How can one construct dynamical systems obeying the first and
second laws of thermodynamics: mean energy is conserved and entropy
increases with time? This book answers the question for classical
probability (Part I) and quantum probability (Part II). A novel
feature is the introduction of heat particles which supply thermal
noise and represent the kinetic energy of the molecules. When
applied to chemical reactions, the theory leads to the usual
nonlinear reaction-diffusion equations as well as modifications of
them. These can exhibit oscillations, or can converge to
equilibrium. In this second edition, the text is simplified in
parts and the bibliography has been expanded. The main difference
is the addition of two new chapters; in the first, classical fluid
dynamics is introduced. A lattice model is developed, which in the
continuum limit gives us the Euler equations. The five
Navier???Stokes equations are also presented, modified by a
diffusion term in the continuity equation. The second addition is
in the last chapter, which now includes estimation theory, both
classical and quantum, using information geometry.
General
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