The generalized second law (nonequilibrium maximum work formulation) is derived for a simple chaotic system. We consider a probability density, prepared in the far past, which weakly converges to an invariant density due to the mixing property. The generalized second law is then rewritten for an initial invariant density. Gibbs-Shannon entropy is constant in time, but the invariant density has a greater entropy than the prepared density. The maximum work is reduced due to the greater entropy of the invariant density. If and only if the invariant density is a canonical distribution, work is not extractable by any cyclic operation. This gives us the unique equilibrium state. Our argument is extended for a power invariant density such as the Tsallis distribution. On the basis of the Tsallis entropy, the maximum q-work formulation is derived. If and only if the invariant density is a Tsallis distribution, the q-work is no longer extractable by any cyclic operation.