## 1 Introduction
In summary, the journey of memristor development from its theoretical inception by [PERSON] in 1971 to its physical realization in 2008 has marked a transformative era in electronic and optoelectronic technologies. The resistive switching mechanism, coupled with advancements in materials science, has propelled memristive devices into the forefront of nonvolatile memory, analog and digital processing circuits, and neuromorphic systems. The evolution from electronic to optoelectronic memristors has expanded their versatility,enabling direct interaction with optical signals and fostering applications in neuromorphic computing, as demonstrated by [PERSON] et al. The emergence of optical memristors, characterized by high bandwidth and energy efficiency, has unlocked new potentials for on-chip integrated photonic circuits, addressing challenges in achieving nonvolatility. Despite their limitations in temperature-related applications, the unique properties of light harnessed by optical memristors position them as key players in next-generation computing technologies. From face recognition tasks to the experimental quantum-optical memristor, these devices exemplify the continuous innovation and exploration within the realm of memristive phenomena, promising a dynamic future where they play pivotal roles in advancing computing capabilities and contributing to the ever-evolving landscape of technology. Despite a notable surge in research focusing on previously discussed memristors, it is noteworthy that thermal memristors have received comparatively limited attention, as depicted in Figure 1b, and emphasized by [PERSON] in his work [23]. [PERSON], through a theoretical framework, put forth the concept of a thermal memristor and explored its potential applications in neuromorphic networks [23]. Notably, the critical characteristic of a thermal memristor, the pinched Lissajous curve (depicting the heat flux-temperature difference relationship), was not demonstrated in his work. Building upon this, [PERSON] et al. addressed this gap in the research landscape two years later [24]. They provided a theoretical framework supporting the existence of a thermal memristor by showcasing the Lissajous curve based on the intrinsic thermal conductivity of phase-change materials (PCMs) [25]. In their study, the thermal memristor's operation was driven by the hysteretic metal-insulator phase transition of vanadium dioxide (VO\({}_{2}\)) near room temperature [26; 27]. This work contributes significantly to the emerging field of thermal memristors, shedding light on their potential applications and providing a more comprehensive understanding of their behavior. While conductive memristors offer several advantages, their performance is constrained by the existence of interface thermal resistances and the relatively slower speeds of the involved phonons and electrons, typically three orders of magnitude smaller than those of photons. To address these limitations, a promising solution lies in the adoption of a radiative thermal memristor with contactless terminals. This approach holds the potential to overcome the hurdles associated with thermal resistances and the comparatively slower dynamics of phonons and electrons, presenting a viable alternative to enhance the overall performance of memristive devices. [PERSON] et al. presented a theoretical model of a radiative thermal memristor in their work [28]. The system is composed of a vanadium dioxide (VO\({}_{2}\)) phase-change material (PCM) and a blackbody that exchange thermal radiation through a vacuum gap in the far-field regime. The theoretical model relies on the emissivity of the surfaces involved in radiative heat transfer and the thermal hysteresis of the VO\({}_{2}\) phase transition. In their demonstration, [PERSON] et al. showed that the Lissajous curve of the system produces a memristance (M). The temperature variations in a closed loop are determined by the hysteresis width of VO\({}_{2}\) and the ratio of emissivities for its insulating and metallic phases.