On the supposed mass of entropy and that of information (2401.15104v1)

Abstract: In the theory of special relativity, energy can be found in two forms: kinetic energy and rest mass. Potential energy of a body is actually stored under the form of rest mass, interaction energy too, temperature is not. Information acquired about a dynamical system can be potentially used to extract useful work from it. Hence the "mass-energy-information equivalence principle" that has been recently proposed. In this paper, it is first recalled that for a thermodynamic system made of non interacting entities at constant temperature, the internal energy is also constant. So that, the energy involved in a variation of entropy ($T\Delta S$) differs from a change in potential energy stored or released and cannot be associated to a corresponding variation of mass of the system, even if it is expressed in term of quantity of information. This debate gives us the opportunity to deepen the notion of entropy seen as a quantity of information, to highlight the difference between logical irreversibility (a state dependent property) and thermodynamical irreversibility (a path dependent property) and to return to the nature of the link between energy and information that is dynamical.

• The paper examines flaws in the mass-energy-information equivalence hypothesis by clarifying that entropy, unlike potential energy, does not contribute to rest mass.
• The paper critiques the Landauer principle by distinguishing logical irreversibility from thermodynamic irreversibility in information processing.
• The analysis emphasizes the dynamic nature of information, arguing that static data lacks the intrinsic mass attributed to energetic systems.

An Analysis of the "Mass-Energy-Information Equivalence" Hypothesis

The paper "On the Supposed Mass of Entropy and That of Information" critically examines the proposal of a "mass-energy-information equivalence principle" within the context of thermodynamics and information theory. The hypothesis, which stems from the works of Vopson and others, suggests a direct equivalence between information and mass based on the principles of special relativity and thermodynamics. Didier Lairez, the author, provides a comprehensive critique of this hypothesis through a detailed exploration of associated concepts in thermodynamics, relativity, and information theory.

Fundamental Distinctions in Thermodynamics

The author begins by making a clear distinction between potential energy and entropy, emphasizing that while potential energy can be considered as rest mass in relativistic terms, entropy should not be. Lairez illustrates this using examples such as a spring's elastic energy, which is due to intermolecular forces and can equate to a difference in mass (as seen in nuclear processes), and the behavior of gases or rubbers, where entropy changes do not alter rest mass. In the case of gases or rubbers, entropy changes correspond to heat exchanges rather than shifts in potential energy or rest mass. This underscores the error in considering the variation of entropy as capable of inducing mass change.

Reappraisal of the Landauer Principle

At the heart of the "mass-energy-information equivalence" proposal lies the Landauer principle, which asserts that logically irreversible operations, like erasure, have a fundamental thermodynamic cost. Lairez critiques this by separating logical irreversibility (a state-based property) from thermodynamic irreversibility (a path-dependent property). Through detailed examples, Lairez demonstrates how logically irreversible processes can be designed to be thermodynamically reversible, challenging the claim of an intrinsic energy cost for irreversible computations.

The Role of Fresh Information

Lairez further critiques the hypothesis by addressing the fundamental role of information as a dynamic quantity, intimately tied to the systems from which it emanates. Information, in Shannon's framework, is related to entropy and is fundamentally dynamic; it loses its utility and link to energy when it becomes static or outdated. The assertion that stored data equates to information, and hence has rest mass, misconstrues the dynamic essence of what information represents in physical systems.

Conclusion and Implications

The implications of this critique are profound both theoretically and practically. The paper posits that the supposed link between mass and information via special relativity is fundamentally flawed. By unraveling the conceptual errors in equating information storage with mass-energy equivalency, Lairez reaffirms the distinct nature of information as entropy and highlights its dynamic relationship with energetic processes, aligned with the principles of thermodynamics.

Moving forward, it is crucial for researchers in fields intersecting information theory, thermodynamics, and quantum mechanics to further explore and clarify the nuanced roles that entropy and information play in these domains, particularly as they pertain to computational processes and thermodynamic transformations. This underscores a continued need for rigor in theoretical grounding as advancements are made in the understanding of the physical realization of information processing.