Thermodynamics of Information Processing in Small Systems

1. Front Matter

   Pages i-xv

   PDF

2. Introduction

   • Takahiro Sagawa

   Pages 1-7

3. Review of Maxwell’s Demon

   • Takahiro Sagawa

   Pages 9-16

4. Classical Dynamics, Measurement, and Information

   • Takahiro Sagawa

   Pages 17-23

5. Quantum Dynamics, Measurement, and Information

   • Takahiro Sagawa

   Pages 25-42

6. Unitary Proof of the Second Law of Thermodynamics

   • Takahiro Sagawa

   Pages 43-52

7. Second Law with Feedback Control

   • Takahiro Sagawa

   Pages 53-60

8. Thermodynamics of Memories

   • Takahiro Sagawa

   Pages 61-73

9. Stochastic Thermodynamics

   • Takahiro Sagawa

   Pages 75-89

10. Nonequilibrium Equalities with Feedback Control

    • Takahiro Sagawa

    Pages 91-113

11. Conclusions

    • Takahiro Sagawa

    Pages 115-118

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.

• Information Thermodynamics
• Jarzynski Equality
• Landauer Principle
• Maxwell’s Demon
• Nonequilibrium Statistical Mechanics
• Quantum Feedback Control
• Quantum Information Theory
• Quantum Measurement Theory
• Second Law of Information Thermodynamics
• Stochastic Thermodynamics
• Szilard Engine

• Kyoto University, Kyoto, Japan

  Takahiro Sagawa

Dr. Takahiro Sagawa
Kyoto University
Kitashirakawa Oiwake-Cho,
Sakyo-Ku, Kyoto
606-8502 Japan

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