Heat capacity of Holographic screen inspires MOND theory

Abstract: It is argued that Planck mass may be considered as a candidate for the mass content of degrees of freedom of holographic screen. In addition, employing the Verlinde hypothesis on emergent gravity and considering holographic screen degrees of freedom as a $q$-deformed fermionic system, it is obtained that the heat capacity per degree of freedom inspires the MOND interpolating function. Moreover, the MOND acceleration is achieved as a function of Planck acceleration. Both ultra-relativistic and non-relativistic statistics are studied.