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fix "in refs...."
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@ -82,4 +82,30 @@ linkcolor=blue,
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% cursive bold in maths
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\unimathsetup{math-style=TeX,bold-style=ISO}
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%% citing "in ref"
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\NewBibliographyString{refname}
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\NewBibliographyString{refsname}
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\DefineBibliographyStrings{english}{%
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refname = {Ref\adddot},
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refsname = {Refs\adddot}
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}
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\DeclareCiteCommand{\refcite}
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{%
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\ifnum\thecitetotal=1
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\bibstring{refname}%
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\else%
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\bibstring{refsname}%
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\fi%
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\addspace\bibopenbracket%
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\usebibmacro{cite:init}%
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\usebibmacro{prenote}}
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{\usebibmacro{citeindex}%
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\usebibmacro{cite:comp}}
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{}
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{\usebibmacro{cite:dump}%
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\usebibmacro{postnote}%
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\bibclosebracket}
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\recalctypearea
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@ -235,7 +235,7 @@ temperature, as we are working in the Heisenberg picture.
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For completeness, it may be of interest to find a solution for
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negative times. This solution is relatively unphysical, as the initial
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condition of a product state\footnote{For a treatment of more general
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initial states see \cite{Grabert1988Oct}.} plays a pivotal role in
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initial states see \refcite{Grabert1988Oct}.} plays a pivotal role in
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open system dynamics~\cite{Rivas2012}. Therefore a system that starts
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out in some entangled state just to reach the perfect product state at
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\(t=0\) is not something that is likely to be applicable to physical
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@ -518,7 +518,7 @@ through energy conservation as in~\cite{Kato2016Dec}, we find
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H_\inter^{(n)}]}
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\end{equation}
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regardless of the (non-) commutativity\footnote{For example, the
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three-level model used in \cite{Uzdin2015Sep,Klatzow2019Mar} has
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three-level model used in \refcite{Uzdin2015Sep,Klatzow2019Mar} has
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non-commuting couplings.} of the interaction
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Hamiltonians. Therefore, we can apply the formalism of the previous
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sections almost unchanged, by taking care that all quantities involved
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@ -413,7 +413,7 @@ This leads to the nonlinear NMQSD equation~\cite{Diosi1998Mar}
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-\ev{L^\dag}_{t}}∫_0^t\dd{s}α(t-s)\fdv{\ket{ψ({\tilde{η}}^\ast_t, t)}}{\tilde{η}^\ast_s}.
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\end{equation}
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There is a subtlety concerning the functional derivative that won't be
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discussed here but in \cite{Hartmann2021Aug,RichardDiss} or
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discussed here but in \refcite{Hartmann2021Aug,RichardDiss} or
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\cref{sec:nonlin_flow}. Crucially, the system state is now recovered
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through
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\begin{equation}
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@ -1443,7 +1443,7 @@ with specific bath degrees of freedom which are independent themselves
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except for their interaction with the system.
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This interpretation is corroborated by a time discrete version of the
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NMQSD discussed in \cite{RichardDiss}. There, the
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NMQSD discussed in \refcite{RichardDiss}. There, the
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\emph{Time-Oscillator picture} is introduced, which shows that a
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variant of the NMQSD can be formulated as the successive interaction
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in time of the system with mode like degrees of freedom. At each time
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@ -1474,9 +1474,9 @@ Note that the short time behaviour discussed here can usually not be
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resolved by the usual Markovian master equations. This is due to the
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fact, that the bath timescale \(\sim 1/ω_{c}\) must be by far the
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shortest, which often isn't the case here. Another demonstration of
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this fact is given in \cite{Link2022Feb}, where Markovian dynamics are
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this fact is given in \refcite{Link2022Feb}, where Markovian dynamics are
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compared with the Redfield and exact dynamics for the spin-boson model
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coupled to a squeezed bath. As in \cite{Xu2022Mar}, the Redfield
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coupled to a squeezed bath. As in \refcite{Xu2022Mar}, the Redfield
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description is found to be adequate for weak coupling. This is due to
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the Redfield master equation not requiring the secular approximation,
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but only weak coupling. It can therefore faithfully capture
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@ -1,7 +1,7 @@
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\chapter{Conclusion and Ideas for future Work}
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\label{cha:concl-ideas-future}
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A worthwhile task for future work would be to verify the results
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summarized in \cite{Binder2018} for the Otto cycle. Especially the
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summarized in \refcite{Binder2018} for the Otto cycle. Especially the
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optimization for optimal power which leads to the
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Novikov–Curzon–Ahlborn efficiency \(η_{ca}=1-\sqrt{T_{c}/T_{h}}\) is
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interesting in the case of stronger coupling.
