Non-equilibrium statistical mechanics has seen some impressive developments in the last three decades, thank to the pioneering works of Evans, Cohen, Morris and Searles
on the violation of the second law, soon followed by the ground-breaking formulation of the Fluctuation Theorem by Gallavotti and Cohen for entropy fluctuation in the early nineties. Their work was by vast literature, both theoretical and experimental.
The extension of these results to the quantum setting has turned out to be surprisingly challenging and it is still an undergoing effort. Kurchan’s seminal work (2000) showed the measurement role has to be taken in account, leading to the introduction of the so called two-time measurement statistics (also known as full counting statistics). However introducing this frameworks leads to surprising phenomena with no classical counterpart. In this talk, I will present two of these phenomena. The first one emerges in the context of energy balance violations, as the result of a lack of trajectory notion. The second one emerges in the context of our attempt to introduce a quantum equivalent of Gallavotti-Cohen (steady) entropic functional and compare it with the Evans-Searls (transient) entropic functional. In both cases, we show that, due to the invasive measurement role, the situation differs considerably to its classical counterpart.
en collaboration avec: T.Benoist, R.Raquépas, Y.Pautrat; et projet en cours avec T.Benoist, L.Bruneau, V.Jaksic, C.A.Pillet.