Reduction from non-Markovian to Markovian dynamics: The case of aging in the noisy-voter model

Abstract

We study memory dependent binary-state dynamics, focusing on the noisy-voter model. This is a non-Markovian process if we consider the set of binary states of the population as the description variables, or Markovian if we incorporate "age", related to the time one has spent holding the same state, as a part of the description. We show that, in some cases, the model can be reduced to an effective Markovian process, where the age distribution of the population rapidly equilibrates to a quasi-steady state, while the global state of the system is out of equilibrium. This effective Markovian process shares the same phenomenology of the non-linear noisy-voter model and we establish a clear parallelism between these two extensions of the noisy-voter model.

References in corpus (7)

• Statistical physics of social dynamics
• The large deviation approach to statistical mechanics
• Uncovering individual and collective human dynamics from mobile phone records
• Decelerating microdynamics can accelerate macrodynamics in the voter model
• Zealots in the mean-field noisy voter model
• Equivalence between non-Markovian and Markovian dynamics in epidemic spreading processes
• Update rules and interevent time distributions: Slow ordering vs. no ordering in the Voter Model

Cited by in corpus (11)

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• Zealots in multi-state noisy voter models
• Aging in binary-state models: The Threshold model for Complex Contagion
• Non-Markovian Majority-Vote model
• Analytical and numerical treatment of continuous ageing in the voter model
• Opinion formation on social networks with algorithmic bias: Dynamics and bias imbalance
• Noisy kinetic-exchange opinion model with aging
• Approach to consensus in models of continuous-opinion dynamics: a study inspired by the physics of granular gases
• Universality of noise-induced transitions in nonlinear voter models
• Polarization-induced stress in the noisy voter model
• Impact of memory and bias in kinetic exchange opinion models on random networks