Stochastic chaos and thermodynamic phase transitions : theory and Bayesian estimation algorithms
Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science.
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The chaotic behavior of dynamical systems underlies the foundations of statistical mechanics through ergodic theory. This putative connection is made more concrete in Part I of this thesis, where we show how to quantify certain chaotic properties of a system that are of relevance to statistical mechanics and kinetic theory. We consider the motion of a particle trapped in a double-well potential coupled to a noisy environment. By use of the classic Langevin and Fokker-Planck equations, we investigate Kramers' escape rate problem. We show that there is a deep analogy between kinetic rate theory and stochastic chaos, for which we propose a novel definition. In Part II, we develop techniques based on Volterra series modeling and Bayesian non-linear filtering to distinguish between dynamic noise and measurement noise. We quantify how much of the system's ergodic behavior can be attributed to intrinsic deterministic dynamical properties vis-a-vis inevitable extrinsic noise perturbations.
Thesis (M. Eng. and S.B.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2007.Includes bibliographical references (p. 177-200).
DepartmentMassachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science.
Massachusetts Institute of Technology
Electrical Engineering and Computer Science.