https://doi.org/10.1140/epjc/s10052-021-09486-x
Regular Article - Theoretical Physics
Tsallis statistics and generalized uncertainty principle
1
Dipartimento di Fisica, Università di Salerno, Via Giovanni Paolo II, 132, 84084, Fisciano, SA, Italy
2
INFN, Sezione di Napoli, Gruppo Collegato di Salerno, Via Giovanni Paolo II, 132, 84084, Fisciano, SA, Italy
Received:
4
June
2021
Accepted:
25
July
2021
Published online:
30
July
2021
It has been argued that non-Gaussian statistics provide a natural framework to investigate semiclassical effects in the context of Planck-scale deformations of the Heisenberg uncertainty relation. Here we substantiate this point by considering the Unruh effect as a specific playground. By working in the realm of quantum field theory, we reformulate the derivation of the modified Unruh effect from the generalized uncertainty principle (GUP) in the language of the nonextensive Tsallis thermostatistics. We find a nontrivial monotonic relation between the nonextensivity index q and the GUP deformation parameter 
, which generalizes an earlier result obtained in quantum mechanics. We then extend our analysis to black hole thermodynamics. We preliminarily discuss our outcome in the broader context of an effective description of Planck-scale gravitational physics based on Tsallis theory.
© The Author(s) 2021
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