Non-extensive entropy in q-deformed quantum groups

Fibonacci oscillators and two-parameter generalized thermostatistics

“…Similar Hamiltonians were also considered by several other authors [9][10][11][12][13][14][15][26][27][28][29][30][31][32][33][34][35][36]. By using the generalized Fibonacci basic integer ½n in (2), the mean value of the ðq 1 ; q 2 Þ-deformed occupation number f k;q 1 ;q 2 can be calculated [29] by…”

“…Some of the high-temperature thermostatistical characteristics such as the internal energy and the equation of state are obtained in terms of some functions of the model deformation parameters q 1 and q 2 . The results obtained in this paper will serve as a two-parameter generalization related to the high-temperature thermostatistics of earlier q-deformed boson gas studies [9][10][11][12][13][14][15].…”

“…It may be called as the ðq 1 ; q 2 Þ-deformed Bose-Einstein distribution. In the limit q 1 ¼ q 2 ¼ 1, (11) reduces to the standard Bose-Einstein distribution function. From (8) and (9), it follows that the logarithm of the partition function has the following standard form:…”

“…Inspired by the one-dimensional q-deformed bosonic and fermionic algebra studies of Lavagno and Swamy [9][10][11][12][13][14][15], in the present paper, we consider a different generalization of bosonic system, which is called the commuting Fibonacci oscillators. By using the formalism of Fibonacci calculus, we particularly study the high-temperature thermostatistical properties of a gas of the commuting Fibonacci oscillators.…”

Quantum Groups GL p,q (2)- and $\mathit{SU}_{q_{1}/q_{2}}(2)$ -Invariant Bosonic Gases: A Comparative Study

“…They have found many applications in a wide spectrum of research in physics. For instance, there are some possible connections between one-parameter deformed quantum groups and generalized statistical mechanics [7][8][9][10][11][12][13][14][15][16][17]. However, in the last few years, a considerable effort has been spent to studies on thermo-statistical properties of two-parameter generalized bosonic and fermionic oscillator gas models which are invariant under the actions of some specific quantum groups.…”