UED Reconstruction Programme — Paper 8: Energetic Reconstruction of Thermal and Statistical Consequence

Paper 8 of the UED Reconstruction Programme reconstructs thermal and statistical consequence from persistent configuration multiplicity, energy exchange, and unresolved transition statistics without assuming a microscopic particle gas, electron-collision heat picture, phonon ontology, or other universal thermal carrier. A thermal macrostate is treated as a coarse description of many accessible persistent configurations compatible with declared constraints. For discrete configuration states with energies EiE_i and probabilities pip_i, entropy is represented by the additive configurational measure S=−kB∑ipiln⁡piS=-k_B\sum_i p_i\ln p_i, reducing to S=kBln⁡ΩS=k_B\ln\Omega for equiprobable accessible configurations. Thermal equilibrium defines the intensive exchange parameter through 1/T=(∂S/∂U)X1/T=(\partial S/\partial U)_X, and canonical configuration weighting follows from the multiplicity of a large thermal environment. The framework recovers mean internal energy, heat capacity, equilibrium energy fluctuations, activated persistence loss, local thermal-energy continuity, Fourier conduction as a constitutive limit, thermal diffusion, lumped thermal relaxation, and nonnegative entropy production in a declared Markov transition regime. Paper 8 explicitly connects earlier UED regimes. Electrical dissipation from Paper 7 becomes internal configurational-energy input rather than an undefined loss; persistence barriers from Paper 5 acquire temperature-dependent escape rates; and Paper 6 configuration populations reduce to thermal statistical weighting under appropriate equilibrium conditions. Thermal relaxation time, structural persistence time, correlation time, event waiting time, and Alignment Threshold Time remain distinct quantities unless an explicit later derivation relates them. The paper does not claim numerical superiority over established thermodynamics and statistical mechanics where the reconstructed equations coincide with successful conventional relations. Its role is to establish a disciplined thermal/statistical layer while keeping microscopic carrier ontology and matter-specific transport mechanisms open.