An introduction to stochastic thermodynamics : from basic to advanced / Naoto Shiraishi.

Author
Shiraishi, Naoto [Browse]
Format
Book
Language
English
Εdition
1st ed.
Published/​Created
  • Singapore : Springer Nature Singapore Pte Ltd., [2023]
  • ©2023
Description
1 online resource (437 pages)

Details

Subject(s)
Series
Summary note
This book presents the fundamentals of stochastic thermodynamics, one of the most central subjects in non-equilibrium statistical mechanics. It also explores many recent advances, e.g., in information thermodynamics, the thermodynamic uncertainty relation, and the trade-off relation between efficiency and power.The content is divided into three main parts, the first of which introduces readers to fundamental topics in stochastic thermodynamics, e.g., the basics of stochastic processes, the fluctuation theorem and its variants, information thermodynamics, and large deviation theory. In turn, parts two and three explore advanced topics such as autonomous engines (engines not controlled externally) and finite speed engines, while also explaining the key concepts from recent stochastic thermodynamics theory that are involved.To fully benefit from the book, readers only need an undergraduate-level background in statistical mechanics and quantum mechanics; no background in information theory or stochastic processes is needed. Accordingly, the book offers a valuable resource for early graduate or higher-level readers who are unfamiliar with this subject but want to keep up with the cutting-edge research in this field. In addition, the author's vivid descriptions interspersed throughout the book will help readers grasp 'living' research developments and begin their own research in this field.
Bibliographic references
Includes bibliographical references and index.
Source of description
Description based on print version record.
Contents
  • Intro
  • Preface
  • Contents
  • 1 Background
  • 1.1 Aims of Stochastic Thermodynamics
  • 1.2 Overview of This Textbook
  • 1.2.1 Overview of Part I
  • 1.2.2 Overview of Part II
  • 1.2.3 Overview of Part III
  • 1.2.4 Overview of Part IV
  • 1.2.5 How to Read This Textbook?
  • 1.3 Notation, Terminologies and Remarks
  • Part I Basic Framework
  • 2 Stochastic Processes
  • 2.1 Markov Process and Discrete-Time Markov Chain
  • 2.2 Continuous Time Markov Jump Process on Discrete System
  • 2.3 Convergence Theorem
  • 2.4 Formal Introduction of Markov Process
  • 3 Stochastic Thermodynamics
  • 3.1 Shannon Entropy
  • 3.1.1 Stochastic Entropy
  • 3.1.2 Shannon Entropy
  • 3.2 Definition of Heat
  • 3.2.1 Time-Reversal Symmetry of Equilibrium State
  • 3.2.2 Heat in Discrete-State Systems and Detailed-Balance Condition
  • 3.3 Entropy Production
  • 3.4 Differences Between Conventional Thermodynamics and Stochastic Thermodynamics
  • 3.4.1 Summary of Conventional Thermodynamics
  • 3.4.2 Summary of Stochastic Thermodynamics
  • 3.4.3 Entropy
  • 3.4.4 Reversible Adiabatic Processes
  • 3.4.5 How to Derive Results for Macroscopic Systems from Stochastic Thermodynamics
  • 4 Stochastic Processes in Continuous Space
  • 4.1 Mathematical Foundations
  • 4.1.1 Wiener Process
  • 4.1.2 Stochastic Differential Equations and Integrals
  • 4.1.3 Differential Chapman-Kolmogorov Equation
  • 4.2 Description of Langevin Dynamics
  • 4.2.1 Langevin Equation
  • 4.2.2 Experimental Verification of Langevin Description
  • 4.3 Heat in Langevin System
  • 4.4 Entropy Production and Mean Local Velocity
  • 4.5 Multi-dimensional Cases
  • 4.6 Discretization and Continuum Limit
  • 4.6.1 Decomposition of Operator
  • 4.6.2 Discretization of the Stochastic Part
  • 4.6.3 Discretization of the Deterministic Part
  • 4.6.4 Space Discretization and Time Discretization
  • Part II Equalities.
