The Ilya Prigogine Center for Studies in
Statistical Mechanics and Complex Systems
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The most interesting feature in the probability plots is the appearance of the horizontal bar in the middle diagram. This featurwas predicted using an extended formalism of quantum mechanics developed by Prof. Ilya Prigogine, called the Liouville Space Extension of Quantum Mechanics.
The most powerful use of Dr. Prigogine's extended formalism of quantum mechanics is that, unlike conventional quantum theory, it may be capable of describing systems which are time-irreversible, that is, systems that display a definite arrow of time.

Described by conventional quantum scattering theory
Although all real physical systems have a definite arrow of time, conventional quantum theory does not describe irrerversible evolution in a fundamental fashion. Much of the on-going research at the Center is devoted to understanding how irreversible processes work.

Described by extended quantum scatttering theory
For more details , please look here.

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Text and Graphics (c) 1999 by Matthew Trump. Original three-panel diagrams by T. Miyasaka