Nonextensive Footprints in Dissipative and Conservative Dynamical Systems

Abstract

Despite its centennial successes in describing physical systems at thermal equilibrium, Boltzmann–Gibbs (BG) statistical mechanics have exhibited, in the last several decades, several flaws in addressing out-of-equilibrium dynamics of many nonlinear complex systems. In such circumstances, it has been shown that an appropriate generalization of the BG theory, known as nonextensive statistical mechanics and based on nonadditive entropies, is able to satisfactorily handle wide classes of anomalous emerging features and violations of standard equilibrium prescriptions, such as ergodicity, mixing, breakdown of the symmetry of homogeneous occupancy of phase space, and related features. In the present study, we review various important results of nonextensive statistical mechanics for dissipative and conservative dynamical systems. In particular, we discuss applications to both discrete-time systems with a few degrees of freedom and continuous-time ones with many degrees of freedom, as well as to asymptotically scale-free networks and systems with diverse dimensionalities and ranges of interactions, of either classical or quantum nature.

Open mathematical issues in nonextensive statistical mechanics

“…1.2) are well fitted by q-exponentials, with q being exhibited in Fig. 1.3 (from [16]); see also [40,45]. of hadrons in proton − proton collisions at central rapidity y with theoretical qexponentials with q ≃ 1.14 ± 0.02 and T ≃ (0.14 ± 0.01) GeV .…”

When may a system be referred to as complex?—an entropic perspective

“…The Hamiltonians of this kind that have been most studied from first principles (Newton's law) are the α-XY, α-Heisenberg, and α-Fermi-Pasta-Ulam d-dimensional ones; see Rodriguez et al (2023) and references therein. In all three models, we consider two-body…”