Stochastic thermodynamics / Udo Seifert.

Format:

Book

Author/Creator:

Seifert, Udo, author.

Language:

English

Subjects (All):

Thermodynamics.

Nonequilibrium thermodynamics.

Stochastic processes.

Physical Description:

1 online resource (xviii, 475 pages) : digital, PDF file(s).

Edition:

1st ed.

Place of Publication:

Cambridge : Cambridge University Press, 2025.

Summary:

Stochastic thermodynamics has emerged as a comprehensive theoretical framework for a large class of non-equilibrium systems including molecular motors, biochemical reaction networks, colloidal particles in time-dependent laser traps, and bio-polymers under external forces. This book introduces the topic in a systematic way, beginning with a dynamical perspective on equilibrium statistical physics. Key concepts like the identification of work, heat and entropy production along individual stochastic trajectories are then developed and shown to obey various fluctuation relations beyond the well-established linear response regime. Representative applications are then discussed, including simple models of molecular motors, small chemical reaction networks, active particles, stochastic heat engines and information machines involving Maxwell demons. This book is ideal for graduate students and researchers of physics, biophysics, and physical chemistry, with an interest in non-equilibrium phenomena.

Contents:

Cover

Half-Title Page

Title Page

Imprints Page

Contents

Preface

Dependence of Chapters and Sections

Notation

1 From Classical Mechanics to Statistical Mechanics

1.1 Histograms from Trajectories: Mesoscopic and Macroscopic Observables

1.2 Foundations

1.3 Total Kinetic Energy and Structure Functions

1.4 Thermodynamic Limit

1.5 Pressure and Temperature and Their Microscopic Identification

1.6 Particle Exchange and Chemical Potential

1.7 Entropy: A First Encounter

1.8 Notes

2 Canonical Distribution

2.1 Setup with System and Bath

2.2 Two Simple Applications

2.3 Weak Coupling

2.4 Free Energy, Internal Energy, and Entropy

2.5 Pressure

2.6 Chemical Potential

2.7 Equivalence of "Ensembles" in the Thermodynamic Limit

2.8 Particle Exchange: Grand-Canonical Distribution

2.9 Strong Coupling Effects

2.10 Notes

3 Processes, First and Second Laws

3.1 Paradigmatic Scenarios

3.2 λ-Processes

3.3 First Law

3.4 Reversible Processes

3.5 Second Law in Classical Thermodynamics

3.6 Master Inequality for Regular Protocols

3.7 Second Laws for Work

3.8 Second Law for Heat Exchange

3.9 Second Laws Involving Entropy

3.10 Notes

4 Work Distributions from Hamiltonian Trajectories

4.1 Basic Concepts

4.2 Integral Fluctuation Relations

4.3 Jarzynski Relation

4.4 Bochkov-Kuzovlev Relation

4.5 Crooks Fluctuation Relation

4.6 Free-Energy Landscapes from Nonequilibrium Measurements

4.7 Notes

5 Discrete States: Equilibrium, Relaxation, and Time-Dependent Driving

5.1 Basic Concepts

5.2 Mesostates and Their Thermodynamic Potentials

5.3 Equilibrium Trajectories

5.4 Markovian Dynamics

5.5 Thermodynamics along a Trajectory in a Relaxation Process

5.6 Thermodynamics along a Trajectory for Time-Dependent Driving.

5.7 Nonequilibrium Thermodynamics: Ensemble Level

5.8 Entropy and Time's Arrow

5.9 Fluctuation Relations

5.10 Thermodynamics along Hamiltonian Trajectories Revisited: Entropy and the Second Law?

5.11 Notes

6 Enzymes and Enzymatic Reactions

6.1 Enzyme in Solution

6.2 A Toy Model

6.3 General Case

6.4 Notes

7 Thermodynamically Consistent Asymmetric Random Walk

7.1 ... as a Minimal Model for a Molecular Motor

7.2 ... Introduced as an Abstract Model

7.3 Fluctuations: Exact Results in Finite Time

7.4 Fluctuations: Concepts from Large Deviation Theory

7.5 Notes

8 Nonequilibrium Steady States

8.1 Basic Theory for General Rates

8.2 Thermodynamic Aspects: Soft Matter and Biosystems

8.3 Thermodynamic Aspects: Classical Transport throughQuantum Dots

8.4 Thermodynamic Uncertainty Relation

8.5 Macroscopic Affinities and Physical Currents

8.6 Unicyclic Systems and Engines

8.7 Multicyclic Systems

8.8 Linear Response to Macroscopic Affinities

8.9 Notes

9 Brownian Motion

9.1 Langevin Equation for the Momentum

9.2 Fluctuation-Dissipation Relation and Diffusion

