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Non-commutative geometry and irreversibility

Ayse Erzan·Ayse Gorbon
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Abstract

A kinetics built upon $q$-calculus, the calculus of discrete dilatations, is shown to describe diffusion on a hierarchical lattice. The only observable on this ultrametric space is the "quasi-position" whose eigenvalues are the levels of the hierarchy, corresponding to the volume ofphase space available to the system at any given time. Motion along the lattice of quasi-positions is irreversible.

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Ayse Erzan, Ayse Gorbon. 1997-08-06. Non-commutative geometry and irreversibility. https://doi.org/10.1007/s100510050159

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