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.
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