We apply the Conservation-Congruent Encoding (CCE) framework to the P versus NP problem by explicitly modeling the thermodynamic tradeoff between reversible information processing (Irev) and irreversible information processing (Iirr). While constructive algorithms theoretically avoid exponential candidate generation, worst-case NP-complete problems possess constraint topologies that are logically irreducible. Mapping this implicitly exponential constraint density into a poly(N) physical memory forces continuous intermediate state erasure. Under the physical identity χ = κ(Irev/Iirr), we demonstrate that processing irreducible logical structures strictly triggers an exponential Landauer tax, yielding the physical contradiction poly(N) + poly(N) ≥ Θ(2N ). We present a physical constraint on scalable realizations of worst-case search on digital substrates, independent of formal mathematical shortcuts.