# Non-commutative geometry and irreversibility

Source: [Non-commutative geometry and irreversibility](<https://www.sota2.com/research/paper/68fa246c2c2a3760193a3f1f>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T09:10:57.035Z

Authors: Ayse Erzan, Ayse Gorbon

Published: 1997-08-06T18:44:25.000Z

## 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.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/cond-mat/9708052>)

[PDF](<https://arxiv.org/pdf/cond-mat/9708052.pdf>)