Disentangling Brillouin's negentropy law of information and Landauer's law on data erasure

TL;DR

The paper challenges the prominence of Landauer's data-erasure principle as the fundamental bridge between information and energy, arguing instead that information is an emergent, observer-dependent concept tied to conventional reasoning in thermodynamics and information theory. By tracing the historical and mathematical threads of thermodynamics, statistical mechanics, and Shannon information, it defends Brillouin's negentropy law as a robust, general result and highlights how Landauer's erasure construction confuses information with data, and states with paths. It emphasizes the essential role of the observer and conventions (e.g., maximum entropy) in defining equilibrium and information measures, and it reframes the information-energy nexus as a conventional, emergent relation rather than a purely reductionist, data-centric one. The work advocates a conventional emergentism stance, arguing that energy and information are meaningful only as emergent, observer-relevant quantities, thereby clarifying foundational misconceptions and their thermodynamic implications.

Abstract

The link between information and energy introduces the observer and their knowledge into the understanding of a fundamental quantity of physics. Two approaches compete to account for this link, Brillouin's negentropy law of information and Landauer's law on data erasure, which are often confused. The first, based on the Clausius' inequality and Shannon's mathematical results is very robust, while the second, based on the simple idea that information needs a material embodiment (data-bits) is today perceived as more physical and prevails. In this paper, we show that Landauer's idea results from a confusion between information (a global emergent concept) and data (a local material object). This confusion leads to many inconsistencies and is incompatible with thermodynamics and information theory. The reason it prevails is interpreted to be due to a frequent tendency of materialism towards reductionism, neglecting emergence and seeking to eliminate the role of the observer. A paradoxical trend given that it is often accompanied by the materialist idea that all scientific knowledge nevertheless originates from observation. Information and entropy are actually emergent quantities introduced in the theory by convention.

Figures (4)

• Figure 1: A piston compressing either a metal spring (left) or a volume of gas (right) experiences a restoring force when it moves away from equilibrium. For the metal spring, this force has a microscopic origin. For the gas, it is emergent.
• Figure 2: Cycle of operations of Szilard's engine. By knowing the location of the particle, a demon (say a computer) can produce mechanical work with no other cost than that of acquiring the information. The first principle implies that information is energy.
• Figure 3: Landauer erasure of a data-bit consisting in a single particle in a two-compartment box. The procedure must be independent of the initial position of the particle: neither a simple shift of the particle towards 0 by means of two pistons keeping constant the volume of the phase space; nor a quasi-static expansion with a single piston is possible. According to Landauer, the first step is necessarily a thermodynamically irreversible free expansion.
• Figure 4: Setting a data-bit in state S by merging two compartments is thermodynamically irreversible (red path) if the initial value is known ($\Delta S=\ln 2$), but it is thermodynamically reversible (green path) if the initial value is unknown ($\Delta S=0$). This is reminiscent of the Gibbs paradox of mixing. Landauer viewpoint conflicts with thermodynamics.