A Large Deviation Approach to Spin-Flip Dynamics
L. Cazzaniga (TU Delft - Electrical Engineering, Mathematics and Computer Science)
F.H.J. Redig – Mentor (TU Delft - Electrical Engineering, Mathematics and Computer Science)
S. Stallinga – Mentor (TU Delft - Applied Sciences)
M. Blaauboer – Graduation committee member (TU Delft - Applied Sciences)
J.M.A.M. van Neerven – Graduation committee member (TU Delft - Electrical Engineering, Mathematics and Computer Science)
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Abstract
This thesis studies how irreversible macroscopic relaxation emerges from reversible microscopic spin dynamics. For an independent spin-flip system, the empirical magnetization converges to a deterministic relaxation law, while typical fluctuations are described by an Ornstein–Uhlenbeck process. Rare deviations are analysed through fixed-time and pathwise large deviation principles, leading to explicit rate functions and optimal trajectories obtained from a Hamiltonian–Lagrangian formulation. The thesis also discusses how interactions in the two-dimensional Ising model introduce domains, interfaces, and metastability. Overall, large deviation theory quantifies both the probability and the most likely realization of trajectories opposing macroscopic relaxation.