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Introduction to dynamical large deviations of Markov processes

Hugo Touchette
摘要
These notes give a summary of techniques used in large deviation theory tostudy the fluctuations of time-additive quantities, called dynamicalobservables, defined in the context of Langevin-type equations, which modelequilibrium and nonequilibrium processes driven by external forces and noisesources. These fluctuations are described by large deviation functions,obtained by solving a dominant eigenvalue problem similar to the problem offinding the ground state energy of quantum systems. This analogy is used toexplain the differences that exist between the fluctuations of equilibrium andnonequilibrium processes. An example involving the Ornstein-Uhlenbeck processis worked out in detail to illustrate these methods. Exercises, at the end ofthe notes, also complement the theory.
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