University of Luxembourg
In this talk I’ll briefly introduce the notion of stochastic dynamics within the framework of a classical master equation. The dynamics will be governed by an irreducible, discrete, and autonomous generator giving rise to a unique stationary state. On the other hand, synchronization is the emergence of a collective behavior that leads to stable oscillations. Thus, naively one expects that irreducible autonomous generator and the emergence of synchronization (stable oscillations) is incompatible. I’ll resolve this apparent paradox via the idea of long-lived quasi-stationary and metastable states in two concrete examples. I’ll show via extensive numerical analysis of how signatures of these long-lived states are encoded in the spectrum and moreover how these states resemble the mean-field dynamics, that displays synchronization. If time permits, I’ll touch upon how it is only the existence of metastable states that permits thermodynamic consistency, whereas the quasi-stationary states are incompatible with a thermodynamic description.