Second Law based definition of passivity/activity of devices

Recently, our efforts to clarify the old question, if a memristor is a passive or active device [1], triggered debates between engineers, who have had advanced definitions of passivity/activity of devices, and physicists with significantly different views about this seemingly simple question. This debate triggered our efforts to test the well-known engineering concepts about passivity/activity in a deeper way, challenging them by statistical physics. It is shown that the advanced engineering definition of passivity/activity of devices is self-contradictory when a thermodynamical system executing Johnson-Nyquist noise is present. A new, statistical physical, self-consistent definition based on the Second Law of Thermodynamics is introduced. It is also shown that, in a system with uniform temperature distribution, any rectifier circuitry that can rectify thermal noise must contain an active circuit element, according to both the engineering and statistical physical definitions.