2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/182033A new method is presented for determining event-by-event fluctuations of elliptic flow, $v_2$, using first-order event planes. By studying the event-by-event distributions of $v_2$ observables and first-order event-plane observables, average flow $\avg{v_2}$ and event-by-event flow fluctuations can be separately determined, making appropriate allowance for the effects of finite multiplicity and non-flow. The method has been tested with Monte Carlo simulations. The connection between flow fluctuations and fluctuations of the initial-state participant eccentricity is discussed.5 pages, 2 figures. Submitted to Phys. Rev. C. The discussions about the assumptions in this paper have been added, as required by the refereeNuclear Experimenttext