Generalization of Kirchhoff’s Law: The inherent relations between quantum efficiency and emissivity

Planck’s law of thermal radiation depends on the temperature, \(T\), and the emissivity, \(\epsilon\), which is the coupling of heat to radiation depending on both phonon-electron nonradiative-interactions and electron-photon radiative-interactions. In contrast, absorptivity, \(\alpha\), only depends on the electron-photon radiative-interactions. At thermodynamic equilibrium, nonradiative-interactions are balanced, resulting in Kirchhoff’s law of thermal radiation, \(\epsilon =\alpha\). For non-equilibrium, Quantum efficiency (QE) describes the statistics of photon emission, which like emissivity depends on both radiative and nonradiative interactions. Past generalized Planck’s equation extends Kirchhoff’s law out of equilibrium by scaling the emissivity with the pump-dependent chemical-potential \(\mu\), obscuring the relations between the body properties. Here we theoretically and experimentally demonstrate a prime equation relating these properties in the form of \(\epsilon =\alpha \left(1-QE\right)\). At equilibrium, these relations are reduced to Kirchhoff’s law. Our work lays out the evolution of non-thermal emission with temperature, which is critical for the development of lighting and energy devices.

A Novel Model Concerning the Independence of Emissivity and Absorptivity for Enhancing the Sustainability of Radiant Cooling Technology

Radiant cooling technology is a sustainable technology for improving built environment. The past research only studied the performance (e.g., radiant heat flux) based on Kirchhoff’s law while the accuracy and its reasons were seldom analyzed. In order to study the mechanism deeply, a new model of radiant heat transfer is derived theoretically which considers emissivity and absorptivity independently. This model is validated by the experimental data then applied in a reference case for further analysis. The analyzing methods of sensitivity and relative deviation are performed to investigate the reasons for the errors. The results of sensitivity analysis show that it is about 20% − 40% more sensitive for the emissivity to the heat flux than the absorptivity. Furthermore, the deviation of the heat flux can reach up to 20% when the absorptivity is in the range from 0.4 to 0.9. This deviation is close to the estimated error range of 21.8% in the past studies. Therefore, the discussion based on the theoretical analysis, shows that the errors in past studies are highly due to the oversimplified preconditions for applying Kirchhoff’s law and they ignored the impact of surface absorption. Additionally, the validation in the previous experiments was highly coincidence, since they neglected the key independent tests of the absorptivity and radiant heat flux. Comprehensively, the new model is valuable to provide a more reliable solution for analyzing the radiant heat transfer and for the future design of an independent test of radiant heat flux.

Induced homomorphism: Kirchhoff’s law in photonics

When solving, modeling or reasoning about complex problems, it is usually convenient to use the knowledge of a parallel physical system for representing it. This is the case of lumped-circuit abstraction, which can be used for representing mechanical and acoustic systems, thermal and heat-diffusion problems and in general partial differential equations. Integrated photonic platforms hold the prospective to perform signal processing and analog computing inherently, by mapping into hardware specific operations which relies on the wave-nature of their signals, without trusting on logic gates and digital states like electronics. Here, we argue that in absence of a straightforward parallelism a homomorphism can be induced. We introduce a photonic platform capable of mimicking Kirchhoff’s law in photonics and used as node of a finite difference mesh for solving partial differential equation using monochromatic light in the telecommunication wavelength. Our approach experimentally demonstrates an arbitrary set of boundary conditions, generating a one-shot discrete solution of a Laplace partial differential equation, with an accuracy above 95% with respect to commercial solvers. Our photonic engine can provide a route to achieve chip-scale, fast (10 s of ps), and integrable reprogrammable accelerators for the next generation hybrid high-performance computing. Summary A photonic integrated platform which can mimic Kirchhoff’s law in photonics is used for approximately solve partial differential equations noniteratively using light, with high throughput and low-energy levels.

Metastatic Site Prediction in Breast Cancer using Omics Knowledge Graph and Pattern Mining with Kirchhoff’s Law Traversal

Prediction of metastatic sites from the primary site of origin is a impugn task in breast cancer (BRCA). Multi-dimensionality of such metastatic sites - bone, lung, kidney, and brain, using large-scale multi-dimensional Poly-Omics (Transcriptomics, Proteomics and Metabolomics) data of various type, for example, CNV (Copy number variation), GE (Gene expression), DNA methylation, path-ways, and drugs with clinical associations makes classification of metastasis a multi-faceted challenge. In this paper, we have approached the above problem in three steps; 1) Applied Linked data and semantic web to build Poly-Omics data as knowledge graphs and termed them as cancer decision network; 2) Reduced the dimensionality of data using Graph Pattern Mining and explained gene rewiring in cancer decision network by first time using Kirchhoff’s law for knowledge or any graph traversal; 3) Established ruled based modeling to understand the essential -Omics data from poly-Omics for breast cancer progression 4) Predicted the disease’s metastatic site using Kirchhoff’s knowledge graphs as a hidden layer in the graph convolution neural network(GCNN). The features (genes) extracted by applying Kirchhoff’s law on knowledge graphs are used to predict disease relapse site with 91.9% AUC (Area Under Curve) and performed detailed evaluation against the state-of-the-art approaches. The novelty of our approach is in the creation of RDF knowledge graphs from the poly-omics, such as the drug, disease, target(gene/protein), pathways and application of Kirchhoff’s law on knowledge graph to and the first approach to predict metastatic site from the primary tumor. Further, we have applied the rule-based knowledge graph using graph convolution neural network for metastasis site prediction makes the even classification novel.