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The Brownian dynamics is examined within the scope of biomolecular electronics, molecular processing and fluidic molecular device physics. With the emphasis on biomimetics to discover novel paradigms, the role of Brownian motion in the cells and fluidic electronic devices is studied. We examine the motion of ions and biomolecules that exhibit directional propagation in stochastic fields. This fundamental concept is utilized to discover and synthesize synthetic molecular electronic devices/modules. The performed research is of a great significance in biomolecular and bio-inspired molecular electronics. In addition to basic results, heterogeneous simulation and data-intensive analysis are carried. We analyze the propagation of information carriers (molecules and ions) in the cells and synthetic molecular devices. The device/module performance is assessed from signal processing viewpoints. The basic theory is developed and verified.