The way I've squared the similar terminologies in different fields is that as thermodynamic entropy increases, the amount of information required to encode/dupl

The way I've squared the similar terminologies in different fields is that as thermodynamic entropy increases, the amount of information required to encode/duplicate the state of the system increases (consider the extremes of maximally compact matter (say pre-big bang) and heat death where all matter is spread out arbitrarily over an unbounded volume). So entropy is equivalent to information as understood as a measure of disorder. This squares with shannon entropy as it can be understood as just a measure of the "disorder" in a random variable. The difficulty is distinguishing the other interpretation of information as a specific correlation, a quantification of order rather than disorder. When we think of communicating the state of a RV as some number of bits of "information", one way to think of it is that we're reducing the "possible disorder" (i.e. uncertainty) by communicating partial state. And so information here is the change in the possible disorder (uncertainty), the more information you receive the less uncertainty that remains.