On the relation between Bekenstein–Hawking entropy and Landauer’s principle

Information is intricately woven into the fabric of physical systems, implying a profound connection between the nature of information and the underlying physics governing computational processes. This deep-seated relationship was illuminated by Landauer in 1961, who revealed that erasing a mere bit of information demands an expenditure of energy equivalent to [Formula: see text], underscoring the thermodynamic costs associated with information processing. In this investigation, Landauer’s principle is applied within the framework of Bekenstein–Hawking entropy. The study demonstrates that the introduction of a single bit of information into a black hole is related to a corresponding tangible increase of one unit of the horizon, namely, [Formula: see text], aligning seamlessly with the holographic principle.