This Wikipedia article,Decision tree model, states that decision tree complexity lower bound $O(n \log_2 n)$ for sorting problem is information theoretic since any algorithm ( modeled as decision tree) must learn $\log_2 n!$ bits of information.
Now, in a Turing machine model (or RAM model), suppose for some computational search problem it is proven that any algorithm must learn $n$ bits of information to produce the solution. The solution is uniquely determined by the $n$ bits. What can we conclude about the complexity lower bound of the problem?
P.S. My motivation is to cary over similar information theoretic lower bound arguments to other computation models. In decision trees model, to solve sorting problem, we have to uniquely identify the permutation that sorts the input list which requires $\log n!$ bits.