Nonequilibrium Statistical Physics of Small Systems: Fluctuation Relations and Beyond(Reviews of Nonlinear Dynamics and Complexity)

This book offers a comprehensive picture of nonequilibrium phenomena in nanoscale systems. Written by internationally recognized experts in the field, this book strikes a balance between theory and experiment, and includes in-depth introductions to nonequilibrium fluctuation relations, nonlinear dynamics and transport, single molecule experiments, and molecular diffusion in nanopores. The authors explore the application of these concepts to nano- and biosystems by cross-linking key methods and ideas from nonequilibrium statistical physics, thermodynamics, stochastic theory, and dynamical systems. By providing an up-to-date survey of small systems physics, the text serves as both a valuable reference for experienced researchers and as an ideal starting point for graduate-level students entering this newly emerging research field.

Table of Contents:
Preface XIII List of Contributors XVII Color Plates XXIII Part I Fluctuation Relations 1 1 Fluctuation Relations: A Pedagogical Overview 3 Richard Spinney and Ian Ford 1.1 Preliminaries 3 1.2 Entropy and the Second Law 5 1.3 Stochastic Dynamics 8 1.4 Entropy Generation and Stochastic Irreversibility 13 1.5 Entropy Production in the Overdamped Limit 21 1.6 Entropy, Stationarity, and Detailed Balance 25 1.7 A General Fluctuation Theorem 27 1.8 Further Results 37 1.9 Fluctuation Relations for Reversible Deterministic Systems 41 1.10 Examples of the Fluctuation Relations in Action 45 1.11 Final Remarks 54 References 55 2 Fluctuation Relations and the Foundations of Statistical Thermodynamics: A Deterministic Approach and Numerical Demonstration 57 James C. Reid, Stephen R. Williams, Debra J. Searles, Lamberto Rondoni, and Denis J. Evans 2.1 Introduction 57 2.2 The Relations 58 2.3 Proof of Boltzmann's Postulate of Equal A Priori Probabilities 62 2.4 Nonequilibrium Free Energy Relations 67 2.5 Simulations and Results 69 2.6 Results Demonstrating the Fluctuation Relations 74 2.7 Conclusion 80 References 81 3 Fluctuation Relations in Small Systems: Exact Results from the Deterministic Approach 83 Lamberto Rondoni and O.G. Jepps 3.1 Motivation 84 3.2 Formal Development 94 3.3 Discussion 108 3.4 Conclusions 110 References 111 4 Measuring Out-of-Equilibrium Fluctuations 115 L. Bellon, J. R. Gomez- Solano, A. Petrosyan, and Sergio Ciliberto 4.1 Introduction 115 4.2 Work and Heat Fluctuations in the Harmonic Oscillator 116 4.3 Fluctuation Theorem 121 4.4 The Nonlinear Case: Stochastic Resonance 128 4.5 Random Driving 132 4.6 Applications of Fluctuation Theorems 142 4.7 Summary and Concluding Remarks 150 References 151 5 Recent Progress in Fluctuation Theorems and Free Energy Recovery 155 Anna Alemany, Marco Ribezzi-Crivellari, and Felix Ritort 5.1 Introduction 155 5.2 Free Energy Measurement Prior to Fluctuation Theorems 156 5.3 Single-Molecule Experiments 159 5.4 Fluctuation Relations 163 5.5 Control Parameters, Configurational Variables, and the Definition of Work 166 5.6 Extended Fluctuation Relations 172 5.7 Free Energy Recovery from Unidirectional Work Measurements 175 5.8 Conclusions 177 References 177 6 Information Thermodynamics: Maxwell's Demon in Nonequilibrium Dynamics 181 Takahiro Sagawa and Masahito Ueda 6.1 Introduction 181 6.2 Szilard Engine 182 6.3 Information