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.
Title resolution pending
2 Pith papers cite this work. Polarity classification is still indexing.
2
Pith papers citing it
abstract
We propose a general approach, named by us hyperstatistics, to treat complex systems, in which Boltzmann-Gibbs statistics breaks down in domains of the system. Hyperstatistics preserves the concavity of nonadditive $q$-entropy. We obtain analytical closed-form expressions for the here proposed $(q, n)$-generalized Boltzmann factor $B^n_q$ considering uniform, $\gamma$, Log-normal, F, and the $q$-$\gamma$ probability distribution functions. Remarkably, for all investigated distribution functions, $B^n_q$ reduces to a $q$-exponential-type function. To demonstrate the applicability of hyperstatistics, we use a table top experiment of the discharge of a capacitor considering $\gamma$-distributed relaxation times, the pressure decay over time associated with the pumping of $^4$He lines of a closed cycle cryostat, midrapidity data for $p$-Pb collisions at the LHC, as well as data set for acceleration distribution in turbulent systems. Furthermore, we deduce the power-law-like dielectric response using the $q$-$\gamma$-distribution function. Our proposal is applicable to systems with inherent non-Boltzmann-Gibbsian statistics in domains of the system.
years
2026 2representative citing papers
Hyperstatistics is a renamed gamma-superstatistics result: Laplace-transforming a gamma distribution of inverse temperatures yields the q-exponential, and the paper fits this form to Brownian VACF data without reconciling q and n.
citing papers explorer
-
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.
-
A few remarks on hyperstatistics and some applications
Hyperstatistics is a renamed gamma-superstatistics result: Laplace-transforming a gamma distribution of inverse temperatures yields the q-exponential, and the paper fits this form to Brownian VACF data without reconciling q and n.