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Thermodynamics of Emergent Orchestration (TEO) — Civilization Simulation

Models civilizations and AI ecologies as coupled dynamical systems to test when societies synchronize, monopolize, polarize, or collapse.

What does this simulate?

teo_simulation.py integrates the coupled ODE system of the working paper "The Viable Corridor: A Three-Constraint Theorem for Survivable Multi-Agent Optimization" (papers/viable-corridor.md), version 0.5. It unifies four control paradigms into one dynamical model:

Paradigm Equation Paper eq. Origin
Market Regulated replicator dynamics (1), (1′) Evolutionary game theory (Taylor–Jonker, 1978)
Harmony Kuramoto synchronization (2), (3) Nonlinear physics (Kuramoto, 1975)
Homeostasis Simplex-preserving redistribution brake (4) Control theory
Substrate veto Cumulative entropy-overshoot budget (5), (5′), (6a), (6b) Thermodynamics (Landauer, 1961)

This is the faithful v0.5 model. It differs from the earlier pre-v0.3 code in three load-bearing ways, each matching a fix in the paper's revision history:

  • the homeostatic brake (4) engages at a regulatory threshold x_reg < x_crit (not at the failure threshold) and is simplex-preserving via a uniform-redistribution term (the simplex Σx=1 is conserved to ~1e-15);
  • the substrate is a cumulative reservoir: only integrated overshoot Ω(t) of the instantaneous ceiling D_max reaching S_max collapses health H (Lemma 3) — a momentary spike does not. The old code applied an instantaneous, fully-recoverable throttle, which the paper explicitly rejects;
  • substrate health H multiplies the replicator drift and the Kuramoto coupling (5′), so the competitive dynamics freeze as H → 0 — but the dissipation (5) tracks raw throughput f0, not H·f0 (v0.5 canonical model, §2.5): a non-self-throttling optimiser keeps producing entropy regardless of substrate health, so the veto binds endogenously.

What it shows (Appendix C of the paper)

Running the script reproduces the necessity tests P1 and prints the viability margins (V1 pluralism max_i x_i < x_crit; V2 coherence r > r_min; V3b substrate Ω/S_max < 1) for four scenarios:

  1. In-corridor — all three constraints hold; trajectory robustly viable.
  2. No regulation (γ = 0) — the strictly-dominant agent's share → 1 (monopolistic concentration, Lemma 1).
  3. Coherence collapse (K < K_c, from a coherent initial condition) — the order parameter dephases to r ≈ 0.31 < r_min (Lemma 2).
  4. Substrate veto (D_max low, η high) — raw throughput exceeds the ceiling, accumulated overshoot crosses S_max (Ω/S_max ≈ 27), H → 0 and the competitive dynamics freeze (Lemma 3, binding endogenously).

The two substrate regimes (entropy_couples_to_H)

The fourth scenario plus a contrast run illustrate the substrate-veto modeling decision resolved in v0.5 (paper §2.5, §6.1):

  • canonical (entropy_couples_to_H=False, the default): dS/dt ∝ f0, entropy tracks raw activity. When mean throughput exceeds D_max, overshoot grows without bound, Ω crosses S_max, and the veto binds (Ω/S_max ≈ 27, H → 0). This is the non-self-throttling optimiser of §4.3.
  • self-regulating (entropy_couples_to_H=True): dS/dt ∝ H·f0, so production throttles with health and Ω self-limits to (1 − D_max/(η·φ̄0))·S_max < S_max (Ω/S_max ≈ 0.86, H plateaus at ≈ 0.14). The veto never binds — the correct model of a system that does back off at the substrate limit.

run_substrate_contrast() runs both; the module docstring documents the decision and its rationale in full.

Running

python teo_simulation.py            # console: the four P1 scenarios + substrate contrast
python teo_simulation.py --save     # also write the Appendix-C figures (P1, P2, P3, P8)
python teo_simulation.py --save -o DIR   # write figures into DIR (default: lab/tools/)

Figures written by --save (consumed by Appendix C of the paper): teo_p1_necessity.png (Lemmas 1–3), teo_p2_gamma_c.png (critical brake strength γ_c ≈ 0.49, matching the closed-form estimate of §3.4), teo_p3_corridor.png (the viable region is a lower corner in (γ, K)), and teo_p8_capability.png (capability δ loads onto two constraints at once; single-axis rescue of a high-capability system fails — the central P8 result).

Requires numpy, scipy, matplotlib (see the repo requirements.txt).