Phenomenological Structure for the Large Deviation Principle in Time-series Statistics ― A Method to Control the Rare Events in Non-equilibrium Systems
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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 this specific structure as the “phenomenological structure for large deviation principle”, the book 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 only be applied 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
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