I didn't claim I'm going to beat the second law. I said if we believe in current second law definition it seems like we may construct (in theory!) a perpetuum mobile of the second kind which works WITHIN the second law.
What is concerning to some particular example, it's pretty difficult to do because we need to agree what is a truly closed system and find it in nature. The Earth may not be a truly closed system and its extremely difficult to isolate any system from surrounding environment.
But let try. For example there is a Belousov chemical reactions which seem to be oscillation of some chemical solution from one chemical state to another and back.
https://en.wikipedia.org/wiki/Belousov%E2%80%93Zhabotinsky_reaction
I have no idea if such type of oscillations could be truly eternal and non-dissipative. But if they do, let imagine a chemical system which exist in thermodynamic equilibrium with surrounding environment. Such system would be divided in two main parts which experience oscillations between these two parts. When one part of the system transfers from amorphous to crystalline state entropy reduces and it cools down. It shrinks in size and absorbs heat from surrounding environment. The other part of the system in the same time experience opposite transition - it transfers from crystalline to amorphous state, releases heat, increases in size and capable produce some useful work, for example, to push a piston. After work is done heat released to environment. However, entire system constantly draws the same amount of heat from environment as it releases. So, it exist in thermodynamic equilibrium with nature.
If according to second law there could exist some processes which remain total amount of entropy in universe unchanged (I assume that under word "process" they also mean conversion of some type of energy into some kind of a useful work), and we could build some engine which harnesses such type of process, then our ability to perform some useful work should never diminish. And we would have a perpetuum mobile. If our ability to perform work diminishes then it means entropy increases during the process. But the second law doesn't state it is the only outcome possible.
This one article mentions some similar ides (though not necessarily the same).
http://phys.org/news/2014-09-physicists-zero-friction-quantum.html