Compactified Time and likely Entropy -- World Inside Time Machine: Closed Time-like Curve --
arXiv:hep-th/0601048
Abstract
If a macroscopic (random) classical system is put into a random state in phase space, it will of course the most likely have an almost maximal entropy according to second law of thermodynamics. We will show, however, the following theorem: If it is enforced to be periodic with a given period in advance, the distribution of the entropy for the otherwise random state will be much more smoothed out, and the entropy could be very likely much smaller than the maximal one. Even quantum mechanically we can understand that such a lower than maximal entropy is likely. A corollary turns out to be that the entropy in such closed time-like loop worlds remain constant.
22pages, To be published in the Proceedings to the 8th Workshop 'What Comes Beyond the Standard Models', Bled, July 19. - 29., 2005, Slovenia.Bled workshops in physics, Vol.6, No. 2, DMFA-Zaloznistvo, Ljubljana
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