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An important extensive property of all systems in thermodynamics, statistical mechanics, and information theory, quantifying their disorder (randomness), i.e., our lack of information about them. It characterizes the degree to which the energy of the system is *not* available to do useful work.
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Information content in black holes
Infomation Content in Black Holes
Your question is essentially (if i interpret it right) can stars with differing sets of initial detailed information--and thus differing information entropy-- converge … cycle, a change in the energy tensor results in a change in entropy corresponding to a change in space-time curvature as measured by the Ricci Tensor. …