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.
