It is impossible to store information without loss at the rate of the decay of the physical substrate where the information is stored; it is also impossible to transmit information without loss at the rate of friction (the distortion of the energy carrying the information caused by its interaction with the medium of transmission); and it is impossible to copy information without loss at the rate of entropy of the mechanism that performs the copying operation. Because all of these entropies are consistent functions of the state of matter and energy, the physical entropy of a map is necessarily the same. But, when you think about the fact that discrete energy states are functions of the quantum information that defines the discrete states of matter, whether quark, electron, proton or molecule, then it is not at all clear that the entropy flows from the state of matter to the state of information, and not the other way around. It may, in fact, make more sense to think of the increase in the entropy of matter and energy as a function of the entropy of the information that establishes the discrete forms, phases, and values of existence. Information, matter, energy and space are, at any rate, deeply entangled, and entropy can shift between them.
Partly, this is because there are two types of momentum, and they have different sources. The first type of momentum is fundamental and quantum: each particle has a fundamental momentum, or rest mass, which is part of its information and does not change regardless of the frame of reference. The second type of momentum depends on the configuration of the mass in the universe: each particle has momentum relative to the frame of reference of the observer. This second type is extremely confusing.
The energy of configuration is not quantised. Rest mass appears to be increased by the speed of the particle relative to the observer’s rest frame of reference (momentum increases relative to the speed of light according to the equation e=mc2).
The energy of configuration is released in quantised units of photons, and it was quantised at the moment of the big bang, but since it became distributed randomly in space, this energy of configuration, or entropy, is not quantised locally. The total is still equal to the original energy released in the big bang, but that value has no meaning in its present distribution. Still, it shows up in quantum mechanical mapping of local energy. Dirac needed special relativity to explain the experimental momentum of an electron in relation to its nucleus because, depending on its orbit, its mass appears bigger than its rest mass.
Mapping always includes both fundamental quanta of information – rest mass, charge, spin, flavour, etc., of the local matter – as well as the relativistic energy distributed in the spacial configuration of the matter – its entropy. The entropy shows up in random collisions, like the body that collided with earth to create the moon or the asteroid that killed the dinosaurs. These events have no impact on the fundamental information in the universe (all of the particles were preserved), but they have a profound impact on local mapping.
It’s hard to find the right word to say what entropy does on its way from one form to another, from energy to matter to space-time to information, but because there is a kind of equivalence that is transferred through the forms, perhaps “commutes” is better than conforms or transfers or even diffuses. There is both a sense of equivalence and movement in the word “commutes”, meaning that it can manifest in motion from one place to another or it can exist in parallel in many places at once.
The problem for physics has been thinking of information as inherently maplike, that to exist it must be stored. This is true for macroscopic data, but the information in the universe is real, not representative of a deeper physical reality. It has been conserved since the Big Bang, commuting through space, mass and light. It has never been stored. Cosmology is like a commuter map from the Big Bang to the final evaporation.