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Transition between metastable equilibria: Applications to binary-choice games.

A Antonov¹, A Leonidov^1,2, A Semenov^1,3,4

¹P. N. Lebedev Physical Institute, Moscow 119991, Russia.

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|September 19, 2023

Summary

Activity spillover enhances finite-time transitions in the Ising game, but this effect disappears in the infinite time limit. This study develops an analytical method to understand these long-term dynamics.

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Area of Science:

Statistical Mechanics
Complex Systems Dynamics

Background:

The Ising game models interactions and phase transitions.
Activity spillover can influence transition dynamics in finite timescales.

Purpose of the Study:

To investigate transitions between metastable states in the Ising game's low-temperature phase over infinite time.
To determine if activity spillover affects transitions in the infinite time limit.

Main Methods:

Development of an analytical description for infinite time trajectories.
Introduction of an analytical approach to estimate transition probabilities in the infinite time limit.
Comparison of analytical results with kinetic Monte Carlo simulations.

Main Results:

Exponential enhancement from activity spillover, observed in finite-time transitions, is absent in the infinite time limit.
An analytical method for estimating infinite time transition probabilities was successfully developed.
Analytical predictions align with kinetic Monte Carlo simulation results.

Conclusions:

Activity spillover does not provide exponential enhancement for transitions in the infinite time limit.
The developed analytical approach accurately describes long-term dynamics of metastable state transitions.
Findings offer insights into complex systems and transitions between metastable states.