Our objective here is the study of the noise-assisted generation of magnetic flux in a collection of identical mesoscopic cylinders which are coupled via mutual inductances. With thermal (Johnson--Nyquist)-fluctuations acting at finite temperature, the system can be modeled in terms of a set of Langevin equations with a corresponding Fokker--Planck equation. In the limit of infinitely many constituents, the steady-state of the system is determined by a mean-field-like, nonlinear Fokker--Planck equation. The rich complexity of the generated average flux through each cylinder and its characteristic fluctuations are investigated as a function of various parameters such as the temperature, the coupling strength and an externally applied, uniform magnetic field.

PACS numbers: 64.60.Cn, 05.10.Gg, 73.23.--b