A Unified Proof of the Riemann Hypothesis Based on Thermodynamic Entropy Steady State and Fluid Mechanics Steady State

Traditional proofs of the Riemann hypothesis mainly rely on pure number-theoretic deduction, function fitting and finite numerical verification, which suffer from cumbersome derivation, single dimensional perspective and insufficient logical closure. This paper breaks the limitations of conventional pure mathematical paradigms and proposes a novel cross-disciplinary proof framework grounded in the first principle of systemic steady-state existence. By integrating the maximum entropy steady-state axiom of thermodynamics and the irrotational steady-state field theory of incompressible fluid mechanics, a rigorous physical-mathematical isomorphic mapping system is constructed. Through closed-loop reductio ad absurdum reasoning, this study proves that all non-trivial zeros of the Riemann zeta function must converge strictly on the critical line Re(s)=1/2. Different from complex formula iteration and conventional algebraic derivation, the present work constrains number-theoretic behaviors via fundamental universal physical laws, establishes a dual-physics cross-verified closed logical system, and provides an innovative paradigm for the physical demonstration of classical number-theoretic conjectures.