Time-Scalar Field Theory and Thermodynamics: The Geometric Origin of Entropy and the Arrow of Time

The Time-Scalar Field Theory (TSFT) reformulates thermodynamic irreversibility as a manifestation of temporal curvature, Θ(x, t). Entropy production arises from ∇ΘS > 0, linking the macroscopic second law to microscopic timescalar asymmetry. This paper derives the scalar Clausius relation dQ = TdSΘ, where SΘ encodes local curvature expansion in Θ. The model predicts measurable deviations from equilibrium in gravitational or accelerated frames, offering a unified geometric interpretation of energy flow, radiation, and vacuum entropy.