Transition between metastable equilibria: applications to binary-choice games

TL;DR

This paper analyzes the transition dynamics between metastable states in a dynamical Ising game with activity spillover, providing an analytical framework for infinite time limits and comparing it with simulations.

Contribution

It introduces an analytical method to estimate transition probabilities between metastable states in the infinite time limit for the Ising game with activity spillover.

Findings

Exponential enhancement due to activity spillover is absent in the infinite time limit.

Analytical predictions agree with kinetic Monte Carlo simulations.

The study improves understanding of metastable state transitions in complex systems.

Abstract

Transitions between metastable equilibria in the low-temperature phase of dynamical Ising game with activity spillover are studied in the infinite time limit. It is shown that exponential enhancement due to activity spillover, which takes place in finite-time transitions, is absent in the infinite time limit. In order to demonstrate that, the analytical description for infinite time trajectory is developed. An analytical approach to estimate the probability of transition between metastable equilibria in the infinite time limit is introduced and its results are compared with those of kinetic Monte Carlo simulation. Our study sheds light on the dynamics of the Ising game and has implications for the understanding of transitions between metastable states in complex systems.