Non-existence of Irreversible Processes in Compact Space Time

TL;DR

This paper proves that in a truly compact spacetime, the likelihood of irreversible processes like entropy increase is virtually zero, challenging the possibility of eternal universe models with non-trivial thermodynamics.

Contribution

It presents a no-go theorem showing that compact spacetime geometries cannot support the typical irreversible processes observed in nature.

Findings

Only about one classical solution exists in compact spacetime.

Irreversible processes are extremely unlikely in such a universe.

Compact spacetime excludes eternal universe models.

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 non-trivial 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 here assume -- compact space time -- excludes that universe could exist eternally.