Content in Thermodynamics 184 6.4 Second Law of Thermodynamics with Feedback Control 189 6.5 Nonequilibrium Equalities with Feedback Control 197 6.6 Thermodynamic Energy Cost for Measurement and Information Erasure 205 6.7 Conclusions 208 Appendix 6.A: Proof of Eq. (6.56) 208 References 209 7 Time-Reversal Symmetry Relations for Currents in Quantum and Stochastic Nonequilibrium Systems 213 Pierre Gaspard 7.1 Introduction 213 7.2 Functional Symmetry Relations and Response Theory 216 7.3 Transitory Current Fluctuation Theorem 220 7.4 From Transitory to the Stationary Current Fluctuation Theorem 224 7.5 Current Fluctuation Theorem and Response Theory 227 7.6 Case of Independent Particles 230 7.7 Time-Reversal Symmetry Relations in the Master Equation Approach 238 7.8 Transport in Electronic Circuits 244 7.9 Conclusions 252 References 254 8 Anomalous Fluctuation Relations 259 Rainer Klages, Aleksei V. Chechkin, and Peter Dieterich 8.1 Introduction 259 8.2 Transient Fluctuation Relations 260 8.3 Transient Work Fluctuation Relations for Anomalous Dynamics 265 8.4 Anomalous Dynamics of Biological Cell Migration 269 8.5 Conclusions 277 References 278 Part II Beyond Fluctuation Relations 283 9 Out-of-Equilibrium Generalized Fluctuation-Dissipation Relations 285 G. Gradenigo, A. Puglisi, A. Sarracino, D. Villamaina, and A. Vulpiani 9.1 Introduction 285 9.2 Generalized Fluctuation-Dissipation Relations 287 9.3 Random Walk on a Comb Lattice 294 9.4 Entropy Production 300 9.5 Langevin Processes without Detailed Balance 301 9.6 Granular Intruder 306 9.7 Conclusions and Perspectives 313 References 314 10 Anomalous Thermal Transport in Nanostructures 319 Gang Zhang, Sha Liu, and Baowen Li 10.1 Introduction 319 10.2 Numerical Study on Thermal Conductivity and Heat Energy Diffusion in One-Dimensional Systems 320 10.3 Breakdown of Fourier's Law: Experimental Evidence 325 10.4 Theoretical Models 327 10.5 Conclusions 331 References 332 11 Large Deviation Approach to Nonequilibrium Systems 335 Hugo Touchette and Rosemary J. Harris 11.1 Introduction 335 11.2 From Equilibrium to Nonequilibrium Systems 336 11.3 Elements of Large Deviation Theory 341 11.4 Applications to Nonequilibrium Systems 347 11.5 Final Remarks 356 References 357 12 Lyapunov Modes in Extended Systems 361 Hong-Liu Yang and Gunter Radons 12.1 Introduction 361 12.2 Numerical Algorithms and LV Correlations 363 12.3 Universality Classes of Hydrodynamic Lyapunov Modes 365 12.4 Hyperbolicity and the Significance of Lyapunov Modes 369 12.5 Lyapunov Spectral Gap and Branch Splitting of Lyapunov Modes in a "Diatomic" System 372 12.6 Comparison of Covariant and Orthogonal HLMs 376 12.7 Hyperbolicity and Effective Degrees of Freedom of Partial Differential Equations 380 12.8 Probing the Local Geometric Structure of Inertial Manifolds via a Projection Method 384 12.9 Summary 388 References 389 13 Study of Single-Molecule Dynamics in Mesoporous Systems, Glasses, and Living Cells 393 Stephan Mackowiak and Christoph BrEUROauchle 13.1 Introduction 393 13.2 Investigation of the Structure of Mesoporous Silica Employing Single-Molecule Microscopy 396 13.3 Investigation of the Diffusion of Guest Molecules in Mesoporous Systems 402 13.4 A Test of the Ergodic Theorem by Employing Single-Molecule Microscopy 407 13.5 Single-Particle Tracking in Biological Systems 409 13.6 Conclusion and Outlook 412 References 413 Index 415