Martingales for physicists: A treatise on stochastic thermodynamics and beyond

Abstract

We review the theory of martingales as applied to stochastic thermodynamics and stochastic processes in physics more generally.

arXiv comment324 pages, 68 figures, submitted to Advances in Physics

References in corpus (109)

• A nonequilibrium equality for free energy differences
• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• The Entropy Production Fluctuation Theorem and the Nonequilibrium Work Relation for Free Energy Differences
• The large deviation approach to statistical mechanics
• Dynamical Ensembles in Nonequilibrium Statistical Mechanics
• Artificial Brownian motors: Controlling transport on the nanoscale
• Entropy production along a stochastic trajectory and an integral fluctuation theorem
• A Gallavotti-Cohen Type Symmetry in the Large Deviation Functional for Stochastic Dynamics
• Fluctuation theorem for stochastic dynamics
• Thermodynamic uncertainty relation for biomolecular processes
• Path ensembles averages in systems driven far-from-equilibrium
• Statistical Mechanics of Interacting Run-and-Tumble Bacteria
• Steady State Thermodynamics of Langevin Systems
• Dissipation bounds all steady-state current fluctuations
• Dissipation: The phase-space perspective
• The Fluctuation Theorem as a Gibbs Property
• Universal trade-off between power, efficiency, and constancy in steady-state heat engines
• Second law and Landauer principle far from equilibrium
• Fluctuation theorems for stochastic dynamics
• Ensemble and Trajectory Thermodynamics: A Brief Introduction
• Classical and Quantum Fluctuation Theorems for Heat Exchange
• Universality Classes for Extreme Value Statistics
• State-dependent diffusion: thermodynamic consistency and its path integral formulation
• The Three Faces of the Second Law: I. Master Equation Formulation
• Anomalous diffusion and ergodicity breaking in heterogeneous diffusion processes
• Nonequilibrium Markov processes conditioned on large deviations
• Elephants can always remember: Exact long-range memory effects in a non-Markovian random walk
• Universal bounds on current fluctuations
• Run and tumble particle under resetting: a renewal approach
• Anomalous Diffusion of Symmetric and Asymmetric Active Colloids
• Steady state, relaxation and first-passage properties of a run-and-tumble particle in one-dimension
• The Three Faces of the Second Law: II. Fokker-Planck Formulation
• Entropy production and the arrow of time
• Nonequilibrium microcanonical and canonical ensembles and their equivalence
• Path-integral analysis of fluctuation theorems for general Langevin processes
• Extreme value statistics of correlated random variables: a pedagogical review
• Universal features in the energetics of symmetry breaking
• Integral fluctuation theorem for the housekeeping heat
• Broken detailed balance and entropy production in the human brain
• Conformal Field Theories of Stochastic Loewner Evolutions
• Generic Properties of Stochastic Entropy Production
• Dissipation and lag in irreversible processes
• Influence of Noise on Force Measurements
• Universal First-passage Properties of Discrete-time Random Walks and Levy Flights on a Line: Statistics of the Global Maximum and Records
• Fundamental Bounds on First Passage Time Fluctuations for Currents
• The Brownian gyrator: a minimal heat engine on the nano-scale
• Fluctuation Relations for Diffusion Processes
• Drift without flux: Brownian walker with a space dependent diffusion coefficient
• The Exclusion Process: A paradigm for non-equilibrium behaviour
• Experimental free energy measurements of kinetic molecular states using fluctuation theorems
• Martingale Models for Quantum State Reduction
• Elephant Random Walks and their connection to Pólya-type urns
• A formal view on 2.5 large deviations and fluctuation relations
• Experimental Realization of a Minimal Microscopic Heat Engine
• Decision Making in the Arrow of Time
• Local detailed balance
• A martingale approach for the elephant random walk
• Two refreshing views of Fluctuation Theorems through Kinematics Elements and Exponential Martingale
• Central Limit Theorem for the Elephant Random Walk
• Fluctuation theorem for counting-statistics in electron transport through quantum junctions
• Thermodynamics of Error Correction
• Convergence of repeated quantum non-demolition measurements and wave function collapse
• Thermodynamics of Gambling Demons
• Nonequilibrium Equalities in Absolutely Irreversible Processes
