The Mechanical Arrow of Time and Entropy: Physical Randomization in the Expanding Stochastic String Network

The arrow of time is traditionally explained through the Second Law of Thermodynamics as an increase in statistical disorder. This paper provides a deterministic mechanical derivation for entropy using the Universal Space Theory (UST) framework. We propose that time is the fundamental oscillation frequency of the 1D Stochastic String Network (SSN). Entropy is redefined as the physical randomization of 1D string vectors caused by the expansion-driven thinning of the manifold. We demonstrate that as the universe expands, the mechanical coupling between strings weakens, leading to an irreversible loss of coherent topological information. This provides a purely structural origin for the unidirectionality of time and the decay of complex systems.