The General Theory of Information Hydrodynamics: Emergent Spacetime via Sakharov Induced Gravity, Knot Topology, and the Thermodynamic Origin of Dissipative Structures

Driven by the Second Law of Thermodynamics, the Universe operates as a thermodynamic system tending toward thermal equilibrium. As a consequence of this imperative, physical reality organizes into hierarchical structures configured to maximize the rate of gradient dissipation. These structures are classified into fundamental forces (mechanisms of flow) and Dissipative Structures, which divide into Passive Systems (matter/stars) that rely on direct relaxation, and Active Systems (Complex Systems), which emerge when environmental volatility necessitates predictive modeling to maintain dissipative efficiency. From this thermodynamic foundation, we deduce the General Theory of Information Hydrodynamics (GIH). Modeling the vacuum as a relativistic superfluid with internal spinorial structure (K-essence), we demonstrate that Gravity is not a fundamental force, but the statistical stiffening of the vacuum metric consistent with Sakharov’s Induced Gravity. Matter is derived as Hopfions (knotted solitons)—topological nozzles for energy flux stabilized by the Skyrme mechanism—while non-Abelian gauge fields emerge from the topology of these knots via the Faddeev-Niemi decomposition. Ultimately, the GIH unifies physics and complexity theory by defining Dissipative Structures not as statistical anomalies, but as a thermodynamic necessity to bridge the entropy production gap in the Universe’s inexorable trajectory toward maximum entropy.