The Causal Graph H-Theorem: Deriving the Second Law from Directed Graph Dynamics

The Second Law of Thermodynamics—the monotonic increase of entropy—is traditionally derived from statistical mechanics assumptions such as "molecular chaos" (Stosszahlansatz) or coarse-graining. This paper presents an alternative derivation based on the Dual-Primitive Ontology. We model physical reality as a causal graph G=(V, E, Λ) where the edges possess a fundamental asymmetry derived from the Asymmetric Causation (AC) field. We prove the Causal Graph H-Theorem, demonstrating that for any system governed by AC-driven dynamics, the Shannon entropy of the vertex probability distribution increases monotonically toward a stationary state (dS/dt >= 0). This establishes that the thermodynamic arrow of time is a topological consequence of the underlying causal structure, rather than a statistical artifact of initial conditions.