Abstract
In this study, we propose an approach to investigate the relationship between MOND theory and the holographic principle by incorporating q-deformed theory. We first present a brief overview of Verlinde's entropic gravity assumption, which suggests that gravity can be interpreted as an entropic force arising from the statistical mechanics of quantum fields. Some thermo-statistical properties of q-deformed fermion gas model in two spatial dimensions are introduced. At the low-temperature limit, we derive the q-deformed thermal energy and analyze the impacts of fermionic q-deformation on MOND theory. Specifically, we consider the q-deformed Fermi-Dirac statistics of the bits on the holographic screen and examine MOND theory depending on q-deformed acceleration scale. Deformed Friedmann equation is studied by taking into account Friedmann–Robertson–Walker (FRW) universe. This equation shows a modified identification of the evolution of the universe that is compatible with both MOND theory and the holographic principle
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