The fluctuation-dissipation theorem (FDT) is a central result in statistical physics, both for classical and quantum systems. It establishes a relationship between the linear response of a system under a time-dependent perturbation and time correlations of certain observables in equilibrium. Here we derive a generalization of the theorem which can be applied to any Markov quantum system and makes use of the symmetric logarithmic derivative (SLD). There are several important benefits from our approach. First, such a formulation clarifies the relation between classical and quantum versions of the equilibrium FDT. Second, and more important, it facilitates the extension of the FDT to arbitrary quantum Markovian evolution, as given by quantum maps. Third, it clarifies the connection between the FDT and quantum metrology in systems with a non-equilibrium steady state.
 D. des Cloizeaux, ``Linear response, generalized susceptibility and dispersion theory,'' (International Atomic Energy Agency, 1968) pp. 325–354.
 J. Jensen and A. R. Mackintosh, ``Rare earth magnetism structures and excitations,'' (Clarendon Press, 1991).
 U. Seifert, Reports on Progress in Physics 75, 126001 (2012).
 G. Verley, R. Chétrite, and D. Lacoste, Journal of Statistical Mechanics: Theory and Experiment 2011, P10025 (2011).
 J. R. Gomez-Solano, A. Petrosyan, S. Ciliberto, R. Chetrite, and K. Gawedzki, Phys. Rev. Lett. 103, 040601 (2009).
 M. Baiesi, C. Maes, and B. Wynants, Phys. Rev. Lett. 103, 010602 (2009).
 J. Prost, J.-F. Joanny, and J. M. R. Parrondo, Phys. Rev. Lett. 103, 090601 (2009).
 G. Tóth and I. Apellaniz, Journal of Physics A: Mathematical and Theoretical 47, 424006 (2014).
 H.-P. Breuer and F. Petruccione, ``The theory of open quantum systems,'' (Oxford University Press on Demand, 2002).
 M. A. Nielsen and I. L. Chuang, ``Quantum computation and quantum information: 10th anniversary edition,'' (Cambridge University Press, New York, NY, USA, 2011) 10th ed.
 M. M. Wilde, ``Quantum information theory,'' (Cambridge University Press, 2013).
 H. M. Wiseman and G. J. Milburn, ``Quantum measurement and control,'' (Cambridge university press, 2009).
 C. W. Gardiner and P. Zoller, ``Quantum noise,'' (Springer, 2004).
 G. Tóth and T. Vértesi, Phys. Rev. Lett. 120, 020506 (2018).
 G. B. Cuetara, A. Engel, and M. Esposito, New Journal of Physics 17, 055002 (2015).
 W. H. Louisell, ``Quantum statistical properties of radiation,'' (Wiley, New York, NY, 1973).
 Amikam Levy, Eran Rabani, and David T. Limmer, "Response theory for nonequilibrium steady states of open quantum systems", Physical Review Research 3 2, 023252 (2021).
 Michael Konopik and Eric Lutz, "Quantum response theory for nonequilibrium steady states", Physical Review Research 1 3, 033156 (2019).
 Sholeh Razavian, Claudia Benedetti, Matteo Bina, Yahya Akbari-Kourbolagh, and Matteo G. A. Paris, "Quantum thermometry by single-qubit dephasing", The European Physical Journal Plus 134 6, 284 (2019).
 Jen-Tsung Hsiang and Bei-Lok Hu, "Fluctuation-dissipation relation for open quantum systems in a nonequilibrium steady state", Physical Review D 102 10, 105006 (2020).
 Mohammad Mehboudi, Juan M R Parrondo, and Antonio Acín, "Linear response theory for quantum Gaussian processes", New Journal of Physics 21 8, 083036 (2019).
 Daochi Zhang, Xiao Zheng, and Massimiliano Di Ventra, "Local temperatures out of equilibrium", Physics Reports 830, 1 (2019).
 Ricardo Costa de Almeida and Philipp Hauke, "From entanglement certification with quench dynamics to multipartite entanglement of interacting fermions", Physical Review Research 3 3, L032051 (2021).
 Gabriel T. Landi and Mauro Paternostro, "Irreversible entropy production: From classical to quantum", Reviews of Modern Physics 93 3, 035008 (2021).
 Ali Motazedifard, A Dalafi, and M H Naderi, "A Green’s function approach to the linear response of a driven dissipative optomechanical system", Journal of Physics A: Mathematical and Theoretical 54 21, 215301 (2021).
 Steve Campbell, Mohammad Mehboudi, Gabriele De Chiara, and Mauro Paternostro, "Global and local thermometry schemes in coupled quantum systems", New Journal of Physics 19 10, 103003 (2017).
 Yi Peng and Heng Fan, "Perturbative analysis of quantum fluctuation theorems in a driven open system", arXiv:1708.08214.
 Maurício Hippert, Gabriel T. Landi, and Jorge Noronha, "Universal many-body diffusion from momentum dephasing", arXiv:2106.10984.
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