Nonequilibrium thermodynamics of the majority vote model

TL;DR

This paper develops a thermodynamically consistent framework for the majority vote model by assigning local heat baths, enabling analysis of energy and heat fluxes at phase transitions across various topologies.

Contribution

It introduces a novel approach to define heat baths for local configurations, allowing thermodynamic analysis of the majority vote model regardless of topology.

Findings

Thermodynamic properties are derived for the model.

Heat flux behavior at phase transitions is characterized.

Dissipation origins are explained through local configurations.

Abstract

The majority vote model is one of the simplest opinion systems yielding distinct phase transitions and has garnered significant interest in recent years. However, its original formulation is not, in general, thermodynamically consistent, precluding the achievement of quantities such as power and heat, as well as their behaviors at phase transition regimes. Here, we circumvent this limitation by introducing the idea of a distinct heat bath per local configuration, in such a way that each neighborhood value is associated with a distinct and well-defined thermal bath. Thermodynamic properties are derived for a generic majority vote model, irrespective of its neighborhood and lattice topology. The behavior of energy/heat fluxes at phase transitions, whether continuous or discontinuous, in regular and complex topologies, is investigated in detail. Unraveling the contribution of each local configuration explains the nature of the phase diagram and reveals how dissipation arises from the dynamics.