Two-Dimensional Linear Matrix Wave Theory: Unified Derivation of Temperature-Time-Frequency Coupling, Gravitational Thermodynamics and Phase Transition Kinetics

The intersection of general relativity and thermodynamics yields the Tolman–Ehrenfest effect, Hawking radiation, and the Unruh effect. Conventional theories merely establish a phenomenological causal relation that spacetime distortion modifies temperature, lacking a unified microscopic wave-based fundamental mechanism. Meanwhile, they fail to resolve century-long intrinsic contradictions among three sets of theoretical frameworks for relativistic temperature transformation in special relativity. Starting from the sole fundamental postulate of two-dimensional linear matrix wave theory, we rigorously redefine four fundamental physical quantities from the perspective of wave ontology: mass corresponds to the bound energy of localized standing waves, intrinsic time is governed by the natural oscillation frequency of standing waves, observable three-dimensional space is a projection of an absolutely flat two-dimensional wave substrate, and temperature serves as a macroscopic statistical quantity measuring the ensemble-averaged oscillation frequency of multi-wavepacket systems. We jointly derive the core coupling relation \ (ddt= T\) and construct a unified underlying dynamical framework linking temperature, oscillation frequency, and intrinsic time. Relying on this coupling mechanism, we derive the Tolman–Ehrenfest effect, Hawking radiation, and the Unruh effect without circular reasoning, proving that all three gravitational thermal phenomena emerge naturally from background standing-wave field modulation of oscillation frequencies. We further fully derive a nonlinear cooling equation, a net phase transition rate constrained by Gibbs free energy, and an integral criterion for phase completion, followed by quantitative numerical calculations of the Mpemba effect comparing \ (80^\) hot water and \ (10^\) cold water. Based strictly on the wave postulate, we deduce the analytical expressions for the kelvin–hertz conversion constant and the Planck temperature. The entire theoretical construction relies solely on a single foundational postulate without any extra ad hoc assumptions, unifying four major branches of physics: gravitational thermodynamics, relativistic thermal transformation, nonequilibrium liquid-phase transition, and quantum wave ontology. Multiple quantitatively testable experimental predictions free of fitting parameters are also proposed.