informationtheoretically

Informationtheoretically is an adverb used to indicate that a statement is grounded in information theory, the mathematical framework for quantifying information, uncertainty, and the fundamental limits of communication. In standard typography it is information-theoretically, often hyphenated; some authors may render it informally as informationtheoretically.

It is used to qualify claims about optimality, limits, or properties that are defined by information theory. For example, a communication scheme can be described as information-theoretically optimal if it achieves a bound that holds for all schemes under the same model, such as attaining channel capacity or minimal possible error probability in the limit of long codes. The term also appears when discussing compression bounds, entropy, mutual information, and the rate-distortion function.

Because the phrase denotes a theoretical criterion rather than a practical guarantee, informationtheoretically statements may differ from what is achievable in real systems due to implementation constraints, finite block lengths, or noise models. The word is common in academic writing in electrical engineering, computer science, statistics, and related fields, and reflects the broader distinction between information-theoretic limits and algorithmic or engineering performance.