  • 5 Fluctuation Theorem
  • 5.1 Detailed Fluctuation Theorem
  • 5.1.1 Stochastic Case
  • 5.1.2 Deterministic Case
  • 5.2 Integral Fluctuation Theorem
  • 5.2.1 Integral Fluctuation Theorem
  • 5.2.2 Jarzynski Equality
  • 5.3 Entropy Production as Phase Volume Change and Expression with KL Divergence
  • 5.3.1 Kullback-Leibler Divergence
  • 5.3.2 Phase Volume
  • 5.3.3 Deterministic Case
  • 5.3.4 Stochastic Case
  • 5.3.5 Absolute Irreversibility
  • 5.4 Thermodynamic Quantities with Strong-Coupling
  • 6 Reduction from Fluctuation Theorem to Other Thermodynamic Relations
  • 6.1 Second Law of Thermodynamics
  • 6.1.1 Standard Derivation of the Second Law
  • 6.1.2 Large Deviation Analysis
  • 6.2 Fluctuation-Dissipation Theorem
  • 6.2.1 Fluctuation-Dissipation Theorem at Zero Frequency
  • 6.2.2 Fluctuation-Dissipation Theorem with Finite Frequency
  • 6.2.3 Higher-Order Relations
  • 6.2.4 Difference from Conventional Linear Response Theory
  • 6.3 Onsager Reciprocity Theorem
  • 7 Fluctuation-Theorem-Type Equalities
  • 7.1 Hatano-Sasa Relation
  • 7.1.1 Dual Transition
  • 7.1.2 Hatano-Sasa Relation and Generalized Second Law
  • 7.1.3 Framework of Steady State Thermodynamics
  • 7.1.4 Hatano-Sasa Inequality and Monotonicity of Kullback-Leibler Divergence
  • 7.2 Entropy Production Under Coarse-Graining
  • 7.2.1 Case Without Nonequilibrium Driving
  • 7.2.2 Case with Nonequilibrium Driving and Hidden Entropy Production
  • 7.2.3 Invariance of Extended Entropy Through Coarse-Graining
  • 8 Various Aspects of Symmetry in Entropy Production
  • 8.1 Introduction to Large Deviation Property and Generating Function
  • 8.1.1 Moments and Cumulants
  • 8.1.2 Counting Field
  • 8.1.3 Large Deviation Theory and Rate Function
  • 8.1.4 Gärtner-Ellis Theorem
  • 8.2 Lebowitz-Spohn Fluctuation Theorem
  • 8.2.1 Symmetry in Cumulant Generating Function of Entropy Production.
  • 8.2.2 Fluctuation-Dissipation Theorem Derived from the Symmetry of Cumulant Generating Function
  • 8.3 Waiting Time Statistics
  • 8.3.1 Martingale Property
  • 8.3.2 First Passage Time Statistics
  • 8.4 Work-Heat Rate Function and Stochastic Efficiency
  • 8.4.1 Stochastic Current and Stochastic Efficiency
  • 8.4.2 Carnot Efficiency as Least Probable Efficiency
  • 9 Information Thermodynamics
  • 9.1 Maxwell's Demon Problem
  • 9.1.1 Maxwell's Original Problem Setting
  • 9.1.2 Breakthrough by Szilard
  • 9.1.3 Arguments by Brillouin and Gabor
  • 9.1.4 Arguments by Landauer and Bennett
  • 9.1.5 Is Maxwell's Demon Problem Solved?
  • 9.2 Second Law of Information Thermodynamics
  • 9.2.1 Mutual Information
  • 9.2.2 Second Law of Information Thermodynamics
  • 9.2.3 Clarification of Maxwell's Demon
  • 9.3 Sagawa-Ueda Relation
  • 9.3.1 Sagawa-Ueda Relation
  • 9.3.2 Additivity
  • 9.4 Problem of Autonomous Maxwell's Demon
  • 9.4.1 Autonomous Maxwell's Demon: 4-State Model
  • 9.4.2 Second Law of Information Thermodynamic in General Information Processes
  • 9.4.3 Limitation of Sagawa-Ueda Relation
  • 9.5 Partial Entropy Production and IFT for General Information Processes
  • 9.5.1 Partial Entropy Production
  • 9.5.2 Fluctuation Theorem for Partial Entropy Production
  • 9.5.3 Fluctuation Theorem for General Information Processes
  • 9.6 Another Extension: Ito-Sagawa Relation
  • 9.6.1 Bayesian Network
  • 9.6.2 Transfer Entropy
  • 9.6.3 Ito-Sagawa Relation and Its Derivation
  • 9.7 Remarks
  • 9.7.1 Partial Entropy Production with Broken Time-Reversal Symmetry
  • 9.7.2 Inequality for Partial Entropy Production
  • 9.7.3 Definition of Heat in Discrete-Time Markov Chains
  • 9.7.4 Information Reservoir
  • 10 Response Relation Around Nonequilibrium Steady State
  • 10.1 Fluctuation-Response Relation at Stalling State.
