The P vs NP problem is one of the most fundamental unsolved questions in computational complexity theory, asking whether every problem whose solution can be verified in polynomial time (NP) can also be solved in polynomial time (P). This paper introduces a novel entropy-based mathematical proof that establishes fundamental limits on the solvability of NP problems within polynomial constraints, providing strong evidence that P≠NPP \neq NPP=NP. By incorporating entropy-driven time constraints, this study rigorously demonstrates that computational complexity follows a strict scaling law, preventing NP-complete problems from collapsing into P. The key contributions of this work include: Entropy-Based Complexity Regulation, proving that NP problems remain exponentially hard under entropy-driven constraints. Time-Dependent Computational Limits, demonstrating how entropy functions govern problem complexity over time. Mathematical Proof of P ≠ NP, showing that NP-complete problems inherently resist polynomial-time solutions due to entropy constraints. This research confirms that if entropy stabilizes over time, NP-complete problems remain exponential in complexity, ensuring that they cannot be solved in polynomial time. Conversely, if entropy decays unboundedly, standard complexity assumptions break down, leading to theoretical inconsistencies. Beyond its implications for computational complexity, this result introduces a new perspective on algorithmic mathematics, information theory, and the role of entropy in problem-solving. By bridging mathematical physics, entropy-driven computation, and complexity theory, this work advances research in cryptographic security, optimization problems, and quantum computing feasibility. The findings align with previous results in theory of computation, combinatorial optimization, and P vs NP research, offering an innovative entropy-based argument that solidifies the impossibility of NP collapse into P.