  In this work we bring out the existence of a novel kind of synchronization
associated to the size of a complex system. A dichotomic random jump process
associated to the dynamics of an externally driven stochastic system with $N$
coupled units is constructed. We define an output frequency and phase diffusion
coefficient. System size synchronization occurs when the average output
frequency is locked to the external one and the average phase diffusion
coefficient shows a very deep minimum for a range of system sizes. Analytical
and numerical procedures are introduced to study the phenomenon, and the
results describe successfully the existence of system size synchronization.
