Nonequilibrium Statistical Mechanics : Basic Concepts, Models and Applications.

Format:

Book

Author/Creator:

Vulpiani, A.

Contributor:

Puglisi, Andrea.

Sarracino, Alessandro.

Series:

IOP Ebooks Series

Language:

English

Physical Description:

1 online resource (349 pages)

Edition:

1st ed.

Place of Publication:

Bristol : Institute of Physics Publishing, 2025.

Summary:

This book explains nonequilibrium statistical physics from the fundamentals to the most recent topics. It covers Brownian motion and Langevin equations, kinetic theory from gases to granular and active matter, it discusses how to model stochastic processes from data, it treats general subjects such as entropy production and fluctuations in small systems.

Contents:

Intro

Acknowledgements

Author biographies

Alessandro Sarracino

Andrea Puglisi

Angelo Vulpiani

Chapter From Brownian motion to the Langevin equation

1.1 From the surprising behaviour of pollen grains to the existence of atoms

1.1.1 Langevin's approach

1.1.2 The relevance of Brownian motion

1.2 Toward a mathematical theory

1.2.1 A discrete time version of the Langevin equation

1.2.2 The Fokker-Planck equation

1.2.3 Relation between Fokker-Planck and Langevin equations

1.2.4 Beyond the Fokker-Planck equation

1.3 Again about the Langevin equation

1.3.1 The Langevin equation from the microscopic dynamics

1.3.2 Langevin equation as a tool for numerical computations

1.4 Further remarks

1.4.1 A pedagogical parenthesis on the Lorentz model

1.4.2 Einstein's approach to Brownian motion

1.4.3 Remarks on Perrin's experiments

1.4.4 The legacy of Brownian motion

References

Chapter The Boltzmann equation

2.1 Boltzmann equation in a nutshell

2.1.1 Master equations

2.2 Boltzmann equation for hard spheres

2.3 The Loschmidt and Zermelo objections

2.4 Other kinetic models

2.4.1 Granular gases

2.4.2 Maxwell models

2.4.3 Redistribution models

2.5 Some remarks about irreversibility

2.5.1 About ensembles and entropies

2.5.2 Ehrenfest model and typicality

2.5.3 Again on chaos and irreversibility

Chapter Statistical and dynamical features of fluctuations

3.1 Fluctuations are small but relevant

3.1.1 Fluctuations and responses

3.1.2 A digression about temperature fluctuations

3.2 Onsager relations

3.2.1 Detailed balance and its relevance

3.2.2 The Onsager relations in chemical reactions

3.2.3 Onsager relations and ideal gas effusion

3.2.4 Variables with different parity under time reversal

3.2.5 Beyond detailed balance.

3.3 Dynamics of fluctuations

3.4 Langevin equation and physics

Chapter Linear response theory and fluctuation-dissipation theorem

4.1 From Einstein and Onsager to Kubo

4.1.1 Response in frequency and Johnson-Nyquist spectrum

4.1.2 van Kampen's objection

4.2 A generalized fluctuation-dissipation theorem even for non-Hamiltonian systems

4.2.1 Finite perturbations and the relevance of chaos

4.3 A series of remarks

4.3.1 The Kubo formula

4.3.2 Gaussian distributions

4.3.3 Apparent violation of the fluctuation-dissipation theorem and marginal distributions

4.3.4 Chaotic dissipative systems

4.3.5 A fluctuation-dissipation theorem in generic noisy systems

Chapter Entropy production, fluctuation relations and beyond

5.1 Irreversible thermodynamics

5.1.1 Thermodynamic forces and fluxes

5.1.2 Onsager coefficients

5.2 Stochastic thermodynamics

5.2.1 Local detailed balance

5.2.2 Fluctuating entropy production

5.2.3 Langevin equations with irreversible currents

5.3 Fluctuation relations

5.3.1 Integral and detailed fluctuation theorem

5.3.2 Jarzynski and Crooks relations

5.4 Thermodynamic uncertainty relations

5.5 Fluctuation-dissipation theorem: alternative approaches

5.5.1 Fluctuation-dissipation theorem and dynamical activity

5.5.2 The fluctuation relation close to equilibrium and its connection to the fluctuation-dissipation theorem

5.5.3 Harada-Sasa relation

5.5.4 Fluctuation-dissipation theorem from local detailed balance

Chapter Model building in systems with multiple scales

6.1 Introduction

6.2 Many levels of description: molecular dynamics, Brownian motion and beyond

6.2.1 The microscopic level: Hamiltonian dynamics

6.2.2 Mesoscopic level: the Kramers and Smoluchowski equations.

6.2.3 Beyond the Kramers and Smoluchowski equations

6.2.4 A parenthesis on the diffusion at large scale in stirred fluids

6.3 Coarse-graining: from the micro-world to the meso-level

6.3.1 A big tracer in a gas, assuming thermodynamic equilibrium

6.3.2 A tracer in a gas without assuming equilibrium

6.3.3 A tracer in a solid

6.3.4 Projection methods and generalized Langevin equations

6.4 Symmetries and coarse-graining

6.4.1 The generalized equilibrium conditions

6.4.2 Loss of symmetry: dissipation without fluctuations

6.5 Inferring Langevin models from data

6.5.1 Inferring a generalized Langevin equation at equilibrium

6.5.2 Inferring a Langevin equation, out of equilibrium

Chapter Applications: from climate to causation

7.1 Langevin equation for the climate dynamics

7.1.1 Exit time and stochastic resonance

7.2 Data analysis via information theory

7.2.1 Shannon entropy

7.2.2 The Kolmogorov-Sinai entropy and the ε-entropy

7.2.3 Information and entropy production

7.3 Causation

7.3.1 Causation and linear response theory

7.3.2 Difficulties in the treatment of data

7.3.3 Toward an understanding of causal relations of paleoclimate dynamics

Chapter Granular and active matter

8.1 Introduction

8.2 Granular kinetic theory

8.2.1 The granular Boltzmann equation

8.2.2 Granular steady states

8.3 The dynamics of a granular tracer

8.3.1 Granular Brownian motion

8.3.2 Tracer in a moderately dense granular fluid: the role of the coupling among variables

8.3.3 Granular Brownian motors

8.4 Hydrodynamics and correlations

8.4.1 Langevin equations for hydrodynamic modes

8.5 Active matter

Chapter Stranger things

9.1 Motion from friction

9.1.1 Langevin equation in the presence of dry friction.

9.1.2 The asymmetric Rayleigh piston in the presence of dry friction

9.2 Getting more from pushing less

9.2.1 Simple models

9.2.2 Negative differential mobility

9.3 Turn right to go left

9.3.1 Absolute negative mobility of an active tracer in a lattice gas model

9.3.2 Absolute negative mobility of an inertial tracer in a laminar flow

9.3.3 Generalized Einstein relation and the role of non-entropic forces

Chapter Pedagogical appendices

Appendix I: Basic facts of the atomic world from a clever use of statistical mechanics and a few experiments

A fast recap of important results

The problem of the interaction potential

A simple experiment for high school students and conclusive remarks

Appendix II: Numerical methods for the Langevin equations

An interlude on random numbers

Appendix III: Bibliographical suggestions

Index.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

0-7503-6229-4