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Thermodynamics of Information Processing in Small Systems / by Takahiro Sagawa

This thesis presents a general theory of nonequilibrium thermodynamics for information processing.  Ever since Maxwell's demon was proposed in the nineteenth century, the relationship between thermodynamics and information has attracted much attention because it concerns the foundation of the second... Full description

PPN (Catalogue-ID): 728221128
Personen: Sagawa, Takahiro
Format: eBook eBook
Enthält: Thermodynamics of Information Processing in Small Systems; Chairman's Foreword; Supervisor's Foreword; Acknowledgments; Contents; 1 Introduction; References; 2 Review of Maxwell's Demon; 2.1 Original Maxwell's Demon; 2.2 Szilard Engine; 2.3 Brillouin's Argument; 2.4 Landauer's Principle; 2.5 Bennett's Argument; References; 3 Classical Dynamics, Measurement, and Information; 3.1 Classical Dynamics; 3.2 Classical Information Theory; 3.2.1 Shannon Entropy; 3.2.2 Kullback--Leibler Divergence; 3.2.3 Mutual Information; 3.3 Classical Measurement Theory; References
Language: English
Published: Tokyo, Springer, 2013
Series: Springer Theses, Recognizing Outstanding Ph.D. Research
Basisklassifikation: 33.28
53.71
Subjects:

Nichtgleichgewichtsthermodynamik / Informationstheorie

Formangabe: Hochschulschrift
Notes: Description based upon print version of record
Physical Description: Online-Ressource, digital.
ISBN: 1-283-63303-5
978-4-431-54168-4
978-1-283-63303-1
Sekundärausgabe Online-Ausg., Springer eBook Collection. Physics and Astronomy

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501 |a Thermodynamics of Information Processing in Small Systems; Chairman's Foreword; Supervisor's Foreword; Acknowledgments; Contents; 1 Introduction; References; 2 Review of Maxwell's Demon; 2.1 Original Maxwell's Demon; 2.2 Szilard Engine; 2.3 Brillouin's Argument; 2.4 Landauer's Principle; 2.5 Bennett's Argument; References; 3 Classical Dynamics, Measurement, and Information; 3.1 Classical Dynamics; 3.2 Classical Information Theory; 3.2.1 Shannon Entropy; 3.2.2 Kullback--Leibler Divergence; 3.2.3 Mutual Information; 3.3 Classical Measurement Theory; References 
501 |a 4 Quantum Dynamics, Measurement, and Information4.1 Quantum Dynamics; 4.1.1 Unitary Evolutions; 4.1.2 Nonunitary Evolutions; 4.2 Quantum Measurement Theory; 4.2.1 Projection Measurement; 4.2.2 POVM and Measurement Operators; 4.3 Quantum Information Theory; 4.3.1 Von Neumann Entropy; 4.3.2 Quantum Kullback-Leibler Divergence; 4.3.3 Holevo Bound; 4.3.4 QC-Mutual Information; 4.3.5 Quantum-Classical Correspondence; References; 5 Unitary Proof of the Second Law of Thermodynamics; 5.1 Second Law of Thermodynamics; 5.2 Initial Canonical Distribution with a Single Heat Bath 
501 |a 5.3 General Situations with Multi-Heat BathsReferences; 6 Second Law with Feedback Control; 6.1 Entropy Inequality; 6.2 Generalized Second Laws; 6.3 Generalized Szilard Engines; References; 7 Thermodynamics of Memories; 7.1 Formulation of Memory; 7.2 Erasure Process; 7.3 Measurement Process; 7.4 Reconciliation with Maxwell's Demon; 7.5 Second Law of Information Thermodynamics; References; 8 Stochastic Thermodynamics; 8.1 Dynamics; 8.2 Nonequilibrium Equalities; 8.2.1 Backward Control; 8.2.2 Formulation of Nonequilibrium Equalities; 8.2.3 General Derivation of the Detailed Fluctuation Theorem 
501 |a 8.3 Markovian Dynamics with Detail Balance8.3.1 General Formulation; 8.3.2 Overdamped Langevin Systems; References; 9 Nonequilibrium Equalities with Feedback Control; 9.1 Effect of Measurements; 9.1.1 Formulation; 9.1.2 Mutual Information; 9.2 Feedback Control; 9.2.1 Formulation; 9.2.2 Probability Distributions with Feedback; 9.2.3 Detailed Fluctuation Theorem for a Fixed Control Protocol; 9.3 Nonequilibrium Equalities with Feedback Control; 9.3.1 Generalized Fluctuation Theorem with Mutual Information; 9.3.2 Generalized Fluctuation Theorem with Efficacy Parameter; 9.4 Examples 
501 |a 9.4.1 Szilard Engine with Measurement Errors9.4.2 Feedback-Controlled Ratchet; References; 10 Conclusions; References; 
520 |a This thesis presents a general theory of nonequilibrium thermodynamics for information processing.  Ever since Maxwell's demon was proposed in the nineteenth century, the relationship between thermodynamics and information has attracted much attention because it concerns the foundation of the second law of thermodynamics.  From the modern point of view, Maxwell's demon is formulated as an information processing device that performs measurement and feedback at the level of thermal fluctuations.  By unifying information theory, measurement theory, and the recently developed theory of nonequilibrium statistical mechanics, the author has constructed a theory of 'information thermodynamics,' in which information contents and thermodynamic variables are treated on an equal footing.  In particular, the maximum work that can be extracted by the demon and the minimum work that is needed for measurement and information erasure by  the demon has been determined.  Additionally, generalizations of nonequilibrium relations such as a Jarzynski equality for classical stochastic systems in the presence of feedback control have been derived.  One of the generalized equalities has recently been verified experimentally by using sub-micron colloidal particles. The results obtained serve as fundamental principles for information processing in small thermodynamic systems, and are applicable to nanomachines and nanodevices. 
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