ID No.: 96HZ67760
NAME OF THE STUDENT: Shaji V. Thomas
DISSERTATION TITLE: The Role of Ergodicity in Foundations of Statistical Mechanics: A Critical Review
ABSTRACT
This thesis analyzes the role of ergodicity in the foundations of statistical mechanics. The first chapter discusses developments in the kinetic theory of matter. Various criticisms against the kinetic explanation of the macroscopic processes led to the formulation of statistical mechanics. The probabilistic interpretation of the second law of thermodynamics and ergodic hypothesis were the responses to the criticism against the kinetic theory. The second chapter deals with Boltzmann’s formulation of ergodic hypothesis and Paul & Tatiana Ehrenfests interpretations to it. In order to formulate the ergodic hypothesis, he assumed that every point on the plane would traverse all possible values of momentum in a single system. Through ergodic hypothesis, Boltzmann introduced the concept of probability in kinetic theory. The third chapter deals with the role of ergodic theory as a foundation to statistical mechanics. Gibbs introduced the concepts of ensembles and probability to forego the boundaries of the atomic hypothesis and formulated the statistical mechanics. The thesis is concluded in the fourth chapter by proposing the possibilities for visualizing ergodic theory as a stepping-stone toward a grounding theory. If we could forget the atomic concept of matter, then we could construct a different phase space for macroscopic systems. So ergodic theory could be reformulated from a different perspective of matter. This new perspective, in turn, could be used to construct certain models of consciousness.