9.3 Experimental Case Study: Brownian Particle in Air

9.4 Linear Generalized Langevin Equation

9.5 Systems with Time-Scale Separation

9.6 Hydrodynamic Effects

9.7 Notes

10 Driven Colloidal Particle

10.1 Langevin Dynamics and Fokker-Planck Equation

10.2 Time-Independent Force

10.3 Application of a NESS: Escape from a Metastable Well

10.4 Mean Local Velocity

10.5 Multiplicative Noise and Stratonovich Calculus: A First Encounter

10.6 Path Integral Representation

10.7 Thermodynamic Quantities

10.8 Detailed Fluctuation Theorems

10.9 Integral Fluctuation Relations

10.10 Notes

11 Correlations and Linear Response

11.1 Introductory Example: Harmonic Oscillator.

11.2 Correlation in Steady State: A Particle in One Dimension as Paradigm

11.3 Response Functions from Path Integral Formalism

11.4 Response Function from Perturbed Generator

11.5 Causality in Fourier Space

11.6 Harada-Sasa Relation

11.7 Notes

12 Molecular Motors

12.1 Ratchet Models

12.2 Discrete Motor Models

12.3 Motors with Probe or Cargo Particles

12.4 Notes

13 Chemical Reaction Networks

13.1 Univariate Reactions: Finite System

13.2 Univariate Reactions: Toward the Thermodynamic Limit

13.3 Fokker-Planck Approximations

13.4 Thermodynamic Quantities for an Individual Reaction Event

13.5 Oscillations: Brusselator as Paradigm

13.6 Multivariate Networks

13.7 Notes

14 Active Particles

14.1 One-Dimensional Toy Model

14.2 Simple Models in Two and Three Dimensions

14.3 Thermodynamically Consistent Minimal Model

14.4 Notes

15 Stochastic Heat Engines

15.1 Classical Heat Engines

15.2 Brownian Heat Engines

15.3 Steady-State Engines with Systems of Discrete States

15.4 Notes

16 Information Processing

16.1 Feedback-Driven Systems

16.2 Bipartite Systems

16.3 Information Reservoirs and Machines

16.4 Notes

17 Coarse-Graining

17.1 Coarse-Grained Data

17.2 Entropy Production from Stationary Time Series

17.3 Coarse-Graining a Markov Model

17.4 Notes

18 Langevin Dynamics: Advanced Topics

18.1 Space-Dependent Friction

18.2 Discretization Rules

18.3 Path Integral Representation

18.4 Multivariate Langevin Dynamics

18.5 Martingales

18.6 Underdamped Langevin Dynamics in One Dimension

18.7 High-Friction Limit and Inhomogeneous Temperature

18.8 Notes

19 Large Deviations

19.1 Key Notions

19.2 Discrete Systems: Spectral Approach

19.3 Discrete Systems: Rate Function from Path Weights

19.4 Langevin Dynamics: Spectral Approach.

19.5 Langevin Dynamics: Rate Function from Path Weights

19.6 Notes

20 Optimization

20.1 Introductory Example: Stiffening of a Harmonic Trap

20.2 Langevin Dynamics

20.3 Discrete States

20.4 Information Geometry

20.5 Speed Limits and Entropic Inequalities

20.6 Slow Processes

20.7 Notes

Appendix A Some Technical Tools for Chapter 1

A.1 Delta and Theta Functions

A.2 Univariate Gaussian Distribution

A.3 Approximative Gaussian Distributions, Laplace's Method of Integration, and Stirling's Formula

A.4 Volume and Area of an n-Dimensional Sphere

A.5 Kinetic Structure Function and Ideal Gas

Appendix B Hamiltonian Dynamics and Liouville's Theorem

Appendix C Isobaric Description or "Pressure Ensemble"

C.1 A Reservoir at Constant Pressure

C.2 ... with an Enzyme Added

C.3 Transition and Reaction Rates

C.4 Heat and Entropy Production

C.5 Summarizing Recipe

Appendix D Legendre Transformations

Appendix E Gaussian Random Variables and Random Functions

E.1 Multivariate Gaussian and Wick's Theorem

E.2 Noncentered Gaussian Variables

E.3 Gaussian Random Functions

E.4 Standard Gaussian White Noise

Appendix F Supplement on the Dynamics for Systems with Discrete States

F.1 Spectrum of the Generator from Perron-Frobenius

F.2 Correlation Functions

F.3 Linear Response in Equilibrium and in NESSs

F.4 Notes

Appendix G Supplement on Interacting Particles

G.1 Smoluchowski Equation for Passive Particles

G.2 Pressure for Passive Particles

G.3 Smoluchowski Equation and Pressure for Interacting Active Particles

G.4 Notes

Appendix H Local Equilibrium and the Identification of Heat Current

References

Index.

Notes:

Title from publisher's bibliographic system (viewed on 09 Jun 2025).

ISBN:

1-009-02165-6

1-009-02435-3