Kadanoff Seminar: Entanglement entropy counts “microstates”: approximate solutions to the quantum marginal problem. - Daniel Ranard, MIT

In closed many-body systems, the global von Neumann entropy fails to capture the usual notion of thermodynamic entropy -- it never increases.  A popular alternative is sometimes called the "coarse-grained entropy," given by the sum of entanglement entropies over all local regions. This quantity better resembles the classical thermodynamic entropy. But what "microstates" does it count?  I show that for any large system, the coarse-grained entropy of a state counts (the logarithm of) the number of orthogonal pure states that approximately match the original state on local regions.  In other words, it counts approximate solutions to the quantum marginal problem.