Memristor Equations: Incomplete Physics and Undefined Passivity/Activity

In his seminal paper, Chua presented a fundamental physical claim by introducing the memristor, "The missing circuit element". The memristor equations originally supposed to represent a passive circuit element because, with active circuitry, arbitrary elements can be realized without limitations. Therefore, if the memristor equations do not guarantee that the circuit element can be realized by a passive system, the fundamental physics claim about the memristor as "missing circuit element" loses all its weight. Recent work of Chua indicates that certain type of memristor features may imply an active device. To make the question more physical, we incorporate thermodynamics into the study of this question. By using the Second Law of Thermodynamics and thermal noise, we prove that the memristor model represents an active device for an infinitely large number of cases of memristor functions M; particularly, any power function with an odd power exponent, including the situation of linear M. This situation implies rectifier features and, according to the Brillouin paradox, driving a passive circuit element of rectifying feature with thermal noise would allow the construction of perpetual motion machines. The memristor equations require an active device at infinitely many situations.