Keywords

1 Summary

In this book, we present twenty theories of theoretical thermotics, divided into two parts, i.e., inside and outside metamaterials. The major difference is the characteristic length. There is an explicit characteristic length in heat transfer for those fourteen theories inside metamaterials, (much) larger than the structural unit size. The other six theories are beyond the scope of characteristic lengths (outside metamaterials). Therefore, theoretical thermotics can guide the design of both metamaterial-based and metamaterial-free phenomena and functions. Theoretical thermotics is not limited to theories, and we also present simulations and experiments for mutual confirmation. Practical applications, such as invisibility, camouflage, nonreciprocity, and bistability, are also demonstrated. These results may provide insights into novel and advanced thermal regulation.

2 Outlook

Although theoretical thermotics has made significant progress during the last decade, many key scientific problems remain explored. For example, nonreciprocal heat transfer is a recent focus. On the one hand, spatiotemporal modulation becomes an intriguing mechanism for achieving diffusive nonreciprocity [1,2,3,4] due to the advectionlike effect. On the other hand, an isolated thermal system with mass conservation prohibits the advectionlike effect [5]. Therefore, it becomes particularly elusive whether spatiotemporal modulation can yield nonreciprocity in heat transfer. The answer may lie in transient heat transfer due to the novel mechanism of Willis coupling [6]. Therefore, it is promising to reveal more asymmetric diffusion mechanisms in transient heat transfer, especially based on wavelike temperature fields. Moreover, topological heat transfer is another research focus. Many pioneering works related to thermal geometric phases [7], thermal Su-Schrieffer-Heeger models [8,9,10,11], thermal edge states [12], thermal skin effects [13, 14], and thermal topological transitions [15,16,17] have been proposed. However, compared with topological wave propagation [18, 19], the related research in heat transfer is just getting started, and much profound physics remains studied, such as high-order thermal topology.

Theoretical thermotics mainly includes fundamental theories, but we should develop more practical applications. In particular, heat regulation is a critical issue in daily life and industrial production. Hence, theoretical thermotics also needs to focus on practical problems and provide guidance for heat regulation. For example, with the miniaturization of chips, heat dissipation becomes increasingly significant for device protection. Moreover, cooling with energy savings is also a crucial problem, and passive radiative cooling has become a powerful tool [20,21,22]. Therefore, theoretical thermotics should also play a role in solving these urgent requirements.

Last but not least, though theoretical thermotics aims to solve thermal problems, its influence should exceed thermotics. Since heat transfer is a branch of diffusion systems, the research paradigms of theoretical thermotics can also be extended to other diffusive systems, such as particle and plasma diffusions, thereby enriching the means of diffusion regulation. Furthermore, could theoretical thermotics inspire the research in wave systems? This question is very challenging but also very rewarding. In fact, a considerable part of the existing content of theoretical thermotics is inspired by the related research in wave systems, such as from transformation optics [23, 24] to transformation thermotics [25, 26] and from photonic crystals to thermal crystals [27]. It is worth pondering how to make theoretical thermotics more enlightening and impact non-thermal fields. For example, the pioneering attempt to control multiphysical fields originates from theoretical thermotics (thermal plus DC fields [28]), which has been extended to wave control, such as electromagnetic, acoustic, plus water waves [29] and magnetic plus acoustic fields [30, 31]. More research could be expected to extend the paradigms of theoretical thermotics to other non-thermal fields.

Undoubtedly, the future of theoretical thermotics is promising, whether in terms of fundamental research, practical applications, or potential impacts.