Title: Some recent developments about quantum entropic fluctuations
Abstract: Since the seminal works of Evans, Searles, Gallavotti and Cohen in the early 90's the study of entropic fluctuations has encountered a fast growing interest in the last decades, and many developments at least in classical systems. Its quantum counterpart however turned out to be very challenging. In this talk I will present some recent developments about possible extensions of these entropic fluctuations to the quantum domain, as well as some open problems.
The talk is based on the following recent series of papers (in collaboration with T. Benoist, V. Jaksic, A. Panati and C.-A. Pillet):
1) A note on two-times measurement entropy production and modular theory. Lett. Math. Phys. (2024).
2) On the thermodynamic limit of two-times measurement entropy production. To appear in Rev. Math. Phys.
3) Entropic fluctuations in statistical mechanics II. Quantum dynamical systems. Preprint arXiv 2409.15485
4) Entropic fluctuation theorems for Spin-Fermion model. In preparation