Effects of bosonic and fermionic q-deformation on the entropic gravity

In this paper, we study thermodynamical contributions to the theory of gravity under the q-deformed boson and fermion gas models. According to Verlinde’s proposal, the law of gravity is not based on a fundamental interaction but it emerges as an entropic force from the changes of entropy associated with the information on the holographic screen. In addition, Strominger shows that the extremal quantum black holes obey neither boson nor fermion statistics, but they obey deformed statistic. Using these notions, we find q-deformed entropy and temperature functions. We also present the contributions that come from the q-deformed model to the Poisson equation, Newton’s law of gravity and Einstein’s field equations.

q-deformed Einstein equations from entropic force

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.

Thermosize effects in a q-deformed fermion gas model

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.