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First of all, you should notice that $h$ in $D(\epsilon)$ is the Planck constant, not a maximum height. The system under consideration has one degree of freedom. Its hamiltonian function has the form you've written. Its phase space is: $x\in(0,\infty)$, $p\in(-\infty,\infty)$. It is known in statistical mechanics, that for such a system the number of states ...


I think Penrose is just trying to use some logic to contradict the common view. My problem with his logic is that the premise is the conclusion. If the entropy increase is caused by the expansion of the universe, then in a universe model where there is a collapsing phase, perhaps entropy will no longer increase and actually start to decrease. I’m not saying ...

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