LC
L. Cazzaniga
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Bachelor thesis
(2026)
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L. Cazzaniga, F.H.J. Redig, S. Stallinga, M. Blaauboer, J.M.A.M. van Neerven
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.
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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.