Abstract: The superstatistics concept was introduced some 22 years ago [1], yet it still finds new applications in a variety of complex systems that exhibit time scale separation in their dynamical variables or where the temperature of the system is a random variable (a non-equilibrium situation). After a brief introduction to the basic concepts, I will discuss some examples of superstatistics in Lagrangian turbulence [2] and for cosmic-ray physics [3]. I will then proceed to more recent work [4] dealing with anomalous velocity distributions observed in slow quantum-tunneling chemical reactions. Here one observes q-Gaussian probability distributions where the entropic index q depends on the density n of the reactants. I will discuss a theory based on superstatistics that explains this density dependence q=q(n). If time remains, I will also talk about simple 1-d maps (generalizations of the continued fraction map) that exhibit q-Gaussian behaviour at critical points [5].
References:
[1] C. Beck and E.G.D. Cohen, Superstatistics, Physica A 322, 267 (2003).
[2] C. Beck, Statistics of 3-dimensional Lagrangian turbulence, Phys. Rev. Lett. 98, 064502 (2007).
[3] G.C. Yalcin and C. Beck, Generalized statistical mechanics of cosmic rays: Application to positron-electron spectral indices, Scientific Reports 8, 1764 (2018).
[4] C. Beck and C. Tsallis, Anomalous velocity distributions in slow quantum-tunneling chemical reactions, Phys. Rev. Research 7, L012081 (2025).
[5] C. Beck, U. Tirnakli, C. Tsallis, Generalization of the Gauss map: A jump into chaos with universal features, Phys. Rev. E 110, 064213 (2024)