Introduction to dynamical large deviations of Markov processes
Abstract
These notes give a summary of techniques used in large deviation theory to study the fluctuations of time-additive quantities, called dynamical observables, defined in the context of Langevin-type equations, which model equilibrium and nonequilibrium processes driven by external forces and noise sources. These fluctuations are described by large deviation functions, obtained by solving a dominant eigenvalue problem similar to the problem of finding the ground state energy of quantum systems. This analogy is used to explain the differences that exist between the fluctuations of equilibrium and nonequilibrium processes. An example involving the Ornstein-Uhlenbeck process is worked out in detail to illustrate these methods. Exercises, at the end of the notes, also complement the theory.
Cite
@article{arxiv.1705.06492,
title = {Introduction to dynamical large deviations of Markov processes},
author = {Hugo Touchette},
journal= {arXiv preprint arXiv:1705.06492},
year = {2022}
}
Comments
19 pages. Lecture notes for the 2017 Summer School on Fundamental Problems in Statistical Physics XIV, 16-29 July 2017, Bruneck (Brunico), Italy. v2: Typos corrected, exercises added. v3: Typos corrected. v4: More typos corrected, footnote and references added. v5: Close to published version. v6: typo corrected. I dedicate this paper to the memory of E. G. D. Cohen (1923-2017)