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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Springer, Nov 6, 2015 - Science - 127 pages

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.

 

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Contents

1 Phenomenological Structure for the Large Deviation Principle
1
2 Iterative MeasurementFeedback Procedure for Large Deviation Statistics
17
3 Common Scaling Functions in Dynamical and Quantum Phase Transitions
41
4 van ZonCohen Singularity and a Negative Inverse Temperature
77
5 Conclusions and Future Perspectives
99
Appendix A For Chapter 2
102
Appendix B For Chapter 3
115
Appendix C For Chapter 4
122
Curriculum Vitae
127
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