Truncation and closure of circular cumulant series
This brief communication is devoted to the concept of cumulant decomposition as an universal tool of statistical physics. Since the cumulant series is infinite, the question of truncation of the cumulant expansions and constructing a finite closure for the equations of the macroscopic system dynamics are of particular interest. For variables on the real line, this issue is quite well elaborated. However, the situation is significantly different for the phase variable on the circumference. A concept of “circular” cumulants was recently introduced for describing the dynamics of such systems. Although truncation of circular cumulant expansions, except for the Ott-Antonsen case, is forbidden, taking into account corrections introduced by higher-order cumulants can significantly improve representation of the dynamics of the analyzed system.