Entropy as the Ontological Foundation of the Spherical Model of the Universe (SMU)

The traditional interpretation of entropy as a measure of disorder leads to a pessimistic conclusion about the heat death of the universe. This article presents an alternative perspective within the Spherical Model of the Universe (SMU), where entropy is not the negation of structure, but a necessary condition of dynamics. Thermodynamic gradients generate thearrow of time, gravity arises from the tendency to maximizeentropy at horizons (ϵ-horizon, EEH), and spacetime arises from the zeroglobal entropy Primordial Planck Black Hole (PPBH, S = 0)axiom. Entropy is the primary driver of cyclical existence in this spherical, non-singular universe.We start from two fundamental axioms,that total energy is exactly zero (Etotal = 0) and total entropy is exactly zero(Stotal = 0), and show that Einstein's gravitational field equations can be reformulated asaccounting constraints: Se+Sg = 0, where Se represents the entropy of matter/energyand Sg represents the entropy of the gravitational field.This framework reconceptualizes physical reality: what we perceive as gravity isnot a fundamental interaction, but an energy debt. Matter borrows energy fromthe vacuum to exist, creating a gravitational potential and at the same time an accounting record ofthis debt. Entropy is not a measure of decay towards equilibrium, but towardsoptimal debt repayment—an arrow that guides the redistribution of energy to maintainglobal equilibrium.Geodesic lines appear to be optimal paths for energy exchange between matter and field, minimizing entropy production while satisfying the constraint Stotal = 0. Thisnaturally explains cosmic expansion as an oscillatory process: the universe movesfrom minimum enthalpy (concentrated quark-gluon plasma, zero debt) to maximum enthalpy (scattered radiation, maximum debt) and back, driven by the interplaybetween local entropy maximization and global entropic equilibrium.We derive modified field equations, compute explicit solutions for the Spherical Model of the Universe (SMU), demonstrate that observed cosmological phenomena (expansion, dark energy evolution, CMB anisotropy) arise naturally from this entropic dynamics, and show that the cosmic microwave background is not a fossil relic but a dynamic response of spacetime at its geometric limits—a boundary condition where photons encounter the distinguishable limits of phase space. The universe is not a material object evolving in time, but a ledger maintaining eternal balance. Existence is the constant differentiation of zero into complementary positive and negative components. The ledgers must be in balance, they always have been and always will be.