• Uniqueness and non-uniqueness in percolation theory
• Symmetric path integrals for stochastic equations with multiplicative noise
• Rules of calculus in the path integral representation of white noise Langevin equations: the Onsager-Machlup approach
• Records in a changing world
• Recovery of free energy branches in single molecule experiments
• Efficiency fluctuations in microscopic machines
• Generalized Haldane Equation and Fluctuation Theorem in the Steady State Cycle Kinetics of Single Enzymes
• Second law of thermodynamics at stopping times
• Integral Fluctuation Relations for Entropy Production at Stopping Times
• Noise-induced drift in stochastic differential equations with arbitrary friction and diffusion in the Smoluchowski-Kramers limit
• Experimental measurement of binding energy, selectivity and allostery using fluctuation theorems
• A Guided Walk Down Wall Street: an Introduction to Econophysics
• Is stochastic thermodynamics the key to understanding the energy costs of computation?
• Growth, competition and cooperation in spatial population genetics
• Asymmetry relations and effective temperatures for biased Brownian gyrators
• Temporal correlations of the running maximum of a Brownian trajectory
• A selection of nonequilibrium issues
• Reflection positivity and phase transitions in lattice spin models
• Quantum Martingale Theory and Entropy Production
• Stochastic Hydrodynamics of Complex Fluids: Discretisation and Entropy Production
• Universal tradeoff relation between speed, uncertainty, and dissipation in nonequilibrium stationary states
• Arbitrarily slow, non-quasistatic, isothermal transformations
• Estimating Entropy Production Rates with First-Passage Processes
• Martingale theory for housekeeping heat
• Extreme reductions of entropy in an electronic double dot
• First-Passage Duality
• Fluctuation Relations for Diffusions Thermally Driven by a Non-Stationnary Bath
• Thermodynamics of computations with absolute irreversibility, unidirectional transitions, and stochastic computation times
• Inflow rate, a time-symmetric observable obeying fluctuation relations
• Anisotropic super-attenuation of capillary waves on driven glass interfaces
• The marginally stable Bethe lattice spin glass revisited
• Universal Property of the Housekeeping Entropy Production
• Extreme value statistics of edge currents in Markov jump processes and their use for entropy production estimation
• Memory Through a Hidden Martingale Process in Progressive Quenching
• Statistical physics of inhomogeneous transport: Unification of diffusion laws and inference from first-passage statistics
• Martingale structure for general thermodynamic functionals of diffusion processes under second-order averaging
• Progressive quenching - Globally coupled model
• Martingale-induced local invariance in Progressive Quenching
• Gumbel Central Limit Theorem for Max-Min and Min-Max
• The full replica symmetry breaking in the Ising spin glass on random regular graph
• Survival and extreme statistics of work, heat, and entropy production in steady-state heat engines
• Progressive quenching --- Ising chain models
• Multicyclic norias: a first-transition approach to extreme values of the currents
• Martingale drift of Langevin dynamics and classical canonical spin statistics
• Interplay between Markovianity and Progressive Quenching

Cited by in corpus (15)

• Stochastic thermodynamics of a probe in a fluctuating correlated field
• Generalized arcsine laws for a sluggish random walker with subdiffusive growth
• Gambling Carnot Engine
• Itô, Stratonovich, and zoom-in schemes in stochastic inflation
• Martingale approach for first-passage problems of time-additive observables in Markov processes
• Thermodynamic bounds and symmetries in first-passage problems of fluctuating currents
• Exactly solvable diffusions from space-time transformations
• Effective Affinity for Generic Currents in Markov Processes
• First-Passage-Time Asymmetry for Biased Run-and-Tumble Processes
• Active energy harvesting and work transduction by hair-cell bundles in bullfrog's inner ear
• Thermodynamic inference in molecular motors: a Martingale approach
• Spikes in Poissonian quantum trajectories
• Generalized replicator dynamics based on mean-field pairwise comparison dynamic
• The Limits of Inference in Complex Systems: When Stochastic Models Become Indistinguishable
• Fluctuation Relations associated to an arbitrary bijection in path space