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A mathematical analysis of irreversible behavior and its origins in
various physical systems is presented.
The lecture will begin with a brief review of relative entropy and with
a survey of sources of irreversible behavior.
Subsequently, the Second Law of thermodynamics, in the forms given to
it by Clausius and Carnot, is derived from quantum statistical mechanics.
In a third part, a derivation of Brownian motion of a quantum particle
interacting with a quantum-mechanical heat bath is sketched. This is
followed by an outline of a theory of Hamiltonian Friction.
In what may be the most important part of the lecture, the fundamental
arrow of time inherent in Quantum Mechanics is discussed.