Phenomenological Structure for the Large Deviation Principle in Time-Series Statistics

This thesis describes a method to control rare events in non-equilibrium systems by applying physical forces to those systems but without relying on numerical simulation techniques, such as copying rare events. In order to study this method, the book draws on the mathematical structure of equilibrium statistical mechanics, which connects large deviation functions with experimentally measureable thermodynamic functions. Referring to this specific structure as the phenomenological structure for the large deviation principle, the author subsequently extends it to time-series statistics that can be used to describe non-equilibrium physics.

The book features pedagogical explanations and also shows many open problems to which the proposed method can be applied only to a limited extent. Beyond highlighting these challenging problems as a point of departure, it especially offers an effective means of description for rare events, which could become the next paradigm of non-equilibrium statistical mechanics.

Nominated as an outstanding contribution by Kyoto University's Physics Department in 2015 Proposes a general rare-event sampling method that can be applied to non-equilibrium systems without relying on numerical techniques such as copying rare events Includes pedagogical explanations of why equilibrium statistical mechanics can connect large deviation statistics with thermodynamic functions Provides an analytical expression of common scaling functions between quantum phase transitions and dynamical phase transitions in a kinetically constrained model Includes supplementary material: sn.pub/extras

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Phenomenological structure for the large deviation principle.- Iterative measurement-feedback procedure for large deviation statistics.- Common scaling functions in dynamical and quantum phase transitions.- van Zon-Cohen singularity and a negative inverse temperature.- Conclusions and future perspectives.