From ee0d9e4a2273127055e558bb48aa2a1038e29404 Mon Sep 17 00:00:00 2001 From: Valentin Boettcher Date: Tue, 27 Sep 2022 19:11:15 +0200 Subject: [PATCH] outro for thermo section --- src/thermo.tex | 28 ++++++++++++++++++++++++++++ 1 file changed, 28 insertions(+) diff --git a/src/thermo.tex b/src/thermo.tex index bb3216e..8689560 100644 --- a/src/thermo.tex +++ b/src/thermo.tex @@ -1516,3 +1516,31 @@ remarks in \cref{cha:concl-ideas-future} about \cite{Uzdin2015Sep}. % \item filter mode: \cref{sec:shift_sp} % \item otto cycle: sensitivity to timing stronger with stronger coupling? % \end{itemize} + +\section{Conclusion} +\label{sec:conclusion-2} + +We have reviewed the notion of unitarily extractable energy +``ergotropy'' and found that this quantity is indeed bounded by +\cref{eq:thermo_ergo_bound} for the models we study in this work, +namely finite dimensional systems coupled to a heat bath. It was +further demonstrated with an analytical calculation that this bound +can apply to baths with infinite degrees of freedom. In the +case of multiple baths, a Gibbs like inequality +\cref{eq:secondlaw_cyclic} was presented which can be interpreted as +thermodynamic cost of a cyclical process. + +Subsequently, we studied a modulated version of the spin-boson model +with the goal of extracting energy from a thermal bath. We found that +a not insubstantial fraction of the theoretical maximum can be +extracted when only the coupling to the bath is modulated and the bath +memory is long. Also, the quantum speed limit and a resonance +phenomenon were demonstrated. The latter elucidated in which way the +strong coupling case differs from the weak coupling regime. + +Finally, we demonstrated the fitness of HOPS to treat arbitrarily +driven systems with multiple baths through the simulation of a quantum +Otto cycle. We achieved finite power and found the Gibbs like +inequality to be valid. An equivalent continuously coupled cycle +without modulation of the coupling performed significantly worse in +terms of power and efficiency.