Nonequilibrium Thermodynamics and Fluctuation Kinetics: Modern Trends and Open Questions

Preface
Contents
Memorials
In Memoriam Professor Viacheslav (Slava) Belyi (1945–2020)
1 I. Veretennicoff: Towards a Productive Scientific Collaboration Between Izmiran and the Vrije Universiteit Brussel (1980–1991)
1.1 Yuri Lvovich Klimontovich and Radu Balescu
1.2 My Own Roots Are to Be Found in St. Petersburg, Russia
1.3 My Arrival in Moscow
1.4 Collaboration
1.5 Traveling with Slava
2 L. Brenig
3 L. Bindler, Formerly at Belgonucleaire, Brussels, Belgium
4 J. P. Boon
5 C. De Mol
6 R. Gerold
7 J. Wallenborn
8 M. Mareschal
9 A. G. Zagorodny
10 N. Brilliantov
Biographic Note
1 Early Life
2 Scientific Exchanges with Belgium
3 Doctor of Science and ‘a Prize Laureate
4 New Sets of Collaboration
5 The Solvay Institutes and Prigogine’s Influence
6 Major Results and Recognition
References
General Problems of Non-equilibrium Thermodynamics and Fluctuation Kinetics. Fluctuation Dissipation Theorem
The Many Faces of Fluctuation-Dissipation Relations Out of Equilibrium
1 Introduction
2 Two Approaches to Non-equilibrium FDR
2.1 An Approach Based upon the Knowledge of the Stationary Distribution
2.2 An Approach Based upon the Knowledge of the Dynamical Model
3 Applications
3.1 The Interesting Case of Causation Through Response
3.2 Spin and Disordered Systems
3.3 Granular Materials
3.4 Application to Biological Systems and Active Particles
4 Conclusions
References
Mandelbrot's Fractal Structure in Decaying Process of a Matter-field Interacting System
1 Introduction
2 Complex Spectral Analysis of Friedrichs' Hamiltonian
3 Nonlinear Map for Iterative Method
4 Mandelbrot Set
5 Concluding Remarks
References
Thermodynamic Flux-Force Closure Relations for Systems out of the Onsager Region
1 Introduction
2 The Thermodynamical Field Theory (TFT)
2.1 The Space of the Thermodynamic Forces
2.2 The De Donder-Prigogine Thermodynamic Invariance
2.3 Remarks on De Donder-Prigogine's Thermodynamic Invariance Formulation
2.4 The Thermodynamic Covariant Transformations (TCT) and the Thermodynamic Covariance Principle (TCP)
2.5 The TCT-Symmetry Group
2.6 The Thermodynamic Action Principle
2.7 The Privileged Thermodynamic Coordinate System
3 Transport Equations
3.1 Onsager's Region
3.2 Near the Onsager Region
4 Two-Dimensional Transport Equations
5 Linearised Transport Equations
5.1 Linearised Transport Equations for n > 2
5.2 Examples of Simplification of the Linearised Transport Equations
5.3 Linearised Transport Equation for n=2
6 TFT Gauge Invariance
6.1 Basic Theorems for the PDEs B(0)µν(h)=W(S)µν
6.2 A Note on the Physical Meaning of the Gauge Invariance
7 Solution of the Linearised Equations
8 Testing the Validity of the PDE (64)—Computation of Heat Loss in L-mode, Collisional FTU-Plasma
9 Conclusions
References
Simulating Deterministic Dynamics by Drawing Coloured Balls at Random in Urns
1 Introduction
2 The Quasi-polynomial Dynamical Systems and Their Canonical Forms
3 Urn Processes
4 Equivalence Between Balanced Urn Processes and the QP Differential systems
5 Examples
5.1 Lotka-Volterra Systems
5.2 The Lorenz System
5.3 Asymmetric Top with Dissipation
5.4 Cosmological Dynamics
6 Conclusive Remarks and Perspectives
References
Langton's Ant as an Elementary Turing Machine
1 Introduction
2 The Automaton Process
3 Concluding Comments
References
Kinetic Theory of Far-from-Equilibrium Processes
Phase Transitions in Active Matter Systems
1 Introduction
2 Phase Transition: An Elementary Discussion
2.1 Critical Phenomena
2.2 Coarsening Phenomena
3 Flocking Transition in Active Matter Systems: A Basic Model
4 Phase Behavior and Critical Aspects in the Vicsek Model
5 Transitions in Variants of the Vicsek Model
6 Kinetics of Flocking Transition: Structure Formation
7 Growth During Flocking Evolution
7.1 Theoretical Background
7.2 Computational Results on Growth of Fractal Clusters
8 Aging in Evolving Active Matter System
9 Conclusion
References
