STEH Trade-off Theorem: Hard Physical Limits for Space, Time, Energy, and Entropy in Computation

We introduce a unified physical framework for algorithmic tradeoffs based on Space (S), Time (T), Energy (E), and Entropy (H) --- abbreviated as STEH. This framework integrates classical and quantum perspectives, and yields rigorous lower bounds on computational processes by linking memory, runtime, thermodynamic cost, and uncertainty. We derive a set of inequalities governing the achievable resource combinations and illustrate how they sharpen classical results such as Landauer's principle and quantum speed limits. The STEH tradeoff formalism provides a systematic approach to study computation as a constrained physical process, highlighting resource complementarity and impossibility results that shape the limits of algorithms.