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Rigid rotators and diatomic molecules via Tsallis statistics

“…The nonextensive generalization of Boltzmann-Gibbs statistics was proposed by Tsallis [1] to study systems involving long-range interactions, long-range microscopic memory, and nonequilibrium phenomenon. The nonextensive statistics has been applied in a wide range of areas like self-gravitating systems [2,3,4], solar neutrinos [5,6], and biological systems [7,8]. The functional form of the generalized entropy reads…”

Notes On The Klein-Gordon Equation

“…Instead of the Gibbs-Boltzmann entropy which yields the extensive statistics, one can use a generalized form of the entropy, the nonextensive entropy, which has become well known after the work of C. Tsallis [5,7] and which yields non-linear partial differential equations for the evolution of the distribution. In cosmology, the non-extensive statistics have been shown to model 'small' systems such as galactic matter distributions, where the range of the interaction (re: gravitational) is on the same scale as the system size [10], the solar neutrino problem [9] and systems that exhibit complex and non-linear dynamics [11]. The present derived result should prove of interest as a new nonlinear theory as nonlinear Klein-Gordon models are of importance in high energy particle physics.…”

Gravity and Cosmology in Kaniadakis Statistics: Current Status and Future Challenges

“…The special limit κ → 0 recovers the classical entropy. In light of these considerations, it is licit to regard Kaniadakis paradigm as an effective generalization of BG entropy that naturally emerges in various high-energy contexts, such as astrophysics, cosmology, gravitation and particle physics [11,12]. In parallel, it is worth mentioning that alternative studies have proposed κ-theory as an approach to epidemiology [13], seismology [14], economics [15] and natural sciences [16], posing it as a serious candidate to extend the ordinary statistical mechanics into systems exhibiting non-trivial correlations [17].…”