The Fluctuation-Dissipation Relations: Growth, Diffusion, and Beyond
arXiv:2312.10134 · doi:10.1016/j.physrep.2025.07.004
Abstract
In this review, we scrutinize historical and modern results on the linear response of dynamical systems to external perturbations with a particular emphasis on the celebrated relationship between fluctuations and dissipation expressed by the fluctuation-dissipation theorem (FDT). The conceptual foundation of FDT originates from the definition of the equilibrium state and Onsager's regression hypothesis. Over time, the fluctuation-dissipation relation has been vividly investigated also in systems far from equilibrium, which often exhibit wild fluctuations in measured parameters. In this review, we recall the major formulations of the FDT, including those proposed by Langevin, Onsager and Kubo. We discuss the role of fluctuations in a broad class of growth and diffusion phenomena and examine the violation of the FDT resulting from a transition from Euclidean to fractal geometry. Finally, we highlight possible generalizations of the FDT formalism and discuss situations where the relation breaks down and is no longer applicable.
arXiv comment54 pages, 16 figures, accepted manuscript for publication in Physics Reports
References in corpus (130)
- A nonequilibrium equality for free energy differences
- Stochastic thermodynamics, fluctuation theorems, and molecular machines
- Active Particles in Complex and Crowded Environments
- The Entropy Production Fluctuation Theorem and the Nonequilibrium Work Relation for Free Energy Differences
- Critical Phenomena and Renormalization-Group Theory
- Shape Fluctuations and Random Matrices
- Surface Electromagnetic Waves Thermally Excited: Radiative Heat Transfer, Coherence Properties and Casimir Forces Revisited in the Near Field
- Lévy walks
- Fluctuation-Dissipation: Response Theory in Statistical Physics
- Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
- Universal Distributions for Growth Processes in 1+1 Dimensions and Random Matrices
- The one-dimensional KPZ equation: an exact solution and its universality
- Violation of the fluctuation-dissipation theorem in glassy systems: basic notions and the numerical evidence
- Measuring multipartite entanglement via dynamic susceptibilities
- Exact Large Deviation Function in the Asymmetric Exclusion Process
- Free-energy distribution of the directed polymer at high temperature
- A KPZ Cocktail- Shaken, not stirred: Toasting 30 years of kinetically roughened surfaces
- Kardar-Parisi-Zhang physics in the quantum Heisenberg magnet
- A pedestrian's view on interacting particle systems, KPZ universality, and random matrices
- Non-local Interaction Effects on Pattern Formation in Population Dynamics
- Stochastic mechano-chemical kinetics of molecular motors: a multidisciplinary enterprise from a physicist's perspective
- Test of Jarzynski and Crooks fluctuation relations in an electronic system
- Diffusion on a solid surface: Anomalous is normal
- Observation of Fluctuation-Dissipation-Theorem Violations in a Structural Glass
- Anomalous diffusion: A basic mechanism for the evolution of inhomogeneous systems
- Onsager's Scars in Disordered Spin Chains
- Eigenvector statistics in non-Hermitian random matrix ensembles
- Non-perturbative renormalization group for the Kardar-Parisi-Zhang equation
- Monte-Carlo simulations of the violation of the fluctuation-dissipation theorem in domain growth processes
- Anomalous spin diffusion in one-dimensional antiferromagnets
- Quantum scars as embeddings of weakly "broken" Lie algebra representations
- Non-perturbative renormalisation group for the Kardar-Parisi-Zhang equation: general framework and first applications
- Fractal Symmetric Phases of Matter
- Renormalization Group and Probability Theory
- Exact short-time height distribution in 1D KPZ equation and edge fermions at high temperature
- Universal fluctuations in the growth of semiconductor thin films
- Instability, Intermittency and Multiscaling in Discrete Growth Models of Kinetic Roughening
- Quantized Scaling of Growing Surfaces
- Dynamics of Rough Interfaces in Chemical Vapor Deposition: Experiments and a Model for Silica Films
- Khinchin theorem and anomalous diffusion
- Path integral approach to quantum thermodynamics
- Experimental study of the Fluctuation-Dissipation-Relation during an aging process
- Response theory: a trajectory-based approach
- Violation of the fluctuation-dissipation theorem in time-dependent mesoscopic heat transport
- Violation of the fluctuation-dissipation theorem for fast superdiffusion
- Crossover from Growing to Stationary Interfaces in the Kardar-Parisi-Zhang Class
- Analytic approaches of the anomalous diffusion: a review
- Roundoff-induced Coalescence of Chaotic Trajectories
- Temporal and spatial persistence of combustion fronts
- Heat transfer between nanoparticles: Thermal conductance for near-field interactions
- Replica Bethe ansatz derivation of the Tracy-Widom distribution of the free energy fluctuations in one-dimensional directed polymers
- Universality of fluctuations in the Kardar-Parisi-Zhang class in high dimensions and its upper critical dimension
- Intermediate dynamics between Newton and Langevin
- Coulomb-gas electrostatics controls large fluctuations of the KPZ equation
- Linear response and correlation of a self-propelled particle in the presence of external fields
