Collective behavior of coupled mesoscopic cylinders

We address the objective of the generation of finite magnetic flux out of unbiased thermal current fluctuations in a collection of identical mesoscopic cylinders which are coupled via mutual inductances. The influence of thermal Nyquist fluctuations are described in terms of a set of Langevin equations or a corresponding Fokker–Planck equation, respectively. In the limit of infinitely many constituents, the steadystate of the system is determined by an effective, nonlinear Fokker–Planck equation. The system exhibits in this thermodynamic limit a second-order phase transition: the average flux through each cylinder changes continuously from zero to non-zero value and the phase diagram depicts a critical line.