March 3, 2026Open Access

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

Key Points

The Shannon entropy of the vertex probability distribution increases monotonically over time with AC-driven dynamics, establishing a connection to the Second Law of Thermodynamics.
The Causal Graph H-Theorem provides a novel departure from traditional statistical mechanics assumptions, emphasizing a topological perspective.
Systems governed by Asymmetric Causation reveal a structured path toward a stationary state, implicating the arrow of time in thermodynamics.
Implications extend to theoretical foundations of thermodynamics, suggesting that the nature of time may stem from causal network structures rather than statistical initial conditions.

Abstract

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.

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

Key Points

Abstract

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