Kinetic Theory of Binary Granular Suspensions at Low Density. Thermal Diffusion Segregation
1 Introduction
2 Granular Suspension Model
3 Homogeneous Steady States
4 Chapman–Enskog Method. First-Order Solution
4.1 Tracer Limit. Diffusion Transport Coefficients
4.2 Leading Sonine Approximation
5 Thermal Diffusion Segregation of an Intruder in a Granular Suspension
5.1 Mechanically Equivalent Particles
5.2 Elastic Collisions
5.3 Inelastic Collisions
6 Concluding Remarks
References
Boltzmann Equation in Aggregation Kinetics
1 Introduction
2 Boltzmann–Smoluchowski Equations for Ballistic Agglomeration
2.1 Boltzmann Equation
2.2 Boltzmann–Smoluchowski Equations
3 Smoluchowski Equations for Space-Uniform Systems
3.1 Velocity Distribution Function and Its Moments
3.2 Smoluchowski Equations. Randomly Aggregative Collisions
3.3 Smoluchowski Equations. Impact Energy-Dependent Aggregation
3.4 Application to the Hypothetical Evolution of Dark Matter
4 Exact and Scaling Solutions
4.1 Exact Solutions
4.2 Scaling Analysis
5 Numerical Methods in Aggregating Kinetics
5.1 Direct Simulation Monte Carlo of the Boltzmann Equation
5.2 Solution of Temperature-Dependent Smoluchowski Equations by Monte Carlo Method
5.3 Solution of Temperature-Dependent Smoluchowski ODE with Low-Rank Methods
5.4 Phase Diagram for the Temperature-Dependent Smoluchowski Equations
6 Discussion
References
Large-Scale Fluctuations in Collisional Dusty Plasmas with Regard to Grain Charging Processes
1 Introduction
2 Fluctuations of the Distribution Function
3 Equations of the Grain Charge Dynamics
4 Stationary Grain Charge, Charging and Collision Frequencies
5 Dielectric Permittivity in the BGK Model
6 Ion-Acoustic Waves
7 Fluctuation Spectra
8 Conclusions
References
Fluctuations and Kinetics in Non-linear Non-equilibrium Systems
Space-Time Dynamics of High-Q Optical Resonators
1 Introduction
2 Space-Time Dynamics of High-Q Resonators
2.1 The Mean-Field Model
2.2 Modulational Instability and Pattern Formation
3 Localized Solutions of the Lugiato-Lefever Equation: Homoclinic Snaking Bifurcation
4 Inhomogeneous High-Q Resonators
4.1 The Lugiato-Lefever Model with Inhomogeneous Injection
4.2 Homoclinic Snaking in the Presence of Inhomogeneities
4.3 The Potential Well Model for the Inhomogeneous LLE
5 Conclusions
References
Optimization in Engineering Processes: An Application of a Generalized Fluctuation–Dissipation Theorem
1 Introduction
2 Generalized Entropy Production in Non-Fourier Heat Transfer
3 Conclusions
References
Co-evolutionary Complex Networks
1 Introduction
2 Spread Dynamics
3 Communication Policies in Organizational Knowledge Networks
4 Experts in Organizational Knowledge Networks
5 Attitude Change and Hidden Influence in Organizational Networks
6 Unreliable Organizational Knowledge Networks
7 Conflict and Polarization in Co-evolutionary Organizational Networks
8 Intelligence Agents and Centralization in Co-evolutionary Knowledge Networks
9 Discussion
References
Thermal Fluctuations Induced Emergence of Umbilical Defects in Nematic Liquid Crystal Cells
1 Introduction
2 Experimental Setup
3 Theoretical Description
4 Vortices Nucleation Law
5 Noise Induced Emergence of One-Dimensional Defect
6 Conclusion and Remarks
References
Thermodynamic Instability of the Atmospheric Boundary Layer as a Precursor of an Earthquake
1 The Thermal Anomalies Before Earthquakes
2 Air Ionization as a Main Source of Pre-earthquake Atmospheric Anomalies
3 Autocatalytic Reaction Leading to Thermal Instability
4 Atmospheric Chemical Potential as a Measure of Thermal Instability in Atmosphere
5 Conclusion
6 Four Dimensions of My Interaction with Slava Belyi
References
Multistability of Vector Solitons in High-Q Resonators
1 Introduction
2 The Vectorial Lugiato–Lefever Model
3 Modulational Instability in the Case of Anomalous Dispersion
4 Front-Locking in the Case of Normal Dispersion
5 Tristability in the Case of Normal Dispersion
6 Conclusions and Perspectives
References