- Entropy production of Multivariate Ornstein-Uhlenbeck processes correlates with consciousness levels in the human brain
- Harmonic oscillator under Levy noise: Unexpected properties in the phase space
- Statistical Thermodynamics of General Minimal Diffusion Processes: Constuction, Invariant Density, Reversibility and Entropy Production
- Non-exponential relaxation for anomalous diffusion
- Run-and-tumble bacteria slowly approaching the diffusive regime
- Mathematical Formalism for Isothermal Linear Irreversibility
- Disentangling sources of anomalous diffusion
- A long-range memory stochastic model of the return in financial markets
- On the Fluctuation-Dissipation Relation in non-equilibrium and non-Hamiltonian systems
- Fluctuation-Dissipation relation in sub-diffusive systems: the case of granular single-file
- Stretched exponential relaxation in the mode-coupling theory for the Kardar-Parisi-Zhang equation
- Entropy production in linear Langevin systems
- Superdiffusive dispersals impart the geometry of underlying random walks
- Two time scales and FDT violation in a Finite Dimensional Model for Structural Glasses
- Heat exchange between two interacting nanoparticles beyond the fluctuation-dissipation regime
- Characterising the nonequilibrium stationary states of Ornstein-Uhlenbeck processes
- Inference in non-equilibrium systems from incomplete information: the case of linear systems and its pitfalls
- Quantum Work in the Bohmian framework
- Normal Stress Distribution of Rough Surfaces in Contact
- Dynamic roughening and fluctuations of dipolar chains
- Violation of the fluctuation-dissipation theorem in a protein system
- Analytical results for long time behavior in anomalous diffusion
- Anomalous statistics of laser-cooled atoms in dissipative optical lattices
- Interface fluctuations for deposition on enlarging flat substrates
- A Paradox in the Langevin Equation with Long-Time Noise Correlations
- Initial pseudo-steady state & asymptotic KPZ universality in semiconductor on polymer deposition
- Local quasi-equilibrium description of slow relaxation systems
- Entropy, non-ergodicity and non-Gaussian behaviour in ballistic transport
- Kardar-Parisi-Zhang Interfaces with Inward Growth
- Stochastic Tools Hidden Behind the Empirical Dielectric Relaxation Laws
- A statistical mechanical model for drug release: relations between release parameters and porosity
- Pattern formation and coexistence domains for a nonlocal population dynamics
- The Kardar-Parisi-Zhang exponents for the dimensions
- Fluctuation-Dissipation Relation from the Nonequilibrium Dynamics of a Nonlinear Open Quantum System
- Growth exponents of the etching model in high dimensions
- From entanglement certification with quench dynamics to multipartite entanglement of interacting fermions
- The fractal geometry of growth: fluctuation-dissipation theorem and hidden symmetry
- Nonlinear diffusion effects on biological population spatial patterns
- Mixing, ergodicity and slow relaxation phenomena
- Fluctuation-dissipation relations under Levy noises
- Diffusion Time-Scale Invariance, Markovization Processes and Memory Effects in Lennard-Jones Liquids
- From synaptic interactions to collective dynamics in random neuronal networks models: critical role of eigenvectors and transient behavior
- Fluctuation-dissipation theorem for non-equilibrium quantum systems
- Stochastic description of the dynamics of the random-exchange Heisenberg chain
- Broken detailed balance and entropy production in directed networks
- Kardar-Parisi-Zhang growth on one-dimensional decreasing substrates
- Modeling the diffusion-erosion crossover dynamics in drug release
- Heat and work distributions for mixed Gauss-Cauchy process
- Infinite horizon billiards: Transport at the border between Gauss and Lévy universality classes
- Synchronization in the presence of memory
- Quantum response theory for nonequilibrium steady states
- Heterogeneities in systems with quenched disorder
- Modified fluctuation-dissipation and Einstein relation at non-equilibrium steady states
- Analysis of etching at a solid-solid interface
- A random rule model of surface growth
- Hopping Models of Charge Transfer in a Complex Environment: New Class of Coupled Memory Continous-Time Random Walks
- Slow dynamics and local quasi-equilibrium. Relaxation in supercooled colloidal systems
- Circular Kardar-Parisi-Zhang interfaces evolving out of the plane
- Dimensional fragility of the Kardar-Parisi-Zhang universality class
- The hidden fluctuation-dissipation theorem for growth
- Anomalous diffusion on crumpled wires in two dimensions
- Critical behavior of noise-induced phase synchronization
- Conceptual and practical approaches for investigating irreversible processes
- Anomalous law of cooling
- Numerical integration of KPZ equation with restrictions
- Lévy Walks and Path Chaos in the Dispersal of Elongated Structures Moving across Cellular Vortical Flows
- Universal scaling relation for growth phenomena
- Fluctuations in multiplicative systems with jumps
- Thermodynamics aspects of noise-induced phase synchronization
- Restoring the fluctuation-dissipation theorem in Kardar-Parisi-Zhang universality class through a new emergent fractal dimension
- A geometrical interpretation of critical exponents
- Spatio-temporal conjecture for diffusion
- Superdiffusive Conduction: AC Conductivity with Correlated Noise
- Freeness in cognitive science
- Quantum fluctuation theorem for initial near-equilibrium system