Convergence of macrostates under reproducible processes
arXiv:1004.4475 · doi:10.1016/j.physleta.2010.07.024
Abstract
I show that whenever a system undergoes a reproducible macroscopic process the mutual distinguishability of macrostates, as measured by their relative entropy, diminishes. This extends the second law which regards only ordinary entropies, and hence only the distinguishability between macrostates and one specific reference state (equidistribution). The new result holds regardless of whether the process is linear or nonlinear. Its proof hinges on the monotonicity of quantum relative entropy under arbitrary coarse grainings, even those that cannot be represented by completely positive maps.
5 pages, no figures; v2: new title and abstract, expanded on motivation and physical meaning