Stochastic chaos and thermodynamic phase transitions : theory and Bayesian estimation algorithms
Name
219714017-MIT.pdf
Description
Full printable version
Size
31.51 MB
Format
Adobe PDF
Checksum (MD5)
a0185be79bf54ae835c25614f6bb60d4
Author(s)
Deng, Zhi-De
Advisor(s)
Chi-Sang Poon.
Date Issued
2007
Publisher
Massachusetts Institute of Technology
Abstract
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.
Description
Thesis (M. Eng. and S.B.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2007.
Includes bibliographical references (p. 177-200).
Subjects
Electrical Engineering and Computer Science.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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