  Finite-size systems of Kuramoto model display intricate dynamics, especially
in the presence of multi-stability where both coherent and incoherent states
coexist. We investigate such scenario in globally coupled populations of
Kuramoto phase oscillators with higher-order interactions, and observe that
fluctuations inherent to finite-size systems drives the transition to the
synchronized state occurring before the critical point in the thermodynamic
limit. Using numerical methods, we plot the first exit time distribution of the
magnitude of complex order parameter and obtain numerical transition
probabilities across various system sizes. Further, we extend this study to a
two-population oscillator system, and using velocity field of the associated
order parameters, show the emergence of a new fixed point corresponding to a
partially synchronized state arising due to the finite-size effect which is
absent in the thermodynamics limit.
