Brussels-Austin Nonequilibrium Statistical Mechanics in the Early Years:
Similarity Transformations between Deterministic and Probabilistic
Descriptions
The fundamental problem on which Ilya Prigogine and the Brussels-Austin Group
have focused can be stated briefly as follows. Our observations indicate that
there is an arrow of time in our experience of the world (e.g., decay of
unstable radioactive atoms like Uranium, or the mixing of cream in coffee).
Most of the fundamental equations of physics are time reversible, however,
presenting an apparent conflict between our theoretical descriptions and
experimental observations. Many have thought that the observed arrow of time
was either an artifact of our observations or due to very special initial
conditions. An alternative approach, followed by the Brussels-Austin Group, is
to consider the observed direction of time to be a basics physical phenomenon
and to develop a mathematical formalism that can describe this direction as
being due to the dynamics of physical systems. In part I of this essay, I
review and assess an attempt to carry out an approach that received much of
their attention from the early 1970s to the mid 1980s. In part II, I will
discuss their more recent approach using rigged Hilbert spaces.Comment: 22 pages, Part I of two parts; updated institutional affiliatio