  • 10.1.1 Fluctuation-Response Relation on Current at Stalling State
  • 10.1.2 Fluctuation-Response Relation on Time-Symmetric Current at Stalling State
  • 10.2 Response Theory of Stationary Distribution
  • 10.2.1 Expression of Stationary Distribution by Matrix-Tree Theorem
  • 10.2.2 Response Equality and Inequality for Stationary Distribution
  • 10.3 Remarks
  • 10.3.1 Alternative Proof of Eq. (10.5) Based on the Generating Function
  • 10.3.2 Proof of Eq. (10.46)
  • 11 Some Results on One-Dimensional Overdamped Langevin Systems
  • 11.1 Path Probability of Dynamics
  • 11.1.1 Onsager-Machlup Functional
  • 11.1.2 Fluctuation Theorem and Hatano-Sasa Relation
  • 11.1.3 Harada-Sasa Relation
  • 11.2 Stationary State of One-Dimensional Overdamped Langevin Systems
  • 11.2.1 Expression of Stationary Distribution
  • 11.2.2 Generating Function of Velocity
  • 11.2.3 Diffusion Constant and Mobility
  • Part III Intermission: Interesting Models
  • 12 Externally-Controlled Systems: Flashing Ratchet and Pump
  • 12.1 Ratchet and Asymmetric Pumping
  • 12.1.1 Flashing Ratchet and Curie Principle
  • 12.1.2 Reversible Transport
  • 12.2 Hidden Pumping
  • 13 Direction of Transport
  • 13.1 Brownian Motor and Adiabatic Piston
  • 13.1.1 Brownian Motor
  • 13.1.2 Adiabatic Piston Problem
  • 13.1.3 Heuristic Argument
  • 13.2 Parrondo's Paradox
  • 13.2.1 Problem and Examples
  • 13.2.2 Similarity to Simpson's Paradox
  • 14 Stationary Systems: From Brownian Motor to Autonomous Macroscopic Engines
  • 14.1 Autonomous Ratchet Model
  • 14.1.1 Feynman's Ratchet
  • 14.1.2 Büttiker-Landauer Model
  • 14.1.3 Unattainability of Carnot Efficiency
  • 14.2 Small Autonomous Models Attaining the Carnot Efficiency
  • 14.3 Macroscopic Autonomous Engines
  • 14.3.1 Setup and Its Coarse-Grained Description
  • 14.3.2 Maximum Efficiency
  • 14.3.3 Attainability of Carnot Efficiency.
  • 14.4 Necessary Condition to Attain Carnot Efficiency
  • 14.4.1 Questions
  • 14.4.2 General Principle
  • 14.4.3 Nonlinear Tight-Coupling Window
  • Part IV Inequalities
  • 15 Efficiency at Maximum Power
  • 15.1 Endoreversible Processes and Curzon-Ahlborn Efficiency
  • 15.2 Onsager Matrix Approach
  • 15.3 Linear Expansion with Velocity
  • 15.4 Remarks
  • 16 Trade-Off Relation Between Efficiency and Power
  • 16.1 Carnot Efficiency and Finite Power: Prelude
  • 16.1.1 No Restriction from General Frameworks
  • 16.1.2 Model Analyses
  • 16.2 Trade-Off Relation Between Heat Current and Entropy
  • 16.2.1 Main Inequalities
  • 16.2.2 Proofs
  • 16.3 Trade-Off Relation Between Efficiency and Power
  • 16.4 Notion of Finite Speed and Finite Power
  • 16.4.1 Inherent Time Scale
  • 16.4.2 Time-Scale Separation
  • 16.5 Remarks
  • 16.5.1 Inequality for General Conserved Quantities
  • 16.5.2 Evaluation of Θ
  • 17 Thermodynamic Uncertainty Relation
  • 17.1 Thermodynamic Uncertainty Relation
  • 17.1.1 Main Claim
  • 17.1.2 Proof Based on Generalized Cramér-Rao Inequality
  • 17.2 TUR-Type Inequalities
  • 17.2.1 Generalization of Thermodynamic Uncertainty Relation
  • 17.2.2 Kinetic Uncertainty Relation
  • 17.2.3 The Optimal TUR-Type Inequality
  • 17.2.4 Attainability of Equality in TUR-Type Inequalities
  • 17.3 Thermodynamic Uncertainty Relation for Ballistic Transport with Broken Time-Reversal Symmetry
  • 17.4 Remarks
  • 17.4.1 TUR in Langevin Systems
  • 17.4.2 Alternative Derivation of Thermodynamic Uncertainty Relation with Large Deviation Techniques
  • 17.4.3 Weaker Relation Derived from Time-Reversal Symmetry
  • 17.4.4 Statistical Meaning of the Cramér-Rao Inequality and the Fisher Information
  • 18 Speed Limit for State Transformation
  • 18.1 Geometric Viewpoint for Speed Limit Inequalities
  • 18.2 Speed Limit for Overdamped Langevin System.
  • 18.2.1 Linear Expansion by Speed.
ISBN
9789811981869 ((electronic bk.))
OCLC
  • 1378936446
  • 1379191557
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