This monograph is intended to summarize the author’s work on some generalizations of the quantum Bose–Einstein statistics and related quantum distributions involving various approaches. Two branches of such generalizations are covered: phenomenological substitutions of the Gibbs factor using the Tsallis q-exponential and complex-valued parameters of statistics. The branches are interwined in one case.
The book is based on the author’s papers
• Phase transition in a system of 1D harmonic oscillators obeying Polychronakos statistics with a complex parameter. Low Temp. Phys. 39(10): 888–892, 2013.
• Complex-valued fractional statistics for D-dimensional harmonic oscillators. Phys. Lett. A. 378(3): 100–108, 2014.
• Weakly nonadditive Polychronakos statistics. Phys. Rev. A. 89(5): 052116, 2014.
• Ideal Bose-gas in nonadditive statistics. Low Temp. Phys. 44(10): 1025–1031, 2018.
• Deforming Gibbs factor using Tsallis q-exponential with a complex parameter: An ideal Bose gas case. Symmetry. 12(5): 732, 2020.
• Nonadditive generalization of the Gentile statistics. Low Temp. Phys. 49(8): 984–990, 2023.
and the following manual (originally published in Ukrainian):
• Exotic Types of Statistics. Lviv: Lviv University Press, 2018.
