Thermodynamics features of quantum memristors

Quantum memristors are devices holding great promise as a platform for quantum computation, especially when considering neuromorphic quantum computation. These devices are characterized by their non-Markovian behaviour. Here we describe such devices as a kind of thermodynamic engine operated by a Maxwell demon, but, instead of work, the output of such engine is non-Markovianity (time correlations), that can be employed to power quantum computation, for instance. We are therefore able to provide a thermodynamic description of this device, thus paving the way for establishing the limits of its applicaility for information processing.