Memristors: a thermodynamics-based proposal for the constitutive relations

The concept of memristor proposed by Leon Chua in 1971 connects four fundamental electrical quantities: charge, current, voltage and magnetic flux, through six relations, one of them relating magnetic flux to electric charge. An experimentally device showing the properties predicted by Chua was proposed by Strukov et al. in 2008, together with a mathematical model incorporating a variable of for taking into account the memory effect. Despite some critics, this device has gain attention from both, theoretical and practical points of view, mainly regarding its applications as a novel type of non-volatile memories, to neuromorphic systems and as hardware for artificial intelligence. Since then, a whole periodic table of circuit elements relating electrical variables and their derivatives has been proposed, giving rise to meminductance, memcapacitance, among others. A problem that emerges from Chua’s definition of memristance as differential relation between flux is the ambiguity between Memristance and Resistance. Some other inconsistencies found in the original quadrangular picture for the electrical relations can be tackled by a triangular periodic table, considering only two fundamental quantities, charge and magnetic flux (Wang, 2013). The fundamental elements relate two fundamental quantities or a fundamental quantity and the derivative of the other. In this picture, the fundamental elements would be the memristance, the capacitance and the inductance, but not the resistance. In this work by exploring energy arguments and using Legendre transformations we show that, based on a triangle periodic table, it is possible to construct a thermodynamics-based picture of the theoretical background for memristivity. Moreover, from this picture the resistance emerges as a particular case of constant memristance, and the origin of the state variable can be theoretically justified.               

F. Z. Wang, IEEE Trans. on Circuit Theory, 60(3), p. 616-622, 2013.