Thermodynamic Censorship of Computation: A Physical No-Go Theorem for NP-Completeness

Abstract We propose a resolution to the P vs NP problem based on the thermodynamics of information. By treating computation as a physical process occurring within a finite entropic graph (Kernel v3), we demonstrate that solving NP-Complete problems requires a global entropy reduction that scales exponentially with energetic cost. Key Results: Spectral Gap Closing: We show that the energy gap between the solution state and error states closes exponentially (e^- N), implying that the time required for adiabatic evolution diverges for large N. Thermodynamic Censorship Principle: We introduce the principle that the universe physically censors the execution of polynomial-time algorithms for NP-Hard problems via the irreducible cost of measurement (TRI) and thermal noise floor. Numerical Validation: Simulations on 3-SAT Hamiltonians confirm that solution fidelity collapses under any non-zero thermal noise as problem size increases. Conclusion: P NP not due to lack of algorithms, but due to the Second Law of Thermodynamics. The class P represents thermodynamically allowed trajectories, while NP represents trajectories requiring exponentially improbable entropy reversals.