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@ -13,10 +13,10 @@ studying the effect of overlapping and shifting strokes is a
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fascinating avenue for future exploration.
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Also, more interesting working media, such as a three level system are
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of interest. In \cite{Uzdin2015Sep} it is shown, that in certain
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of interest. In \refcite{Uzdin2015Sep} it is shown, that in certain
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regimes quantum coherence can lead to superior power output. In the
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same regime different types heat engines are equivalent. Both these
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effects have been observed experimentally in \cite{Klatzow2019Mar}. It
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effects have been observed experimentally in \refcite{Klatzow2019Mar}. It
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would be interesting to see if the slight deviations from theory in
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\cite{Klatzow2019Mar} could be explained using HOPS.
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@ -30,9 +30,9 @@ consequence of the energy time uncertainty it is being argued, that
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the origin of this advantage is truly quantum. The tools for the
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exploitation of this effect and its verification are provided in this
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work. However, a strong coupling analysis has already been performed
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using HEOM in \cite{Xu2022Mar}.
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using HEOM in \refcite{Xu2022Mar}.
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In \cite{Santos2021Jun} a cycle is proposed that first creates states
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In \refcite{Santos2021Jun} a cycle is proposed that first creates states
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of finite ergotropy by letting energy flow through the working medium
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and then extracting this ergotropy in a separate stroke. This work
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could be verified and expanded to the non-Markovian regime.
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@ -96,7 +96,7 @@ passive iff the maximizing \(U\) \cref{eq:ergo_def} is the identity
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\(\id\). In other words, a state is passive if its energy can not be
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reduced through unitary transformations and its ergotropy vanishes.
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In \cite{Niedenzu2018Jan} the ergotropy of the system is employed for
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In \refcite{Niedenzu2018Jan} the ergotropy of the system is employed for
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the definition of heat to derive a tighter second law. The immediate
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appeal of this quantity for the purposes of this work however is its
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to the full unitary dynamics of system \emph{and} bath which is
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@ -813,7 +813,7 @@ relaxed, as \cref{eq:secondlaw_cyclic} holds as soon as
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\(ΔS_\sys^\cyc\) vanishes.
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The left hand side could be called ``bath entropy production'' as is
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motivated in \cite{Riechers2021Apr}, where heat is identified with
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motivated in \refcite{Riechers2021Apr}, where heat is identified with
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\(ΔE_{\bath^i}\). There, the entropy production bound
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\cref{eq:bathenergyandsystementro} that takes into account system and
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bath is being considered and brought into connection with
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@ -892,7 +892,7 @@ densities have been shifted such that their maxima coincide with
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\(1 + Δ\) which relates to \cref{sec:energy-transf-char}. The
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resonance criterion for modulated systems is derived from Floquet
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theory~\cite{Kurizki2021Dec} which once again is a weak coupling
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result, that carries over to other regimes. In \cite{Xu2022Mar} it is
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result, that carries over to other regimes. In \refcite{Xu2022Mar} it is
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shown, that for stronger coupling the situation is more complicated
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but that, just like in \cref{sec:energy-transf-char}, the resonance
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criterion is still a good starting point.
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