Seminario di Annalisa Panati (U. de Toulon & Politecnico di Milano)

Non-equilibrium statistical mechanics has seen some impressive developments in the last three decades, since the ground-breaking formulation of the transient and steady entropic Fluctuation Relations (FR) in the early nineties. The extension of these results to the quantum setting has turned out to be surprisingly challenging and it is still an ongoing sort. Kurchan and Hal Tasaki's seminal works (2000) showed quantum formulation of the transient version of FR is possible by introducing the two-time measurement framework. In this talk, we present some results in a recent series of papers, where we attempt to introduce a quantum equivalent of steady entropic functional and compare it to the transient version for open quantum system. In order to deal with the thermodynamic limit and to have general results, we use methods of C*- algebras and modular theory.

We will consider idealised direct projective measurement on the reservoirs. We show in particular that the direct measurement has an invasive role, leading to dramatic consequences about stability with respect to the initial state. Therefore it is natural to consider experimentally accessible indirect measurement through coupling with an ancilla. In this context, a parallel with the classical case is restored, but we can prove robustness of the protocol with respect to the first measurement time.

Joint work with T. Benoist, L. Bruneau, V. Jaksic, C.A. Pillet.