Classical and quantum mechanics on information spaces with applications to cognitive, psychological, social and anomalous phenomena

TL;DR

This paper develops classical and quantum models on p-adic information spaces to better understand information processes in cognitive, social, and anomalous phenomena, offering a new mathematical framework for information reality.

Contribution

It introduces a novel p-adic framework for modeling information processes, combining classical and quantum mechanics on these spaces for the first time.

Findings

P-adic models effectively describe information flow in cognitive systems

Classical and quantum formalisms are adapted to p-adic information spaces

Potential applications in social and anomalous phenomena analysis

Abstract

We use the system of p-adic numbers for the description of information processes. Basic objects of our models are so called transformers of information, basic processes are information processes, the statistics are information statistics (thus we present a model of information reality). The classical and quantum mechanical formalisms on information p-adic spaces are developed. It seems that classical and quantum mechanical models on p-adic information spaces can be applied for the investigation of flows of information in cognitive and social systems, since a p-adic metric gives quite natural description of the ability to form associations.