Tuesday 10 November 2026, 16:00 - 17:00 in HG 00.071
Klaas Landsman (Radboud)
Entropy and operator algebras
Abstract: Following a historical survey of various mathematical concepts of entropy, I will try to explain the problem of defining a good (relative) entropy for states of infinite quantum systems that is also computable via traces and density operators, as in the simplest definition for finite systems proposed by John von Neumann in 1927 (which predated Shannon’s famous definition of classical entropy from 1948). Such a definition is needed for example in black hole thermodynamics, but it also relates to quite beautiful mathematics. The solution to this problem seems to lie in Haagerup’s theory of noncomutative L^p spaces over von Neumann algebras. There will be no geometry in this talk (except perhaps for some noncommutative geometry in disguise): the mathematical tools are functional analysis and probability theory. Literature: The Okinawa Lectures on Entropy