Definition · Chain Position 141 of 346

LAW VI DEFINITION (COHERENCE NON-INCREASE)

Romans 8:20-21 "creation subjected to futility"

**Law VI (Coherence Non-Increase):** Closed systems cannot increase their own coherence; entropy increases or remains constant.

Scripture Bridge
Romans 8:20-21 "creation subjected to futility": The theological grounding for this concept.

Connections

Assumes

  • None

Enables

  • None
Objections & Responses
Objection: Life Appears to Decrease Entropy
"Living organisms create order from disorder. Doesn't this violate Law VI?"
Response

Life is not a closed system. Living organisms are open systems that import low-entropy energy (sunlight, food) and export high-entropy waste (heat, excrement). The total entropy of organism + environment always increases. Law VI applies to closed systems only. This is precisely why grace must be external ([[059_BC2_Grace-External-To-System|BC2]]).

Objection: Quantum Fluctuations Create Order
"Vacuum fluctuations create particle-antiparticle pairs—order from nothing."
Response

Vacuum fluctuations are constrained by Heisenberg's uncertainty principle: ΔE·Δt ≥ ℏ/2. They are temporary borrowings against the vacuum, not permanent entropy violations. The pairs annihilate, restoring the original state. No net coherence is created.

Objection: Self-Organizing Systems Disprove This
"Bénard cells, chemical oscillators, and other dissipative structures create order spontaneously."
Response

Dissipative structures require energy flux through the system—they are far-from-equilibrium open systems. Remove the temperature gradient (Bénard cells) or chemical potential (oscillators), and the order disappears. This confirms rather than refutes Law VI: order requires external input.

Objection: The Universe's Entropy Was Low at Big Bang
"If entropy always increases, why did the universe start with low entropy?"
Response

This is the "past hypothesis" problem. Theophysics answers it: the initial low entropy state required an external source—the Creator. The Big Bang's low entropy is evidence for [[063_BC6_Infinite-Energy-Source|BC6]] (infinite energy source required for entropy defeat). The universe's subsequent entropy increase confirms Law VI.

Objection: Maxwell's Demon Can Decrease Entropy
"A sufficiently intelligent being could sort molecules and decrease entropy."
Response

Maxwell's demon was refuted by Bennett and Landauer. The demon must store information about molecular velocities, and erasing this information (as memory fills) costs at least kT ln(2) per bit—exactly compensating any entropy decrease. Intelligence cannot circumvent Law VI; it can only temporarily defer entropy at the cost of greater entropy elsewhere.

Physics Layer

Thermodynamic Formulation

The Second Law in various forms:

Clausius Statement: Heat cannot spontaneously flow from cold to hot

\delta Q_{cold \to hot} \leq 0 \text{ (spontaneous)}

Kelvin-Planck Statement: No cyclic process can convert heat entirely to work

\eta = W/Q_H < 1

Entropy Statement: Total entropy of isolated system never decreases

dS_{total} \geq 0

Mathematical Layer

Formal Statement and Proof

Theorem (Law VI): For an isolated chi-system, von Neumann entropy is non-decreasing:

S(\rho_\chi(t)) \geq S(\rho_\chi(0))

Proof (via subadditivity):

1. Let system + environment start in product state: \rho_{tot}(0) = \rho_\chi \otimes \rho_E

2. Total system evolves unitarily: \rho_{tot}(t) = U\rho_{tot}(0)U^\dagger

3. Unitary evolution preserves total entropy: S(\rho_{tot}(t)) = S(\rho_{tot}(0))

4. By subadditivity: S(\rho_{tot}) \leq S(\rho_\chi) + S(\rho_E)

5. Initially: S(\rho_{tot}(0)) = S(\rho_\chi(0)) + S(\rho_E(0)) (product state)

6. At time t: S(\rho_{tot}(t)) \leq S(\rho_\chi(t)) + S(\rho_E(t))

7. From (3): S(\rho_\chi(0)) + S(\rho_E(0)) \leq S(\rho_\chi(t)) + S(\rho_E(t))

8. If environment entropy bounded: S(\rho_\chi(t)) \geq S(\rho_\chi(0)) \square

Evidence
Empirical Grounding
This isn't philosophy. This is measured.
  • Landauer's Principle
Defeat Conditions

To Falsify This

  1. **Entropy Decrease in Isolation:** Demonstrate a genuinely closed system where entropy decreases spontaneously without external input
  2. **Self-Organization Without Energy Input:** Show coherence increase in a system with no external work, energy flow, or information input
  3. **Perpetual Motion Machine:** Construct a device that produces work indefinitely without external energy source
  4. **Spontaneous Order ex Nihilo:** Prove that order can arise from chaos without any organizing principle or external intervention
Cross-Domain Mappings
Domain Mapping
Physics Second Law of Thermodynamics
Theology Fallen State / Decay
Consciousness Cognitive Entropy
Quantum Decoherence Direction
Scripture Romans 8:20-21 "creation subjected to futility"
Evidence Thermodynamic Arrow
Information Landauer Principle

Bridge Count: 7