Barrow black hole variable parameter model connected to information theory

One of the greatest challenges of theoretical physics today is to unveil the quantum information theory concerning what happens when one bit of information enters the black hole (BH) horizon. The Landauer principle showed that a certain amount of energy is generated when one-bit of information is erased as it enters the event horizon system. In this paper we used the recently developed Barrow BH model to calculate the addition to the area of the event horizon of his toy model by using the Landauer concept. Besides we make this computation considering $\Delta$ as a constant and a variable parameter. We formulate the Barrow parameter ($\Delta$) as a function of the energy/mass, which is new in the Barrow BH literature. We will investigate the differences between the Bekenstein-Hawking entropy ($\Delta=0$) and the fractal ($\Delta=1$) cases concerning the addition in the area of the BH. The asymptotical analysis is also mentioned and we will see that it affects only the fractal case. All the results accomplished here are new concerning BHs in general and the Barrow model literature in particular.