Experiment V2.77: Non-Equilibrium Triple Coincidence (FRW/Vaidya)

Status: COMPLETE

Goal

Test the hypothesis that General Relativity is uniquely selected by thermodynamic equilibrium among diffeomorphism-invariant theories of gravity, using FRW cosmologies and Vaidya spacetimes.

Evaluate theories across multiple geometry regimes by computing the non-equilibrium triple: (heat flux deviation, internal entropy production, temperature mismatch).

Theoretical Framework

For horizons in GR, the Clausius relation holds exactly: δQ = T dS_geo. For modified gravity, the non-equilibrium extension is:

δQ = T (dS_geo + d_iS)

where d_iS >= 0 is the internal entropy production. The key discriminator is the decomposition:

d_iS = d_iS_GR_viscous + d_iS_theory_excess

The theory-excess term is zero for GR and nonzero for modified gravity.

Key Results

GR achieves perfect thermodynamic equilibrium (L_total = 0) while all tested modified gravity theories exhibit non-zero theory-excess entropy production across dynamical geometry regimes (FRW cosmologies, Vaidya spacetimes).

Scaling laws:

• f(R): L proportional to alpha^2 (quadratic in modification strength)
• BD: L proportional to 1/omega^2 (stronger coupling = larger deviation)

Modules

Module	Purpose
bd_scalar_dynamics.py	Brans-Dicke scalar field evolution
cosmological_perturbations.py	Perturbation theory on FRW backgrounds
frw_timevarying.py	Time-varying FRW geometries
horizon_utils.py	Horizon location and property utilities
kerr_vaidya.py	Kerr-Vaidya geometry implementation
vaidya_geometry.py	Vaidya spacetime geometry
diagnostics.py	Loss function diagnostics
ne_triple_loss.py	Non-equilibrium triple loss function
hessian_analysis.py	Hessian analysis around equilibrium
ne_optimizer.py	Non-equilibrium optimizer
sampling.py	Theory space sampling
tolerance_ball.py	Tolerance ball analysis
scenes_config.py	Test scene configuration
theory_space.py	Theory space parameterization
heat_flux.py	Heat flux computation
internal_entropy.py	Internal entropy production d_iS
temperature_structural.py	Structural temperature extraction
wald_entropy.py	Wald entropy computation