I guess this question is more about definition than about any physical principle. Can a given physical system (or can there be a physical system) admit microstates that have identical macroscopic variables, but that evolve into states with different macroscopic variables?
I would think it is obvious that something like this can happen, think of a chaotic system, which may be in a state that is macroscopically indistinguishable from one that will remain stable, but that after some time evolves into a system with e.g. large macroscopic local pressure differences, due to arbitrarily small changes in the microstate (and you could set this up in such a way that you get into a new equilibrium state).
The reason why this might be a question of definition is that two ways in which the answer could be "no" would be:
- by saying that microstates that evolve into different macrostates were not indistinguishable to begin with
- by saying that a system that can get out of equilibrium was not in equilibrium to begin with.
Since this knowledge can not be inferred from any macroscopic information at this moment in time (or possibly even any information about the system), these solutions do not seem to be very satisfactory, but maybe I am mistaken.
In any case, I am interested in the answer to the question "Can indistinguishable microstates evolve into different macroscopic states?"