Air-breathing animals do not return to breathing water.

No, irreversible is an adjective. The noun could be irreversibility or irreversibleness (both mean that something cannot be undone).

Irreversibility.

Also, something which, once done, cannot be changed, is irrevocable.

Such an equation would represent an ill-posed problem for all positive time (i.e. the solution is not defined). The irreversibility of diffusive processes is closely related to the second law of thermodynamics.

Petr