The Second Law of Thermodynamics has been called the most important
law of nature: It is the law that gives a direction to processes
that is not inherent in the laws of motion, that says the state of
the universe is driven to thermal equilibrium. Its mathematical
formulation is simple: The entropy of a closed system cannot
decrease. Since the recognition that macroscopic phenomena have an
atomic basis, it has remained a fundamental problem to reconcile
the increase of entropy with the known reversibility of all the
laws of microscopic physics. Professor Michael Mackey of McGill
University here explores the dynamical basis for the Second Law,
that is, he seeks to illuminate the fundamental dynamical
properties required for the construction of a successful
statistical mechanics. Aimed at physicists and applied
mathematicians with an interest in the foundations of statistical
mechanics, the book includes such new material as: a demonstration
that the black body radiation law can be deduced from maximal
entropy principles; a discussion of sufficient conditions for the
existence of at least one state of thermodynamic equilibrium; a
description of the behavior of entropy in asymptotically periodic
systems; a necessary and sufficient condition for the evolution of
entropy to a global maximum; and a presen- tation of the three main
types of ergodic theorems and their proofs. He also explores the
potential role of incomplete knowledge of dynamical variables,
measurement imprecision, and the effects of noise in giving rise to
entropy increases.
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