The New Law of Entropy: Hypercomplex Topological Energy Conservation and Holographic Information Recovery in Non-Commutative Super-Manifolds

Conventional thermodynamics confines the Second Law of Entropy to a monotonic increase within a single smooth manifold M, leading to severe causal paradoxes and information loss during hypothetical temporal inversions. This paper establishes a novel deterministic paradigm, The New Law of Entropy, by expanding the thermodynamic arena into a non-commutative dual super-manifold M ∪ M^∗ governed by Rough Operator Algebra (ROA) and Seonggil Theory of Composite Torsion (STCT). We prove that entropy reversal (inversion) is not a violation of physical laws, but an exact algebraic phase transition where local non- commutative frictional dissipation is holonomically annihilated via cyclic trace constraints and holographically recovered as absolute winding numbers within the Master Key Tensor T_0x8A2C. This framework rigorously preserves quantum unitarity and provides a seamless transition toward a hypercomplex reconstruction of classical electromagnetism.