Illustration of the Unified Field Theory: Navier–Stokes and Yang–Mills Insights through Entropic Time (Preprint)

This paper applies the entropic time framework—defining time as a tally of irreversible entropy production—to the celebrated Clay Millennium Problems: global regularity in three-dimensional Navier–Stokes flow and the Yang–Mills mass gap. Using a generalised d’Alembert principle, the work demonstrates, both analytically and through comprehensive numerical simulations, that recasting evolution in terms of entropic time ensures global regularity in all tested dissipative flows and preserves a mass gap in dissipative quantum Yang–Mills systems. The manuscript clearly distinguishes between physically observable dissipative systems and mathematical abstractions such as inviscid or strictly unitary limits, providing a transparent account of the limitations and implications for a Unified Field Theory of energy and time. Versions of these manuscripts are currently under review with a peer-reviewed journal. These documents are initial drafts, technical notes, and are work-in-progress research contributions. All results, proofs, and arguments are provisional and may require further mathematical development or rigour. The main purpose is to establish priority for the entropic time reparametrisation framework and to invite feedback, critique, and collaboration from the scientific community. These manuscripts present novel applications of entropic time (from a further paper which is also under review) to open problems in physics and mathematics. The topics—Navier–Stokes global regularity and the Yang–Mills mass gap—were chosen for their broad relevance, with the ultimate aim of drawing attention to the core hypothesis: that time is the perception of energy transitioning through entropic states via entropic time. This work is not yet peer-reviewed. All content is subject to future revision.