Eur. Phys. J. B 1, 111-116 (1998)
https://doi.org/10.1007/s100510050159

Non-commutative geometry and irreversibility

¹ Department of Physics, Faculty of Sciences and Letters, Istanbul Technical University, Maslak 80626, Istanbul, Turkey
² TÜBITAK Research Institute for Basic Sciences, P.K. 6, Çengelköy, Istanbul 81220, Turkey

Corresponding author: ^a erzan@sariyer.cc.itu.edu.tr

Received: 24 June 1997
Revised: 15 September 1997
Accepted: 6 October 1997
Published online: 15 January 1998

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 of phase space available to the system at any given time. Motion along the lattice of quasi-positions is irreversible.