How to Introduce Temperature to the 1 Dimensional Sznajd Model

TL;DR

This paper extends the one-dimensional Sznajd model by incorporating temperature and additional interactions, analyzing equilibrium states, detailed balance, and fluctuations to better understand social dynamics modeling.

Contribution

It introduces a temperature parameter and new interaction types into the Sznajd model, providing a framework for analyzing equilibrium and fluctuation effects.

Findings

Characterized different equilibrium states

Linked detailed balance to microscopic reversibility

Defined a temperature-like fluctuation measure

Abstract

We investigate the possibility of introducing the temperature to the one dimensional Sznajd model and propose a natural extension of the original model by including other types of interactions. We characterise different kinds of equilibria into which the extended system can evolve. We determine the consequences of fulfilling the detailed balance condition and we prove that in some cases it is equivalent to microscopic reversibility. We propose a simple definition of the temperature-like quantity that measures the size of fluctuations in the system at equilibrium. The complete list of zero-temperature degenerated cases is provided.