The Saeidi Thermodynamic Fixed Point: A Novel Framework for Energy Equilibrium in Quantum Systems

This preprint introduces the Saeidi Thermodynamic Fixed Point as a phenomenological framework for energy equilibrium in quantum systems. The work investigates a thermodynamic mechanism that links three quantum energy scales associated with a wavelength: the Planck photon energy, a de Broglie-type kinetic contribution, and relativistic rest energy. By minimizing an effective thermodynamic energy functional, the model shows that equilibrium selects a mass–wavelength relation of the form m(λ) ∝ λ⁻¹ and produces a scale-invariant dimensionless fixed point χ* = mcλ/h = 1/√2. At this fixed point, the rest-energy term mc² and the de Broglie contribution become balanced, while the explicit mass dependence of the Boltzmann factor cancels. The paper further connects this fixed-point structure with two earlier conceptual frameworks by the author: a mechanical reinterpretation of relativistic mass–energy equivalence through wavelength-scale work, and the Saeidi Quantum Acceleration (SQA) formulation of the Planck–de Broglie relation. Within this interpretation, hf is treated as a peak oscillatory quantum-energy scale, while mc² represents an effective mechanically coupled energy selected by thermodynamic equilibrium, following the relation mc² = hf/√2. The framework is applied to massive-photon blackbody spectra and shows that mass-dependent deviations are shifted primarily into the density-of-states factor and appear at order (ω₀/ω)². This provides a possible thermodynamic explanation for why a small effective photon mass could remain hidden within current COBE/FIRAS and Planck constraints on CMB spectral distortions. The work also identifies a structural connection between the resulting massive spectral kernel and the Generalized Inverse Gaussian distribution, suggesting a possible statistical duality behind the thermodynamic fixed point. The paper is theoretical and phenomenological in nature and is intended as a conceptual contribution to quantum thermodynamics, photon-mass phenomenology, and effective energy modeling.