I don’t know if GR or some cosmological thing (inflation) breaks reversibility. But classical and quantum mechanics are both reversible. So I would say that all of the lowest-level processes used by human beings are reversible. (Although of course thermodynamics does the normal counter-intuitive thing where the reversibility of the underlying steps is the reason why the overall process is, for all practical purposes, irreversible.)
I don’t know if GR or some cosmological thing (inflation) breaks reversibility. But classical and quantum mechanics are both reversible. So I would say that all of the lowest-level processes used by human beings are reversible. (Although of course thermodynamics does the normal counter-intuitive thing where the reversibility of the underlying steps is the reason why the overall process is, for all practical purposes, irreversible.)
This paper looks at mutual information (which I think relates to the cross entropy you mention), and how it connects to reversibility and entropy. https://bayes.wustl.edu/etj/articles/gibbs.vs.boltzmann.pdf
(Aside, their is no way that whoever maintains the website hosting that paper and the LW community don’t overlap. The mutual information is too high.)