I've been reading about Claude Shannon and Information Theory. I see he is credited with developing the concept of entropy in information theory, which is a measure of the amount of uncertainty or randomness in a system. Do you ever wonder how his concepts might apply to the predicted red giant phase of the Sun in about 5 billion years? Here are a few thoughts that don't include much uncertainty or randomness -
In about 5 billion years the Sun is supposed to expand into a red giant and engulf Mercury and Venus and possibly Earth (the expansion would probably make Earth uninhabitable in less than 1 billion years). It's entirely possible that there may not even be a red giant phase for the Sun. This relies on entropy being looked at from another angle - with the apparent randomness in quantum and cosmic processes obeying Chaos theory, in which there's a hidden order behind apparent randomness. Expansion to a Red Giant could then be described with the Information Theory vital to the Internet, mathematics, deep space, etc. In information theory, entropy is defined as a logarithmic measure of the rate of transfer of information. This definition introduces a hidden exactness, removing superficial probability. It suggests it's possible for information to be transmitted to objects, processes, or systems and restore them to a previous state - like refreshing (reloading) a computer screen. Potentially, the Sun could be prevented from becoming a red giant and returned to a previous state in a billion years (or far less) - and repeatedly every billion years - so Earth could remain habitable permanently. Time slows near the speed of light and near intense gravitation. Thus, even if it's never refreshed/reloaded by future Information Technology, our solar system's star will exist far longer than currently predicted.
All this might sound a bit unreal if you're accustomed to think in a purely linear fashion where the future doesn't exist. I'll meet you here again in 5 billion years and we can discuss how wrong I was - or, seemingly impossibly, how correct I was.
"Expansion to a Red Giant could then be described with the Information Theory"
Expansion to a Red Giant IS described with Physics (entropy included). It's irreversible, insofar as while most stars go through a second visit to the red giant phase, their intermediate compact phase (Helium fusing core) is never the same as the previous compact phase (Hydrogen fusing core). You cannot return to the same initial conditions.
It's not that information theory is wrong, it's that it's absolutely peripheral to the physical processes that govern stellar evolution.