BFUT Paper 7  ·  Simulation V5.1

Thermal Equilibrium
in an Isotropic Radiative Medium

A three-dimensional thermal-body simulation demonstrating that 18 sparse luminous bodies occupying only ~0.047% of simulated volume produce a near-uniform ambient background - without requiring a primordial hot-origin assumption.

Vijay Shankar Sharma  ·  Independent Researcher  ·  Gurugram, India  ·  2026
Ambient Field Relaxation - Deviation from Equilibrium
Spatial Uniformity - Coefficient of Variation (log scale)
Press Run to start
Speed
Final Results

Numerical Outcomes

Parent Mean Temperature
14.375455
Scaled units
Child Mean Temperature
14.375508
Scaled units
Parent CV
1.410e-05
Coefficient of variation
Child CV
9.704e-06
Coefficient of variation
Child–Parent Mismatch
0.000367%
Mean temperature difference
Masked Mismatch
0.000362%
Body voxels excluded
Body Mean Temperature
8.239953
Final thermal body state
Luminous Occupancy
~0.047%
Of total simulated volume
Simulation Figures

Visual Output

Convergence Plot
Figure 1 - Ambient Field Relaxation. Top: deviation from final equilibrium, converging to zero. Bottom: CV decreasing toward ~10⁻⁵ on a log scale.
Mid-Plane Temperature Slice
Figure 2 - Mid-Plane ΔT Slice. Ambient temperature deviation from mean. Near-uniform ambient field despite extremely sparse luminous occupancy. Gold circles mark body locations.
Child Frame Histogram
Figure 3 - Child Frame ΔT Distribution (masked). Near-perfect Gaussian centred on zero - confirming symmetric, extremely small ambient temperature deviations.
Configuration

Simulation Parameters

ParameterValue
Model type3D thermal-body equilibrium (hall-with-bulbs analogue)
Boundary conditionPeriodic
Parent frame72 × 72 × 54 grid units
Child frame24 × 24 × 18 grid units
Total steps1,800  ·  dt = 0.045
Thermal bodies18 (stratified 3×3×2 placement)
Exchange radius7.2 grid units
Exchange coefficient k0.016
Body heat capacity420.0
Internal power mean0.613420 (min 0.520 / max 0.708)
Ambient diffusion D0.78
Luminous occupancy~0.047% of total volume
Data saved every50 steps (36 data points total)
What This Means

Interpretation

18 thermal bodies occupy only 0.047% of the total simulated volume. Despite this extreme sparsity, the ambient field converges to near-perfect uniformity: child-frame CV of ~9.70 × 10⁻⁶ and a child-parent mismatch of only ~0.00037%. The upper chart shows the ambient temperature rising from zero toward the equilibrium value of 14.375, reaching it exactly at step 1800. The CV chart shows spatial uniformity improving steadily, reaching its minimum around step 1350 before stabilising. Uniformity is not imposed - it emerges from thermodynamic equilibration through diffusion and radiative exchange. No primordial event required.

"Once sparse hot bodies are embedded in a large isotropic radiatively coupled medium, a nearly uniform background is not surprising at all. It is exactly what ordinary thermodynamic equilibration would lead one to expect."

Paper sentence (V5.1):

A three-dimensional thermal-body equilibrium simulation was constructed in which localised luminous structures were modelled as thermally active bodies with internal power, finite heat capacity, and two-way energy exchange with the surrounding medium under periodic boundary conditions. With sparse luminous occupancy (~0.047% of total volume), the model produced an extremely uniform ambient field - parent and child frames differing by only ~3.67 × 10⁻⁴% in mean temperature, with a child-frame coefficient of variation of ~9.70 × 10⁻⁶ - supporting the BFUT claim that large-scale thermal uniformity can arise naturally as an equilibrium property of an isotropic radiatively coupled medium.