IET: A Physical Analytical Method for Computing the Energy–Information–Time Relationship

This work introduces Information–Energetic Thermodynamics (IET) as a physical, design-level analytical framework for advanced computing architectures. The central contribution is a dimensionless invariant that quantitatively links energy expenditure, effective information content, and time, thereby making explicit the physical cost of preserving and processing information under realistic conditions of dissipation, noise, and irreversibility. The framework reframes modern computation as a physical design problem rather than a purely algorithmic one, showing that scalability, stability, and long-term reliability are fundamentally constrained by energetic and temporal considerations. IET provides a unified metric that enables comparison across heterogeneous architectures, including quantum, neuromorphic, and large-scale artificial intelligence systems, prior to physical implementation. The analysis is intentionally formulated at an abstract and architecture-agnostic level. A canonical minimal example illustrates the core principles of the invariant, while a separate illustrative application to superconducting qubit readout near the Landauer limit demonstrates its operational meaning in a concrete physical setting. The work is intended as a methodological reference and conceptual foundation for both theoretical research and hardware-oriented design optimization in energy-limited computing.