Narrow Results

We construct a two-parameter deformed SUSY algebra by constructing SUSY generators which are bilinears of n (p,q)-deformed fermions covariant under the quantum group SU_p/q(n) and n undeformed bosons. The Fock space representation of the algebra constructed is discussed and the total deformed Hamiltonian for such a system is obtained. Some physical applications of the quantum group covariant two-parameter deformed fermionic oscillator algebra are also considered.

In this study, to investigate the very nature of quantum black holes, we try to relate three independent studies: (q, p)-deformed Fermi gas model, Verlinde’s entropic gravity proposal and Strominger’s quantum black holes obeying the deformed statistics. After summarizing Strominger’s extremal quantum black holes, we represent the thermostatistics of (q, p)-fermions to reach the deformed entropy of the (q, p)-deformed Fermi gas model. Since Strominger’s proposal claims that the quantum black holes obey deformed statistics, this motivates us to describe the statistics of quantum black holes with the (q, p)-deformed fermions. We then apply the Verlinde’s entropic gravity proposal to the entropy of the (q, p)-deformed Fermi gas model which gives the two-parameter deformed Einstein equations describing the gravitational field equations of the extremal quantum black holes obeying the deformed statistics. We finally relate the obtained results with the recent study on other modification of Einstein equations obtained from entropic quantum corrections in the literature.

In this study, we investigate the influences of fermionic q-deformation on the Einstein equations by taking into account of Verlinde’s entropic gravity approach and Strominger’s proposal on quantum black holes. According to Verlinde’s proposal, gravity is interpreted as an entropic force. Moreover, Strominger’s suggestion claims that extremal black holes obey deformed statistics instead of the standard Bose or Fermi statistics. Inspired by Verlinde’s and Strominger’s suggestions, we represent some thermostatistical functions of VPJC-type q-deformed fermion gas model for the high-temperature limit. Applying the Verlinde’s entropic gravity approach to the q-deformed entropy function, q-deformed Einstein equations with the effective cosmological constant are derived. The results obtained in this work are compared with the related works in the literature.

We study the the high-temperature thermodynamic properties of the q-deformed fermion gas model by taking into account of the size effect of the gas particles. Starting from the logarithm of the grand partition function of the model, we calculate several thermodynamic functions of the model such as internal energy, entropy, and Helmholtz free energy by means of the deformation parameter q. Furthermore, the influences of the fermionic q-deformation on the thermosize effect in the confined deformed quantum gas systems such as the Seebeck-like and Peltier-like thermosize effects are discussed. Especially, we focus on the absorbed or released heat of the model in the Peltier-like thermosize effect. In the light of the results obtained in this work, we can conclude that the present q-deformed fermion model can be used to desing the new types of the micro-/nano-scaled quantum heat engines.