Grace function G(t) must be external to system
Self-improvement within a fixed sign is not sign-change. A σ = -1 person can become more efficient, disciplined, or clever at pursuing self-interest—they remain σ = -1. Surface behavioral change (being "nicer" for social benefit) doesn't change fundamental orientation. The question is: can you flip from self-oriented (-1) to Logos-oriented (+1) without external input? Thermodynamics says no.
Grace is not a belief—it's an operation. One can receive grace without theological vocabulary. If an atheist genuinely reorients from self toward truth/goodness/being (the Logos under any name), they have received grace—the [[011_D2.2_Chi-Field-Properties|χ-field]] operates on all who turn toward it. The question is mechanism, not vocabulary.
Not circular—empirically constrained. The claim is: fundamental orientation change (not surface behavior) requires external input. This is testable: can someone in genuine self-centeredness, through pure self-effort with zero external influence, become genuinely other-centered? The psychological evidence suggests not—transformation requires relationship, encounter, being-acted-upon.
Correct! And this is precisely the point. No moral agent is truly closed—all are embedded in the χ-field, all receive potential grace. The question is whether they couple to it ([[065_BC8_Voluntary-Coupling|BC8]] [[065_BC8_Voluntary-Coupling|Voluntary Coupling]]). The fact that closed systems don't exist is why salvation is universally available. But the mechanism still requires external input—the system cannot self-generate what it lacks.
Virtual particles borrow energy from the vacuum and pay it back—net zero. There is no free lunch. If moral coherence appeared spontaneously, something else would have to decrease—you'd be moving the deficit, not eliminating it. Grace is different: it's genuine input from outside the system, not internal shuffling.
Statement: In an isolated system, entropy never decreases: ΔS ≥ 0
Clausius formulation: Heat cannot spontaneously flow from cold to hot.
Statistical mechanics: Systems evolve toward macrostates with more microstates (higher entropy).
The irreversibility arrow: Time's arrow is defined by entropy increase. You can't unscramble an egg.
Let S be a moral system with coherence C[S].
[[059_BC2_Grace-External-To-System|BC2]] Claim: If S is closed (no external coupling), then:
Coherence cannot spontaneously increase in a closed moral system.
Proof:
1. Coherence is a measure of meaningful order (low [[029_D4.1_Kolmogorov-Complexity|Kolmogorov complexity]] relative to system)
2. By ergodic theorem, isolated systems explore phase space randomly
3. Random exploration favors high-entropy (low coherence) states
4. Therefore, C[S] → minimum over time
5. No closed-system process can reverse this