Thermodynamics

A System Theoretic Foundation

Professor Wassim M. Haddad

School of Aerospace Engineering

Georgia Institute of Technology

Atlanta, GA 30332-1150

Abstract

This presentation provides a system-theoretic foundation for thermodynamics so as to harmonize it with classical mechanics. Using the highest standards of exposition and rigor, a novel formulation of thermodynamics is developed that can be viewed as a moderate-sized system theory as compared to statistical thermodynamics. This middle-ground theory involves deterministic large-scale dynamical system models that bridge the gap between classical and statistical thermodynamics. This work is motivated by the fact that a discipline as cardinal as thermodynamics entrusted with some of the most perplexing secrets of our Universe demands far more than physical mathematics as its underpinning. Even though many great physicists such as Archimedes, Newton, and Lagrange, have humbled us with their mathematically seamless eurekas over the centuries, a great many physicists and engineers who have developed the theory of thermodynamics seem to have forgotten that mathematics, when used rigorously, is the irrefutable pathway to truth. This presentation uses system theoretic ideas to bring coherence, clarity, and precision to an extremely important and poorly understood classical area of science. While it seems impossible to reduce thermodynamics to a mechanistic world picture due to microscopic reversibility and Poincare recurrence, our system thermodynamic formulation provides a harmonization of classical thermodynamics with classical mechanics. In particular, our dynamical system formalism captures all of the key aspects of thermodynamics, including its fundamental laws, while providing a mathematically rigorous formulation for thermodynamical systems out of equilibrium by unifying the theory of heat transfer with that of classical thermodynamics. In addition, the concept of entropy for a nonequilibrium state of a dynamical process is defined, and its global existence and uniqueness is established. This state space formalism of thermodynamics shows that the behavior of heat, as described by the conservation equations of thermal transport and as described by classical thermodynamics, can be derived from the same basic principles and is part of the same scientific discipline.

Friday, April 13, 2007

3:30 – 4:30 p.m.

Rm. 1500 EECS