G: Choice of Description Level as the Second Factor of Entropy Fundamental Concept

In the standard definition, Boltzmann entropy S = k ln Omega is presented as a function of a single parameter Omega – the number of available microstates. However, this definition implicitly assumes that Omega is defined with a fixed description of the system. This article shows that entropy is a function of two factors: the number of available microstates (Omega) and the choice of description level G (the degree of coarse‑graining). Formally: S = f(Omega, G). One and the same physical system (for example, a gas in a container) can have different entropy values at different G – from macroscopic (only temperature, pressure, volume) to microscopic (coordinates and momenta of each molecule). All values are correct, but for different tasks. The choice of G is not arbitrary: it is determined by the research task, the available information, the instrumental capabilities, and the fundamental quantum limit (the Heisenberg uncertainty principle). Historically, the idea of the dependence of entropy on coarse‑graining goes back to Gibbs (fine‑grained vs coarse‑grained entropy), Jaynes (the principle of maximum entropy and its paradox), and von Neumann (observer entropy). Contemporary academic physics develops this idea within the framework of "observational entropy" (Šafránek, Aguirre, Deutsch, 2020–2024), giving it a mathematically rigorous formulation. Classical examples (a gas in a container, black hole entropy) illustrate the dependence of entropy on G. Recognising the role of G does not abolish the second law of thermodynamics, but makes its application more conscious. The article is foundational in nature and is addressed to physicists and methodologists of science.