Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# Dendrogramic Representation of Data: CHSH-Violation vs. Nonergodicity

Version 1 : Received: 13 June 2021 / Approved: 14 June 2021 / Online: 14 June 2021 (14:58:40 CEST)

A peer-reviewed article of this Preprint also exists.

Shor, O.; Benninger, F.; Khrennikov, A. Dendrogramic Representation of Data: CHSH Violation vs. Nonergodicity. Entropy 2021, 23, 971. Shor, O.; Benninger, F.; Khrennikov, A. Dendrogramic Representation of Data: CHSH Violation vs. Nonergodicity. Entropy 2021, 23, 971.

Journal reference: Entropy 2021, 23, 971
DOI: 10.3390/e23080971

## Abstract

This paper is devoted to the foundational problems of dendrogramic holographic theory (DH-theory). We use the ontic-epistemic (implicate-explicate order) methodology. The epistemic counterpart is based on representation of data by dendrograms constructed with hierarchic clustering algorithms. The ontic Universe is described as the p-adic tree; it is zero dimensional, totally disconnected, disordered, and bounded (in p-adic ultrametric). Interrelation classical-quantum loses its sharpness; generally simple dendrograms are more quantum’’ than complex one. We use the CHSH-inequality as a measure of quantum(-likeness). We demonstrate that it can be violated by classical experimental data represented by dendrograms. The seed of this violation is neither nonlocality nor rejection of realism. This is nonergodicity of dendrogramic time series. Generally, violation of ergodicity is one of the basic features of DH-theory. We also consider DH-theory for Minkovski geometry and monitor the dependence of CHSH-violation and nonergodicity on geometry as well as a Lorentz transformation of data.

## Keywords

ontic; epistemic; dendrograms; dendrogramic holographic theory,; clustering algorithms; quantumness; CHCH inequality; nonergodicity

## Subject

PHYSICAL SCIENCES, Acoustics

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