Paralleling the Bekenstein bound, we encounter Landauer’s principle—a postulate that has roused both fascination and contention within scientific discourse. At its heart lies a notion of elegance and profundity: the expungement of a solitary information unit exacts a toll, quantified as k_b·T·ln2, where k_b symbolizes Boltzmann’s constant, and T signifies the temperature of a thermic reservoir. Despite scrutiny, Landauer’s principle remains anchored as a bedrock law, buttressed by its thermodynamic origins and its resonance within both quantum and classical feedback systems.

However, the amalgam herein isn’t an assemblage of preexisting constituents; it embodies a leap into uncharted terrain. Within this scholarly fabric resides a seminal disclosure—the extension of Landauer’s principle. This revelation casts luminance upon the fact that information erasure may precipitate an escalation in entropy devoid of anticipated energy dissipation. This revelation establishes fresh conduits interlinking information processing and entropy dynamics.

The annals of this article chronicle pivotal landmarks: the epochal quantification of heat release during singular-bit data manipulation in 2012; an assemblage of experiments affirming Landauer’s principle and quantifying energy outlays in bit transitions; the quantum choreography of molecular magnets, elegantly broadening the principle’s purview into this esoteric quantum dominion.

Notwithstanding, akin to all groundbreaking postulates, challenges manifest. Skepticism emerges, unfurling the banner of circular reasoning and flawed axioms. However, the bastion of Landauer’s principle remains unassailable, rooted within the second law of thermodynamics, intrinsically intertwined with entropy vicissitudes concomitant to information manipulation.

The confluence of the Bekenstein bound and Landauer’s principle resonates with repercussions transcending the realm of theoretical contemplation. The susurrus of quantum computation reverberates, underscoring the imperative of comprehending the pivotal thresholds of information. Simultaneously, the domain of thermodynamics concedes to the inextricable connection between information and entropy, affording avenues to innovative frameworks for energy-efficient thermal reservoirs.

The incorporation of the Bekenstein boundary and Landauer’s principle has ushered an estimation below 1.4·10³⁰ bits/m³ encapsulated within a black hole. The precision of this quantification, hitherto unsettled within anterior literature, propounds a compelling challenge to Hawking’s conundrum of information erasure within these enigmatic cosmic vacuums.

Incorporating the Bekenstein boundary and Landauer principle has facilitated the estimation of fewer than 1.4·10³⁰ bits/m³ stored within a black hole. This value presents a compelling challenge to Hawking’s paradox of information erasure within black holes.

The harvested value (1.4·10³⁰ bits/m³) holds significant implications for advancing scientific research across various fields, including black hole thermodynamics, astrophysics, astronomy, information theory, the Bekenstein limit, and the exploration of new laws of nature. It’s worth emphasizing that the precise quantification of the stored bits within a black hole of one cubic meter remains uncertain within current scientific literature. This circumstance prompts inquiries concerning not only its exact magnitude but also the comprehensiveness of documented findings on this subject.

Considering these findings, the value presented stands as a significant and pioneering estimation. Further investigation is warranted to refine this estimation and determine the precise number of bits within one cubic meter of a black hole, contributing to a deeper understanding of these enigmatic cosmic entities and the complexities of information storage within them.

The integration of the Bekenstein bound and Landauer’s principle represents a substantial advancement in comprehending the fundamental limits and principles governing information and energy. By merging these principles, researchers forge a framework that offers fresh insights and potential avenues of exploration.

The motivation for uniting the Bekenstein bound and Landauer’s principle arises from the aspiration to establish a unified framework encompassing constraints on information storage and the energetic costs associated with processing. This integrated approach promises a deeper understanding of the intrinsic connections between thermodynamics, information theory, and quantum mechanics. By grasping their significance and exploring their integration, researchers gain insights that surpass the sum of their individual contributions, leading to a more comprehensive understanding of the underlying principles governing information and energy.

The amalgamation of the Bekenstein bound and Landauer’s principle provides a more comprehensive grasp of the limitations and principles governing information and energy. This synthesis enables the exploration of the intricate interplay between information storage, processing, and energy dissipation in physical systems. It furnishes deeper insights into the constraints and fundamental principles shaping information and energy dynamics.

The significance of merging these principles extends beyond theoretical contemplation, with practical implications spanning various disciplines. In the realm of quantum computing, where information processing transpires at the quantum level, understanding the limits of information storage and the energetic costs of manipulation is crucial for developing efficient and scalable quantum systems.

In the domain of thermodynamics, the fusion of the Bekenstein bound and Landauer’s principle contributes to a deeper understanding of the fundamental connections between information and entropy. It sheds light on the relationship between the microscopic characteristics of physical systems and their macroscopic thermodynamic behavior. This understanding carries implications for designing and optimizing energy-efficient thermal storage systems, where the interplay of information and energy plays a pivotal role.

This article introduces a thought-provoking concept—a potential explanation for “dark matter” rooted in information physics. This idea posits information as the fifth form of physical matter, with previous studies exploring the information content of the Universe. If information carries mass, its influence would solely manifest through gravitational interactions, rendering it invisible to electromagnetic detection. This proposition challenges traditional notions and suggests that information could be the source of the elusive dark matter in the universe. Ongoing efforts in information physics, such as those by the Information Physics Institute (IPI), are poised to yield advancements that enrich our understanding of the universe and its core laws.

In summary, the integration of the Bekenstein bound and Landauer’s principle represents a milestone in comprehending the limits and principles governing information and energy. By weaving these concepts together, we illuminate pathways that span various disciplines, enriching our comprehension of the natural world’s intricacies. This integrated framework beckons us to explore further, advancing quantum computing, thermodynamics, and even shedding light on the cosmos’s mysteries. As we traverse these intersections, the scientific community is poised to unveil deeper truths, drive technological progress, and cultivate a holistic understanding of the profound interplay between information and energy.

It’s essential to bridge the gap between these profound concepts and the realm of information professionals and students. This integration may pave the way for revolutionary insights in information management and data processing practices, potentially transforming the way we harness and understand information in various fields. As the boundaries of our understanding expand, so too does our capacity to explore the limitless horizons that beckon from the convergence of Bekenstein’s bound and Landauer’s principle.

Translation of the article: From Black Holes to Information Erasure: Uniting Bekenstein’s Bound and Landauer’s Principle, in Journal of Applied Mathematics and Physics, 11(8), 2185-2194, 2023