2026/04/23 by Lucas Squillante, Samuel M. Soares, Constantino Tsallis +1 · 1 voice
Physics and Astronomy · #cond-mat.stat-mech #hep-ex #hep-th #nucl-th #physics.acc-ph #physics.data-an #physics.ins-det
arxiv published 2026/04/23 · arxiv updated 2026/07/01
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-generalized Boltzmann factor Bq considering uniform, γ, Log-normal, F, and the q-γ probability distribution functions. Remarkably, for all investigated distribution functions, Bq 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 γ-distributed relaxation times, the pressure decay over time associated with the pumping of 4He 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-γ-distribution function. Our proposal is applicable to systems with inherent non-Boltzmann-Gibbsian statistics in domains of the system.