Authors Eric Lutz and Sergio Ciliberto implicitly assume time-reversal invariance. Indeed, to date, scientists have put forth thermodynamic arguments that implicitly made that assumption, and many have fretted about how to produce the arrow of time that entropy entails. However, time-reversal violation in scattering processes has been experimentally observed. Also, the expansion of the universe provides a “local” arrow of time in this universe—that is, a symmetry-violating vacuum state. When time-reversal invariance is broken, the analysis and conclusions made by Lutz and Ciliberto do not hold, and an effective Maxwell’s demon may appear for distinguishable particles.1
Rolf Landauer’s argument for the physical nature of information may be an even more significant fault point. Integers have physical representations, but I suspect that few mathematicians would accept the notion that integers are subject to the laws of physics. Indeed, many mathematical constructs—whether represented by symbols on paper or electronically or, as the authors say, “stored in physical systems”—from number theory through topology, hardly seem likely to be subject to the laws of physics, however useful to physics they so often turn out to be.
