Unified Framework of the Arrow of Time and Entropy Flow in Rigid Fractal Structures

This paper proposes a novel model of the nature of time, positing that time is a dynamic manifestation embedded within rigid fractal geometry. Based on this model, the directionality of time (the arrow of time) and the flow of entropy (the second law of thermodynamics) are unified as natural outcomes of recursive dynamics in fractal geometry. By re-examining the relationship between time and entropy from geometric and dynamical perspectives, we show that entropy increase is essentially the process of the rigid fractal structure becoming more complex along the time dimension, while the directionality of time is driven by the irreversibility of fractal recursion depth. Through mathematical formulations, we establish unified equations linking time, entropy, and fractal geometry, predicting that the irreversibility of the arrow of time and entropy flow originates from the intrinsic properties of fractal geometry. Finally, we discuss experimental validation and the potential physical implications of this theory.