Any system that is very low complexity and also deterministic (or has a deterministic interpretation, i.e. many worlds), ought to exhibit time reversal pretty easily. I.e. common reactions whose reversal occurs often. No?

Are there any non-reversible reactions at any level of physics that don't have a statistics component to them?

This sounds like a purely mathematical output that hasnt been observed yet. Interesting, but like string theory, its pretty much math manipulation until you get what you want.

It's very different than string theory.

In string theory, the proposal is to change the Laws of Physics. Each particle is a small string instead of a point, each point of the universe is actually something more complicated, like a circle in a new dimension. But we are not sure if each point must be replaced by a circle or a sphere, or a torus/donut or whatever. In string theory the proposal is to change the laws of physics, but there are many versions that are possible and currently we can make no experiment to be sure any of them is good.

In this paper they don't propose to change the Laws of Physics. They use the current laws to get a a theoretical result. They make a theoretical "experiment" and calculate the expected outcome. The "interesting" part is how they interpret the result as a weird time flow. As Nevermark says, in small system it's expected that sometimes evolve in unexpected ways. For me the research article looks like an overhyped interpretation.

Time is just Hyman's perception.