A fundamental insight into the expanding universe is its isentropic nature, indicating that the overall entropy or randomness of the cosmos remains unchanged. This concept can be clarified through three primary consequences. Firstly, the entropy of relativistic particles, like photons, predicted gravitons, and neutrinos, remains constant despite the universe's expansion. This constancy arises because entropy is directly tied to the number of these particles, denoted as 𝙉, and this count stays the same as the universe expands. Whether considering the past or the future, the quantity of these particles remains consistent.
Secondly, the entropy density of photons or any other relativistic particle, denoted as 𝙨 remains constant. To demonstrate this, we can rely on the relationship that the entropy density 𝙨 is proportional to the cube of its temperature{𝘀 ~ 𝗧^𝟯}. As the temperature of the universe is inversely related to its size, meaning the universe was much hotter when it was smaller, as particles lose energy with the expansion of the universe {λ~𝙖} and {𝙏~1/𝙖}, where 𝙖 being scale factor. The volume 𝙑 of the system considered for this reference measurement is {𝙑~ 𝙖^3}. Combining all these factors, the entropy S of the photons in any volume expanding with the expansion of the universe is:
The combined effect is a constant entropy for photons in any expanding volume, illustrating the isentropic nature of the universe on a larger scale.
Thirdly, the expansion of the universe does not increase the rate at which mass accretes into black holes. Thus, expansion does not increase the entropy of the universe. The adiabatic expansion of an ideal gas into empty space is irreversible, and thus entropy, which is proportional to volume, increases. This is not the case in cosmology because the CMB photons are not expanding into empty space.
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