The thermodynamic arrow is often linked to the cosmological arrow of time, because it is ultimately about the boundary conditions of the early universe. According to the Big Bang theory, the Universe was initially very hot with energy distributed uniformly. For a system in which gravity is important, such as the universe, this is a low-entropy state (compared to a high-entropy state of having all matter collapsed into black holes, a state to which the system may eventually evolve).As the Universe grows, its temperature drops, which leaves less energy available to perform useful work in the future than was available in the past. Additionally, perturbations in the energy density grow (eventually forming galaxies and stars). Thus the Universe itself has a well-defined thermodynamic arrow of time. But this does not address the question of why the initial state of the universe was that of low entropy. If cosmic expansion were to halt and reverse due to gravity, the temperature of the Universe would once again grow hotter, but its entropy would also continue to increase due to the continued growth of perturbations and the eventual black hole formation,[2] until the latter stages of the Big Crunch when entropy would be lower than now.

The genuinely cogent worry is not that the early Universe was in a high entropy state, nor that it had higher entropy than the present Universe, but that it is apparently in thermal equilibrium, and hence in the maximum-entropy state available to it; this, it would seem, is incompatible with the fact that the present-day Universe is not in thermal equilibrium. Let us call this the Initial State Problem.

There is a proposed approach to this problem which has become extremely popular in the literature on the foundations of statistical mechanics. Its claim: the assumption that uniformity equates to high entropy ignores the existence of gravitation. Given the attractive nature of gravity (it is claimed), a uniform state is actually much lower-entropy than a much more clumped state. Various forms of argument are given for this; frequently, it is argued that when attractive long-range forces are present, matter has a higher entropy when highly concentrated than when diffuse, and black holes (with their well-known stratospheric entropies) are exhibited as a limiting case

Nevertheless, we have a rough idea of how entropy evolves . In situations where gravity is negligible, such as a cup of coffee, a uniform distribution of particles has a high entropy. This condition is a state of equilibrium. Even when particles reshuffle themselves, they are already so thoroughly mixed that nothing much seems to happen macroscopically. But if gravity is important and the volume is fixed, a smooth distribution has relatively low entropy. In this case, the system is very far from equilibrium. Gravity causes particles to clump into stars and galaxies, and entropy increases noticeably— consistent with the second law. Indeed, if we want to maximize the entropy of a volume when gravity is active, we know what we will get: a black hole.