Reversing the irreversible: from limit cycles to emergent time symmetry
  In 1979 Penrose hypothesized that the arrows of time are explained by the
hypothesis that the fundamental laws are time irreversible. That is, our
reversible laws, such as the standard model and general relativity are
effective, and emerge from an underlying fundamental theory which is time
irreversible. In Cort\^{e}s and Smolin (2014a, 2014b, 2016) we put forward a
research program aiming at realizing just this. The aim is to find a
fundamental description of physics above the planck scale, based on
irreversible laws, from which will emerge the apparently reversible dynamics we
observe on intermediate scales. Here we continue that program and note that a
class of discrete dynamical systems are known to exhibit this very property:
they have an underlying discrete irreversible evolution, but in the long term
exhibit the properties of a time reversible system, in the form of limit
cycles. We connect this to our original model proposal in Cort\^{e}s and Smolin
(2014a), and show that the behaviours obtained there can be explained in terms
of the same phenomenon: the attraction of the system to a basin of limit
cycles, where the dynamics appears to be time reversible. Further than that, we
show that our original models exhibit the very same feature: the emergence of
quasi-particle excitations obtained in the earlier work in the space-time
description is an expression of the system's convergence to limit cycles when
seen in the causal set description.
