Memristor equations: incomplete physics and undefined passivity/activity

TL;DR

This paper critically examines the fundamental physics of memristor equations, revealing they are incomplete regarding passivity and can lead to unphysical results, challenging the claim of memristors as a missing circuit element.

Contribution

It demonstrates that current memristor equations are physically incomplete and violate thermodynamic principles, suggesting the need for more comprehensive models including fluctuation dissipation theory.

Findings

Memristor equations can violate the Second Law of thermodynamics.

Current models are incomplete regarding passivity and activity.

Memristor physics requires incorporation of thermodynamics and fluctuation dissipation theory.

Abstract

In his seminal paper, Chua presented a fundamental physical claim by introducing the memristor, "The missing circuit element". The memristor equations were 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. The question of passivity/activity belongs to physics thus we incorporate thermodynamics into the study of this problem. We show that the memristor equations are physically incomplete regarding the problem of passivity/activity. As a consequence, the claim that the present memristor functions describe a passive device lead to unphysical results, such as violating the Second Law of thermodynamics, in infinitely large number of cases. The seminal memristor equations cannot introduce a new physical circuit element without making the model more physical such as providing the Fluctuation Dissipation Theory of memristors.