Non-Equilibrium Triple Coincidence (Unified BH Framework)
Experiment V2.78: Non-Equilibrium Triple Coincidence (Unified BH Framework)
Status: COMPLETE
Goal
Extend the non-equilibrium triple coincidence test to a unified framework covering all horizon types: static black holes (Schwarzschild, Kerr, Reissner-Nordstrom), dynamical black holes (Vaidya, generalized Vaidya), FRW cosmology, and local Rindler.
Evaluate 9 theories across 27 test scenes spanning 4 geometry regimes.
Key Results
GR achieves perfect thermodynamic equilibrium (L_total = 0) while modified gravity theories exhibit non-zero theory-excess entropy production.
| Theory | L_total | L_theory_excess | Equilibrium? | Criteria Passed |
|---|---|---|---|---|
| GR | 0.00 | 0.00 | YES | 8/8 |
| Starobinsky-Viable | 5.51e-16 | 1.00e-16 | YES | 8/8 |
| BD-SolarSystem | 1.22e-4 | 4.00e-6 | YES | 8/8 |
| Diagnostic-WrongG | 1.00e-2 | 0.00 | YES | 8/8 |
| f(R)-Weak | 5.51e-2 | 1.00e-2 | NO | 4/8 |
| f(R)-Strong | 5.51 | 1.00 | NO | 2/8 |
| BD-Extreme | 1.45e+4 | 816 | NO | 1/8 |
| GB-Topological | 1.00e+6 | 0.00 | YES | 7/8 |
| 4D-EGB | 1.00e+14 | 100 | NO | 1/8 |
Regime Analysis
Static Black Holes
All theories pass static BH equilibrium. Static configurations have no heat flux and no entropy change, so the Clausius relation is trivially satisfied.
Dynamical Black Holes (Vaidya)
Strongest discrimination regime:
| Theory | BH Dynamical Loss | Equilibrium? |
|---|---|---|
| GR | 0.0 | YES |
| Starobinsky | 1.0e-16 | YES |
| BD-Solar | 4.0e-6 | YES |
| f(R)-Weak | 0.01 | NO |
| f(R)-Strong | 1.0 | NO |
| BD-Extreme | 816.3 | NO |
| 4D-EGB | 100.0 | NO |
FRW Cosmology
Similar discrimination pattern. GR at equilibrium, all modified theories with significant deviations fail.
Local Rindler
All theories pass. Local Rindler patches test entanglement equilibrium, which is less sensitive to theory modifications than dynamical horizons.
Physical Conclusions
-
GR Uniqueness: GR is the unique theory (among those tested) that achieves perfect thermodynamic equilibrium across all horizon types and dynamical regimes.
-
Observational Viability Correlation: Theories that pass solar system and cosmological tests also achieve near-equilibrium, suggesting a deep connection between thermodynamic equilibrium and observational viability.
-
Scaling Laws:
- f(R): L proportional to alpha^2
- BD: L proportional to 1/omega^2
- 4D-EGB: L proportional to alpha_GB^2
Integration Validation
Tolman Redshift
The Tolman relation T_local = T_H / sqrt(f(r)) validated at 5 radii to machine precision (relative error < 10^{-15}).
Modules
| Module | Purpose |
|---|---|
bh_dynamical.py | Dynamical black hole geometries |
bh_static.py | Static black hole geometries |
frw_cosmology.py | FRW cosmological backgrounds |
horizon_utils.py | Horizon location utilities |
local_rindler.py | Local Rindler wedge construction |
exp23_bridge.py | Bridge to Exp 23 results |
exp25_bridge.py | Bridge to Exp 25 results |
exp26_bridge.py | Bridge to Exp 26 results |
diagnostics.py | Loss diagnostics |
ne_triple_loss.py | Non-equilibrium triple loss |
regime_losses.py | Per-regime loss decomposition |
scenes_config.py | Scene configuration |
theory_space.py | Theory space parameterization |
clausius.py | Clausius relation verification |
heat_flux.py | Heat flux computation |
internal_entropy.py | Internal entropy production |
temperature_geometric.py | Geometric temperature extraction |
wald_entropy.py | Wald entropy computation |