  The entropy of a thermally isolated system should not decrease after a quench
or external driving. For a classical system following Hamiltonian dynamics, we
show how this statement emerges for a large system in the sense that the
extensive part of the entropy change does not become negative. However, for any
finite system and small driving, the mean entropy change can well be negative.
We derive these results using as micro-canonical entropy a variant recently
introduced by Swendsen and co-workers called "canonical". This canonical
entropy is the one of a canonical ensemble with the corresponding mean energy.
As we show by refining the micro-canonical Crooks relation, the same results
hold true for the two more conventional choices of micro-canonical entropy
given either by the area of a constant energy shell, the Boltzmann entropy, or
the volume underneath it, the Gibbs volume entropy. These results are
exemplified with quenched $N$-dimensional harmonic oscillators.
