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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 <br /><br /><br /><br /><br /><br />reservoir R so that an unambiguous stochastic thermodynamics ... [more ▼]

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

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

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