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The system is not in equilibrium in an irreversible expansion, because unlike in a reversible expansion, the pressure is reduced quickly, allowing the gas to expand and do work on the external pressure. I'm not entirely sure why it is called irreversible though.
I believe it is called irreversible because the large change in volume in a quicker process, makes it difficult to compress the gas/system back to its original volume. In a reversible process the external and system pressures are very close in value at each step, so the change in volume is so small - that the work required to compress the gas back is much easier and more reversible in a sense.
Irreversible means that the direction of expansion/contraction will not be changes by a tiny amount of change in external pressure. For example, if the gas of 1 atm is expanding against an external surrounding of 1 atm, if the outside pressure increases even a little bit, the gas will go from expanding to contracting.
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