Hyperstatistics produces a q-exponential Boltzmann factor independent of the averaging density f(β) for 1D KGO and DO, reproducing high-T limits while distinguishing the systems via degeneracy and avoiding unphysical negatives.
Superstatis- tical properties of the Dirac oscillator with Gamma, log- normal, and F distributions,
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Hyperstatistical thermodynamics of the one-dimensional Klein-Gordon and Dirac oscillators: a closed-form q-generalized Boltzmann factor and a quantitative comparison with Beck's superstatistics
Hyperstatistics produces a q-exponential Boltzmann factor independent of the averaging density f(β) for 1D KGO and DO, reproducing high-T limits while distinguishing the systems via degeneracy and avoiding unphysical negatives.