Semigroups and Symmetry: an investigation of Prigogine's theories

Edens, Bram (2001) Semigroups and Symmetry: an investigation of Prigogine's theories.

Abstract

It has been claimed that Ilya Prigogine's theories constitute a paradigm shift unheard of since the impact of Newton. The shift would consist in Prigogine's specific approach towards the problem of time's arrow i.e.
how to reconcile the observed macroscopic time asymmetry with the underlying fundamental microscopic time symmetrical laws. Whereas well
known approaches as coarse-graining or interventionism are based upon external considerations, Prigogine's proposal, reminiscent of the early
Boltzmann, is instead to derive irreversibility due to the dynamics of a
system alone. Physics should no longer treat time as a mere parameter, but
has to be united with our asymmetrical experience of time.

In this paper I discuss whether Prigogine succeeds in deriving intrinsic
irreversibility. After an introduction to Prigoginian thinking, I propose my main heuristic in assessing Prigogine's scientific work called symmetry breaking and semigroup
selection. I clarify this heuristic by discussing the Kac ring model.
Finally, in a chronological order, I distinguish between several
approaches in Prigogine's work and discuss each of them briefly. I arge that Prigogine's attempt fails.