NONEXISTENCE OF IRREVERSIBLE PROCESSES IN COMPACT SPACE–TIME

Abstract

It is shown that if physical space–time were truly compact there would only be of the order-of-one solutions to the classical field equations with a weighting to be explained. But that would not allow any peculiar choice of initial conditions that could support a nontrivial second law of thermodynamics. We present a no-go theorem: irreversible processes would be extremely unlikely to occur for the almost unique solution for the intrinsically compact space–time world, although irreversible processes are well known to occur in general. What we assume here — the compact space–time — is that universe could not exist eternally. In other word if universe stays on forever (i.e. noncompact in time direction) our no-go theorem is not applicable.