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##### Conference on "Mathematical properties of large quantum systems"Organizers: Maria J. Esteban (CNRS), Mathieu Lewin (CNRS), Robert Seiringer (McGill, Montréal) & Jan Philip Solovej (Copenhagen)

Vojkan Jaksic (Montréal, Canada): "Entropic Fluctuations of Quantum Dynamical Semigroups"
Tuesday 18 June 2013, 09:30 - 10:15
Amphi Hermite

I will discuss a class of finite dimensional quantum dynamical semigroups ${e^{t{cal L}}}_{tgeq 0}$ whose generators ${cal L}$ are sums of Lindbladians satisfying the detailed balance condition. Such semigroups arise in the weak coupling (van Hove) limit of Hamiltonian dynamical systems describing open quantum systems out of equilibrium. I will describe  a general entropic fluctuation theorem for this class of semigroups that arises by  relating the cumulant  generating function of entropy transport to the spectrum of a family of deformations of the generator ${cL}$, and show  that, besides the celebrated Evans-Searles symmetry, this cumulant generating function also satisfies the translation symmetry recently discovered by Andrieux  et al.. In the linear regime near equilibrium these two symmetries yield Kubo's and Onsager's linear response relations.

This talk is based on a joint work with C-A. Pillet and M. Westrich