Entropy production and non-Markovian dynamical maps

Marcantoni, Stefano; Alipour, S.; Benatti, Fabio; Floreanini, Roberto; Rezakhani, A. T.

doi:10.1038/s41598-017-12595-x

Cited by 55 publications

(63 citation statements)

References 26 publications

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“…Finally, we show that, within this approach, it is possible to establish a thermodynamic signature of non-Markovianity (see also [43,45,69,70]). Suppose the dynamical map Λ t to be CP divisible [46][47][48] (actually P-divisible is enough [71]); namely, it can be decomposed as Λ t = Λ t,s Λ s for any pair t > s with Λ t,s CPTP.…”

Section: B Non-markovianitymentioning

confidence: 91%

Strong Coupling Thermodynamics of Open Quantum Systems

Rivas¹

2020

Phys. Rev. Lett.

103

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A general thermodynamic framework is presented for open quantum systems in contact with a thermal reservoir. The first and second law are obtained for arbitrary system-reservoir coupling strengths, and including both factorized and correlated initial conditions. The thermodynamic properties are adapted to the generally strong coupling regime, approaching the ones defined for equilibrium, and their standard weak-coupling counterparts as appropriate limits. Moreover, they can be inferred from measurements involving only system observables. Finally, a thermodynamic signature of non-Markovianity is presented in the form of a positive entropy production rate.

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Section: B Non-markovianitymentioning

confidence: 91%

Strong Coupling Thermodynamics of Open Quantum Systems

Rivas¹

2020

Phys. Rev. Lett.

103

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“…In 1959, Scovil et al have established the equivalence between a three-level maser and a Carnot heat engine [166,167]. Later, the Lindblad-Gorini-Kossakowski-Kossakowski semi-group master equation [102,103] has been employed to address quantum thermodynamics from a dynamic perspective [160,168] and to explore non-equilibrium thermodynamic processes such as heat flow and entropy production [154,165,169]. Despite this progress, there are still many unsolved or controversial problems in quantum thermodynamics, and experimental verifications of theoretical predictions are far from adequate [170][171][172].…”

Section: Physical Motivations To Extend the Concept Of Temperature Oumentioning

confidence: 99%

Local temperatures out of equilibrium

2019

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The temperature of a physical system is operationally defined in physics as "that quantity which is measured by a thermometer" weakly coupled to, and at equilibrium with the system. This definition is unique only at global equilibrium in view of the zeroth law of thermodynamics: when the system and the thermometer have reached equilibrium, the "thermometer degrees of freedom" can be traced out and the temperature read by the thermometer can be uniquely assigned to the system. Unfortunately, such a procedure cannot be straightforwardly extended to a system out of equilibrium, where local excitations may be spatially inhomogeneous and the zeroth law of thermodynamics does not hold. With the advent of several experimental techniques that attempt to extract a single parameter characterizing the degree of local excitations of a (mesoscopic or nanoscale) system out of equilibrium, this issue is making a strong comeback to the forefront of research. In this paper, we will review the difficulties to define a unique temperature out of equilibrium, the majority of definitions that have been proposed so far, and discuss both their advantages and limitations. We will then examine a variety of experimental techniques developed for measuring the non-equilibrium local temperatures under various conditions. Finally we will discuss the physical implications of the notion of local temperature, and present the practical applications of such a concept in a variety of nanosystems out of equilibrium. Figure 4: (a) The product of the density of states η(E) times the global distribution function ϕ|ρ|ϕ forms a strongly pronounced peak at the expectation value of the global system energyĒ. (b) The logarithm of the local distribution function a|ρ|a (solid line) and the logarithm of a canonical distribution (dashed line) with the same local temperature for a harmonic chain. (a) and (b) are reprinted with permission from [74].

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“…Equally important with understanding the underlying mechanisms that govern the dynamics of an open quantum system is assessing their thermodynamic principles [2]. Advances in this regard have been made for both Markovian [3][4][5][6][7] and, to a lesser extent, non-Markovian dynamics [8][9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

System-environment correlations and Markovian embedding of quantum non-Markovian dynamics

Campbell¹,

Ciccarello²,

Palma³

et al. 2018

Phys. Rev. A

117

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We study the dynamics of a quantum system whose interaction with an environment is described by a collision model, i.e. the open dynamics is modelled through sequences of unitary interactions between the system and the individual constituents of the environment, termed "ancillas", which are subsequently traced out. In this setting non-Markovianity is introduced by allowing for additional unitary interactions between the ancillas. For this model, we identify the relevant system-environment correlations that lead to a non-Markovian evolution. Through an equivalent picture of the open dynamics, we introduce the notion of "memory depth" where these correlations are established between the system and a suitably sized memory rendering the overall system+memory evolution Markovian. We extend our analysis to show that while most system-environment correlations are irrelevant for the dynamical characterization of the process, they generally play an important role in the thermodynamic description. Finally, we show that under an energy-preserving system-environment interaction, a non-monotonic time behaviour of the heat flux serves as an indicator of non-Markovian behaviour.

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Entropy production and non-Markovian dynamical maps

Cited by 55 publications

References 26 publications

Strong Coupling Thermodynamics of Open Quantum Systems

Strong Coupling Thermodynamics of Open Quantum Systems

Local temperatures out of equilibrium

System-environment correlations and Markovian embedding of quantum non-Markovian dynamics

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