Prof Francesco Buscemi

von Neumann’s "other" entropy: properties, interpretations, and applications

In addition to the quantity now eponymously known as von Neumann entropy, in his 1932 book von Neumann also discusses another entropic quantity, which he calls "macroscopic", and argues that it is the latter, and not the former, that is the relevant quantity to use in the analysis of thermodynamic systems. For a long time, however, von Neumann's "other" entropy was largely forgotten, appearing only sporadically in the literature, overshadowed by its more famous sibling. In this talk I will discuss a recent generalization of von Neumann's macroscopic entropy, called "observational entropy", focusing on its mathematical properties (leading to a strong version of the Petz recovery theorem), its statistical interpretation (as statistical deficiency on the one hand, and as "irretrodictability" on the other), and its application in explaining the emergence of the Second Law and an "H-like Theorem" for closed systems evolving unitarily.