External Upper Bounds on Reliably Extractable Classical Information from Physical Black-Box Computational Systems

We formulate and prove a conditional external upper-bound principle for physical computational systems treated as black boxes. The internal architecture, algorithmic mechanism, and microscopic dynamics of the system are not assumed to be known. The analysis uses only external physical invariants: finite available energy, finite observation time, nonzero noise or entropy production, finite measurement capacity and precision, and a reproducibility requirement expressed as an admissible error probability. Under these assumptions, the number of reliably distinguishable classical outcomes obtainable from the system is finite and bounded by an external information budget. The resulting bound is independent of the internal architecture as an upper bound, while the achievable fraction of the bound may depend on architecture and algorithmic design. Consequences are discussed for classical computation, artificial intelligence systems, quantum computation, quantum error correction, and the Physical Church–Turing thesis.