Regarding the problem of the low entropy state at the big bang, people like Penrose, Page, Carroll etc. do not think that inflation solves the problem. I recently read and listen to Seth Lloyd and his explanations about the beginning of the universe from the point of view of entropy as information. In my layman-interpretation of Lloyd's proposal, the universe at the beginning (at the beginning of inflation) is small and very simple, containing only a few qbits of information. Being small, the energy it contains is also little so it doesn't need to be in a very uncommon low entropy configuration. In fact at this moment the universe is not smooth so almost all energy it contains must be used to describe the system, implying a high entropy state. During inflation, the inflation energy grows as potential gravitational energy grows. Being the universe still almost empty of particles and matter, and as it become bigger and thus smoother and ordered, the rise in energy is more substantial compared to the rise in the information needed to describe the system. So entropy is lower (the system has a lot of free energy not required to describe the system). This is the core of my question. It is possible that the process i just described leads to a temporary lowering of the entropy of the universe, untill reheating populate the universe with particles and the entropy goes high again, but, coming from a lower state, the time-asymmetry and the arrow of time emerge, and the subsequent interaction of particles with the gravitational field and the quantum fluctuations in energy density (cmb) give rises to galaxies, and all kind of lower entropy systems? I know the first law of thermodynamics states that energy is conserved, but, as in inflation, the positive energy is balanced by the negative gravitational energy. I also know the second law of thermodynamics, that says that entropy has to increase, both in the future as in the past. But that is a law based on statistics and probabilities, so it should be possible, given a process like the one i described above, to reach a lower entropy state from a higher one. I also know about Maxwell's demon, so i know that any attempt to do this NOW will result in a process that overall requires more information than it can produce, in the end increasing the entropy of the whole system. But conditions at the beginning of inflation were different from now, as i described above. Could not be it that a small system very simple to describe, injected with energy by an inflation field coupled with a gravitational field (preserving the first law of thermodynamics), would result in a decrease in entropy (interpreting entropy as the ratio between energy and the amount of information required to describe the system)?