You can implement a microscopic bit-reversible molecular dynamics (so there is no round-off error), that is in contact with a thermostat (noise source). You run the simulation for a given length of time, then reverse the simulation. The reverse simulation will track the original system back in time for a little while, then suddenly run away. The length of time it stays with the original system depends on the Liapunov exponents of the system.
This is well-documented in the literature. In fact, if you have a MD code you can do it and see it for yourself. So molecular dynamics simulations with a thermostat is inherently irreversible.
I don't care what your physics models tell you. In real life all processes happen in an environment that is similar to a thermostat. So most of these processes are also irreversible.