The status of the concept of information in the physical world, and in particular its relation to entropy, continues to attract discussion and controversy. A relation between information and physical entropy, and hence energy, was first shown by Leo Szilard, while Rolf Landauer and Charles Bennett later showed that erasing information has an inescapable energy cost. This led to Landauer’s statement that “information is physical” being taken as the strapline for ideas of ‘information physics’, with information seen as a fundamental aspect of the physical universe.
Exactly what this means has remained rather mysterious. If information can be equated with energy and entropy, does that mean it is a form of matter; and does it have mass in its own right? Could we take some information, divorced from any context or carrier, and weigh it on a scale? This has led rather over-excited claims, such as that information is indeed a fifth state of matter in its own right, and that the enigmatic dark matter which appears to constitute the majority of the universe may be nothing other than ‘raw information’, not instantiated in any other substance.
These exaggerated viewpoints have been criticised in more measured analyses. The late Mark Burgin, in a 2022 open access paper, applied his General Theory of Information to argue that these were misunderstandings, stemming from “a confusion between the definitions of information, the matter that represents information, and the matter that is a carrier of information”. Information, in this understanding is not physical by itself, although it can have physical or mental representations. It does not have mass, although the physical substances that instantiate it do. The same amount of information (measured in bits) can have multiple physical instantiations – a symbol on a piece of paper, an electrical charge or current, the state of a logic circuit, etc. – and these different physical instantiations will have different masses, although the information they represent is the same.
A new analysis by Didier Lairez in a 2024 open access paper gives a careful thermodynamic analysis so as to define the relations between information, energy, and entropy, and in particular to criticise the idea that information per se can have mass. This analysis also strengthens and clarifies the link between information and entropy, Didier holding that “entropy is information [and that] information is entropy and is just that”.
Whether it is helpful to regard information and entropy are the same is, I think, far from clear, and no doubt this will be far from the last word on the matter. But perhaps we getting nearer to a clear understanding of the intricacies of these ideas; of information as indeed a feature of the physical universe, but always instantiated in a carrier, and of its close relation entropy.
The Occasional Informationist 