Notes on Deterministic and Stochastic Approaches in Electromagnetic Information Theory

This paper investigates the relationship between the Number of Degrees of Freedom ($N_{\rm DoF}$) of the field in deterministic and stochastic source models within Electromagnetic Information Theory (EIT). Our findings demonstrate a fundamental connection between these two approaches. Specifically, we show that a deterministic model and a stochastic model with a spatially incoherent and homogeneous source yield not only the same $N_{\rm DoF}$ but also identical eigenvalues and basis functions for field representation. This key equivalence not only explains the effectiveness of deterministic approaches in EIT but also corroborates the use of classical electromagnetic methods within this new discipline.