The Irreversibility of the Voter Model

The Ising model is a paradigmatic example of spin alignment dynamics in statistical mechanics. A single spin flip occurs according to microscopic reversibility and, in simulations, following the Metropolis rule based on the mean alignment in the ensemble of neighboring spins. The voter model, instead, was devised as a minimalist rule for opinion dynamics in society: a person "flips" their opinion according to the comparison with that of a randomly picked neighbor. Such dynamics is not related to detailed balance. For this reason, this thesis aims to study the irreversibility of the voter model, which is quantified by nonequilibrium statistical mechanics' concept of entropy production. The model contains long-range interactions between each of the N units. To better understand the model's steady state (excluding the absorbing conditions of all voters of the same kind), this project plans to use analytical tools and advanced numerical techniques, including sparse matrices, to characterize the distribution of states and the fluxes in the network of states, also as a function of N.