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you are right back where you were.
But the stirring quickly degenerates into the same random motion as if it were not stirred.
And in reality no more work is done by the piston whether or not shock waves are produced. As a transient process, the energy may be divided differently than before with some of the energy in shock waves and less in T, but when the shock wave is dissipated you are right back where you were.
Bob at PC