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.

324 pages, 68 figures, submitted to Advances in Physics

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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