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See detailResponse functions as quantifiers of non-Markovianity
Strasberg, Philipp UL; Esposito, Massimiliano UL

in Physical Review Letters (2018)

Quantum non-Markovianity is crucially related to the study of dynamical maps, which are usually derived for initially factorized system-bath states. We here demonstrate that linear response theory also ... [more ▼]

Quantum non-Markovianity is crucially related to the study of dynamical maps, which are usually derived for initially factorized system-bath states. We here demonstrate that linear response theory also provides a way to derive dynamical maps, but for initially correlated (and in general entangled) states. Importantly, these maps are always time-translational invariant and allow for a much simpler quantification of non-Markovianity compared to previous approaches. We apply our theory to the Caldeira-Leggett model, for which our quantifier is valid beyond linear response and can be expressed analytically. We find that a classical Brownian particle coupled to an Ohmic bath can already exhibit non-Markovian behaviour, a phenomenon related to the initial state preparation procedure. Furthermore, for a peaked spectral density we demonstrate that there is no monotonic relation between our quantifier and the system-bath coupling strength, the sharpness of the peak or the resonance frequency in the bath. [less ▲]

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See detailStochastic thermodynamics in the strong coupling regime: An unambiguous approach based on coarse graining
Strasberg, Philipp UL; Esposito, Massimiliano UL

in Physical Review. E : Statistical, Nonlinear, and Soft Matter Physics (2017)

We consider a classical and possibly driven composite system X ⊗ Y weakly coupled to a Markovian thermal reservoir R so that an unambiguous stochastic thermodynamics ensues for X ⊗ Y . This setup can be ... [more ▼]

We consider a classical and possibly driven composite system X ⊗ Y weakly coupled to a Markovian thermal reservoir R so that an unambiguous stochastic thermodynamics ensues for X ⊗ Y . This setup can be equivalently seen as a system X strongly coupled to a non-Markovian reservoir Y ⊗ R. We demonstrate that only in the limit where the dynamics of Y is much faster than X, our unambiguous expressions for thermodynamic quantities, such as heat, entropy, or internal energy, are equivalent to the strong coupling expressions recently obtained in the literature using the Hamiltonian of mean force. By doing so, we also significantly extend these results by formulating them at the level of instantaneous rates and by allowing for time-dependent couplings between X and its environment. Away from the limit where Y evolves much faster than X, previous approaches fail to reproduce the correct results from the original unambiguous formulation, as we illustrate numerically for an underdamped Brownian particle coupled strongly to a non-Markovian reservoir. [less ▲]

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See detailQuantum and Information Thermodynamics: A Unifying Framework Based on Repeated Interactions
Strasberg, Philipp UL; Schaller, Gernot; Brandes, Tobias et al

in Physical Review X (2017), 7(021003),

We expand the standard thermodynamic framework of a system coupled to a thermal reservoir by considering a stream of independently prepared units repeatedly put into contact with the system. These units ... [more ▼]

We expand the standard thermodynamic framework of a system coupled to a thermal reservoir by considering a stream of independently prepared units repeatedly put into contact with the system. These units can be in any nonequilibrium state and interact with the system with an arbitrary strength and duration. We show that this stream constitutes an effective resource of nonequilibrium free energy, and we identify the conditions under which it behaves as a heat, work, or information reservoir. We also show that this setup provides a natural framework to analyze information erasure (“Landauer’s principle”) and feedback-controlled systems (“Maxwell’s demon”). In the limit of a short system-unit interaction time, we further demonstrate that this setup can be used to provide a thermodynamically sound interpretation to many effective master equations. We discuss how nonautonomously driven systems, micromasers, lasing without inversion and the electronic Maxwell demon can be thermodynamically analyzed within our framework. While the present framework accounts for quantum features (e.g., squeezing, entanglement, coherence), we also show that quantum resources do not offer any advantage compared to classical ones in terms of the maximum extractable work. [less ▲]

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