Recent theoretical investigations of the two-times
measurement entropy production in quantum statistical mechanics have
shed a new light on the mathematics and physics of the
quantum-mechanical probabilistic rules. Among notable developments are
the extensions of entropic fluctuation relations and Ruelle’s
transfer operators to the quantum domain and a novel observational
status of the modular structure of operator algebras via
identification of the the two-times measurement entropy production
with the phase space contraction of the modular theory.
In this talk we will review these developments and discuss a novel
link with entropic ancilla state tomography. The introduction of the
entropic ancilla state tomography sheds a new light on the concept
of quantum entropy production and in particular on possible quantum
formulations of the celebrated classical Gallavotti-Cohen fluctuation
relation.

This talk is based on joint works with T. Benoist, L. Bruneau, A.
Panati and C-A. Pillet.