The Second Factor of Entropy: The Choice of the Level of Description (G)

This paper proposes to view entropy not as an absolute property of a system, but as a function of two factors: the number of accessible microstates (Ω) and the choice of the level of description (G), also referred to as the degree of coarse‑graining. The standard Boltzmann formula S = k_B ln Ω implicitly assumes a fixed G, which leads to incompleteness: the same physical body can have different entropy values depending on which degrees of freedom we take into account. A rigorous definition of G is introduced — it is the observer‘s decision about which degrees of freedom are considered essential and which are “lumped together” into a macrostate. A classification of G is provided according to the scale of description (from macro to supermicro), the goal of the study (functional, diagnostic, scientific), the available information, and psychosocial factors (biases, mainstream pressure, motivation). The choice of G depends on the researcher’s task, instrumental capabilities, cognitive limitations, and subjective factors that can distort scientific conclusions (e.g., data fitting). Illustrative examples are given: the same coin under different G yields different entropy; gas in a container; a book on a table; the entropy of a collapsar (black hole) under an extremely macroscopic G (only the horizon area) and under alternative G. It is shown that “black hole entropy” is not absolute but depends on the chosen level of description. Understanding G as an active choice of the observer allows us to correctly interpret different entropy values of the same object, avoid pseudo‑paradoxes, and recognize entropy as a working tool rather than a mystical entity.