Work

Discrete system phase space modification by vanishing noise

Year: 2025

Type: article

Abstract: We investigate two classes of discrete systems: the Hopfield model with deterministic update dynamics and elementary cellular automata. We obtain a sampling of the attractor space of the Hopfield model and the complete phase space of all minimal elementary cellular automata for small lattice sizes. Starting from the maximal entropy distribution (all configurations equiprobable), we show how the dynamics affects this distribution. We then investigate how a vanishing noise alters this phase space, connecting attractors and modifying the asymptotic probability distribution. For both the Hopfield model and Cellular Automata, this modification does not always decrease the entropy.

Source: Natural Computing

DOI: 10.1007/s11047-025-10043-8

Authors: Franco Bagnoli, Michele Baia, Tommaso Matteuzzi

Institutions: Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, University of Florence

Language: English

Topic: Cellular Automata and Applications

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: Università degli Studi di Firenze, NextGenerationEU