Will entropy decrease if the Universe recollapses?

Abstract

Hawking has proposed a wave function for the Universe which is CPT invariant and which appears to be dominated by smooth configurations when the Universe is small but by irregular configurations when large. He has argued that this behavior connects the thermodynamic arrow of time with the cosmological arrow. Here it is pointed out that although the total wave function may have the properties Hawking describes, an individual WKB component of it that is classically observable generically will not be CPT invariant and will not have its thermodynamic arrow of time reverse if it enters a recollapsing phase.