Entropic Fluctuations of Quantum Dynamical Semigroups |
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Authors: | V Jakšić C-A Pillet M Westrich |
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Institution: | 1. Department of Mathematics and Statistics, McGill University, 805 Sherbrooke Street West, Montreal, QC, H3A 2K6, Canada 2. Aix-Marseille Université, CNRS, CPT, UMR 7332, Case 907, 13288, Marseille, France 3. Université de Toulon, CNRS, CPT, UMR 7332, 83957, La Garde, France 4. FRUMAM, Marseille, France
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Abstract: | We study a class of finite dimensional quantum dynamical semigroups $\{\mathrm {e}^{t\mathcal{L}}\}_{t\geq0}$ whose generators $\mathcal{L}$ 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. We prove a general entropic fluctuation theorem for this class of semigroups by relating the cumulant generating function of entropy transport to the spectrum of a family of deformations of the generator ${\mathcal{L}}$ . We show that, besides the celebrated Evans-Searles symmetry, this cumulant generating function also satisfies the translation symmetry recently discovered by Andrieux et al., and that in the linear regime near equilibrium these two symmetries yield Kubo’s and Onsager’s linear response relations. |
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