Bose–Einstein condensation in the framework of κ-statistics

Abstract

In the present work we study the main physical properties of a gas of κ-deformed bosons described through the statistical distribution function

Theoretical Foundations and Mathematical Formalism of the Power-Law Tailed Statistical Distributions

“…In the last twelve years various authors have considered the foundations of the statistical theory based on the κdistribution, in connection with the historical evolution of the research on the power-law tailed statistical distributions [7,11] e.g. the H-theorem and the molecular chaos hypothesis [12,13], the thermodynamic stability [14,15], the Lesche stability [16][17][18][19], the Legendre structure of the ensued thermodynamics [20,21], the thermodynamics of nonequilibrium systems [22], quantum versions of the theory [23][24][25][26], the geometrical structure of the theory [27], various mathematical aspects of the theory [28][29][30][31][32][33][34][35][36], etc. On the other hand specific applications to physical systems have been considered, e.g.…”

On Quantum Superstatistics and the Critical Behavior of Nonextensive Ideal Bose Gases

“…Phase transitions of systems obeying modified statistics have been studied particularly for generalized q-statistics in [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39], where the corresponding critical condensation temperature has also been calculated [29]. An extended study of the thermodynamic properties presented in this work and other interesting ones will be reported elsewhere.…”

“…We will follow this path in order to estimate the critical temperature where the Bose condensation occurs for a quantum system characterized by the generalized statistics depending only on the probability [12,14]. This analysis has already been considered for the quantum statistics of q-generalized entropies, and quite interesting results arise [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39]. This particular result will also be explored here for other generalized entropies.…”

Negentropy in Many-Body Quantum Systems

“…If the systems are non-ideal, the distribution functions change, due to the presence of particle correlations beyond the ideality. This requires the introduction of q-or κ-Fermi-Dirac and q-or κ-Bose-Einstein, or Gentile, or Griffiths, or Swamy et al [18,27,28] distribution functions, depending on the deviation from ideality considered.…”