Optimization of Stochastic Heat Engines in the Underdamped Limit
Nikolas Zöller examines the working principles and the underlying theoretical foundations of a microscopic heat engine. In particular, he investigates the system’s stochastic dynamics in the underdamped regime which has hardly been studied in the past, bu
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Optimization of Stochastic Heat Engines in the Underdamped Limit
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Nikolas Zöller
Optimization of Stochastic Heat Engines in the Underdamped Limit
Nikolas Zöller Potsdam, Germany
BestMasters ISBN 978-3-658-16349-5 ISBN 978-3-658-16350-1 (eBook) DOI 10.1007/978-3-658-16350-1 Library of Congress Control Number: 2016956641 Springer Spektrum © Springer Fachmedien Wiesbaden GmbH 2017 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This Springer Spektrum imprint is published by Springer Nature The registered company is Springer Fachmedien Wiesbaden GmbH The registered company address is: Abraham-Lincoln-Str. 46, 65189 Wiesbaden, Germany
Contents 1 Introduction 1.1 Stochastic Dynamics . . . . . . . . . . . . . . . 1.1.1 Langevin Equation . . . . . . . . . . . . 1.1.2 Fokker-Planck Equation . . . . . . . . . 1.1.3 Wiener Process . . . . . . . . . . . . . . 1.1.4 Stochastic Differential Equations (SDE) 1.1.5 High-Friction Limit . . . . . . . . . . . . 1.2 Stochastic Energetics . . . . . . . . . . . . . . . 1.2.1 Thermodynamics of Single Trajectories . 1.2.2 Ensemble Averages . . . . . . . . . . . . 1.3 Classical Heat Engines . . . . . . . . . . . . . . 1.3.1 Carnot Engine . . . . . . . . . . . . . . . 1.3.2 Curzon-Ahlborn Engine . . . . . . . . .
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2 Stochastic Heat Engine - Overdamped Regime 2.1 Carnot-type Model of a Stochastic Heat Engine . 2.2 Optimal Protocols in the Overdamped Limit for Potential . . . . . . . . . . . . . . . . . . . .
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