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

Peralta, Antonio F.;Khalil, Nagi;Toral, Raul
Journal of Statistical Mechanics 2020, 024004 (2020)

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.

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