A Geometric Framework for Reconciling the Contradiction Between Quantum Mechanics and Thermodynamics

The contradiction between the unitarity of quantum mechanics and the irre?versibility of thermodynamics is one of the core challenges in modern physics. Tra?ditional statistical mechanics explains macroscopic disorder and entropy increasethrough the concept of entropy but fails to uncover its geometric essence. This pa?per proposes the Dynamic Rigid Fractal Theory, redefining the geometric propertiesof the wavefunction, the physical meaning of entropy increase, and the quantum-to?classical transition mechanism from the perspective of dynamic fractal geometricevolution. By introducing the dynamic fractal dimension Df (t) and the fractaltension field Tf (x, t), the geometric attributes of the wavefunction are redefined,the dynamic evolution equation of fractal dimensions is derived, and the underly?ing geometric laws of entropy increase are revealed in conjunction with the physicalphenomena of decoherence and measurement. This paper further demonstrates howthe theory aligns with the traditional definitions of entropy in statistical mechanics(e.g., Boltzmann entropy) while extending the geometric interpretation of entropy.Ultimately, the Dynamic Rigid Fractal Theory not only resolves the core contradic?tion between quantum mechanics and thermodynamics but also provides a deeperexplanation for entropy increase and proposes specific experimental predictions tovalidate its key results.