The infinitesimal environmental dust as a photonic bath at infinity

In far-field thermal radiation, electromagnetic waves emitted by an object propagate to infinity, requiring the far region to be modeled as an effective thermal bath. This bath was proposed as infinitesimal environmental "dust", but explicit calculations with such distributed dust involve integrals over infinite space that are difficult to evaluate. In this work, we map this environmental dust to a photonic bath at infinity within the nonequilibrium photonic Green's function formalism. By explicitly evaluating the spatial integral over the dust, we show that its contribution reduces to a simple local self-energy, for which we derive analytical expressions for both three-dimensional objects and planar systems. We further demonstrate that the bath behaves as a black body and clarify its role in far-field thermal radiation. An alternative derivation based on the surface Green's function framework is also provided in Appendix B, demonstrating the theoretical consistency of the results without invoking the dust model. The photonic bath at infinity provides a convenient framework for both analytical and numerical calculations in far-field thermal radiation.