Identifying in the second law of thermodynamics the logical foundation of physical theories

Arthur Eddington once famously wrote: “If your theory is found to be against the second law of thermodynamics, […] there is nothing for it but to collapse in deepest humiliation.” So why not take the second law as an axiom, on which physical theories are built, rather than as a consequence to be tested? The problem is that, in its conventional thermodynamic formulation, the second law relies on quite a lot of physics to have been already introduced, and it is not clear how one could assume its validity before other concepts like “work” or “heat” are even defined.

In a paper published today on Physical Review Research, we identify in von Neumann’s information engine the conceptual device that allows us to discuss the second law already from the early stages of the construction of a physical theory, when its most fundamental logical structures are being laid down. What we find is that, by concatenating two information engines in a closed cycle, the second law can be thought of as the requirement that no information can be created from nothing, thus guaranteeing the internal logical consistency of the theory.