PNMS Case Study: Landauer Limit: Computational Energy in Planck Signature Space

This case study analyzes the Landauer limit — the thermodynamic minimum energy required to erase one bit of information — within the Property-Neutral Matrixscope (PNMS) framework. Energies associated with the Landauer principle and seven semiconductor technology nodes (1971–2022) are projected into Planck signature space using the operator Σ = Φ_R(x) against the reference basis R₈. The analysis demonstrates that the Planck information channels Sₚ (entropy per bit) and Eₚ(bit) (Planck energy per bit) encode direct structural relations: E_L / Sₚ = T and E_L / Eₚ(bit) = T / Tₚ. Technology nodes form a monotonic trajectory in signature space toward the thermodynamic limit, allowing structural distance to the Landauer bound to be quantified across decades of semiconductor scaling.