talking about something as simple as, say, concept formation in the brain (i.e. the process of thinking) you would be wrong to assert that there is informational generation that violates thermodynamics, as the processes create a net increase in entropy that is roughly 10^8 times greater than the decrease in entropy due to concept/thought creation. The DNA in living things behaves exactly like any other molecule, requiring an entropy/enthalpy gradient to execute its complex behaviors. Lacking an external gradient, the process stops.
The bottom line is that information creation is perfectly permissible with the caveat that the net entropy of the system is always increasing. Biological systems create vast quantities of entropy in their reproductive and complexity building processes, and the only reason it has been sustainable is that the solar system has a very large enthalpy gradient (from the sun mostly) that is being used up and converted into entropy as rapidly as possible in the process of building complex biological systems and organisms. If the sun went dark tomorrow, the process of "informational generation" would grind to a halt as it is an endothermic process ultimately. Which is all exactly what basic thermodynamics predicts (2nd Law and all that).
Does this answer the question?