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.
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]]).
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.
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.
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.
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.
The Second Law in various forms:
Clausius Statement: Heat cannot spontaneously flow from cold to hot
Kelvin-Planck Statement: No cyclic process can convert heat entirely to work
Entropy Statement: Total entropy of isolated system never decreases
Theorem (Law VI): For an isolated chi-system, von Neumann entropy is non-decreasing:
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
| 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