Non-Equilibrium Thermodynamics in the Scalar Drag Emergence Framework

This work develops non-equilibrium thermodynamics within the Scalar Drag Emergence Framework (SDEF) as a dynamical consequence of transport–ancestry interactions under coarse-graining. Starting from the primitive generator, macroscopic transport is shown to arise from correlations of unresolved fluctuations, yielding gradient-driven fluxes without introducing phenomenological transport laws. Entropy production emerges from flux–gradient interactions and is positive at the coarse-grained level under dissipative conditions. The framework recovers linear response behavior near equilibrium as a small-gradient approximation, while nonlinear and far-from-equilibrium regimes arise when transport outpaces ancestry regulation and saturation effects become significant. In these regimes, transport becomes anisotropic, gradient-dependent, and capable of generating localized structures. This establishes non-equilibrium thermodynamics as the dynamical extension of the hydrodynamic and thermodynamic limits within SDEF, without introducing additional primitives, conservation assumptions, or external statistical formalisms.