Condensation and Metastable Behavior of Non-reversible Inclusion Processes

Metastability of Blume-Capel model with zero chemical potential and zero external field

“…Extensive research has been carried out on metastability since the mid-20th century, ranging from the early works [6,7] to recently developed methodologies [1][2][3]17]. As a result, various stochastic systems have been known to exhibit such behavior; important examples include the small random perturbations of dynamical systems [6,18,25], condensing interacting particle systems [12,13,17,26], and ferromagnetic spin systems at low temperatures [4,10,15,16,21,23]. We refer to the classic monographs [5,24] for detailed explanation on the history and perspectives regarding the phenomenon of metastability.…”

Second Time Scale of the Metastability of Reversible Inclusion Processes

“…[7] reported a result on the metastable behavior for reversible inclusion processes. Moreover, in [19], Seo and the author of the current paper worked on the setting of general non-reversible inclusion processes.…”

“…In contrast, the metastability of non-reversible inclusion processes occurs in an entirely different manner. It has been established in [19] that there are two types of first time scales in the system, namely 1/d N if the limit dynamics is symmetric (and thus generalizes the reversible case), and 1/(d N N ) if it is asymmetric. Succeeding time scales are entirely unidentified and deserve extensive future research.…”

“…Succeeding time scales are entirely unidentified and deserve extensive future research. Further information is provided in [19,Theorems 3.10 and 3.12].…”

“…In this case, yet another type of condensation and metastability is detected. [9] provides formulation and computational data, while [11] reports various condensation results depending on the behavior of d N , and [19,Theorems 3.21,3.22,and 3.23] present the general result of metastability on the torus.…”