Free expansion and the Kelvin/Clausius statements of the 2nd law It is perfectly possible to have a thermally-isolated gas expanding freely into a vacuum, as in the Joule expansion. And yet, if we were to film the process and then play it back in reverse, we witness a process that is never observed in nature.
Is it possible to explain the impossibility of the backwards process by showing that it would violate either the Kelvin or the Clausius statements of the 2nd law of thermodynamics?
 A: I found a very well-phrased answer to this exact question in Planck's treatise on thermodynamics.
If the reverse process of a free expansion were possible, you could arrange the following cycle: allow a gas to expand isothermally against some pressure, consuming a quantity of heat then delivering all of it as work to the surroundings. Then reverse the process using the "reverse" free expansion, for which q=0 and w=0. Then lather rinse and repeat, and you've got an engine converting heat fully into work with no other changes, violating the Kelvin statement of the second law.
A: I believe you can only say it is statistically "impossible" due to the bulky nature of this experiments. If the observation of such phenomenon goes to small scales where statistical fluctuation comes into play and you may want to refer to Crook's Fluctuation theorem. The fluctuation contains certain actions in the system to "violate" the 2nd law, but the 2nd law is still statistically valid if you average over all actions.
Please refer to the classical paper by G.E.Grooks:
The Entropy Production Fluctuation Theorem and the Nonequilibrium Work Relation for Free Energy Differences
Also please correct me if you can any mistakes in my answer. 
A: If a spontaneous reversal of free expansion of a thermally isolated gas were possible then one could place a piston in front of the expanding gas to get net work out of it in cycles (we can design a mechanism that takes out work both during expansion and its reversal). This net work may be utilized to drive heat from colder to hotter body. This violates Clausius statement because the process, considered as a whole, is spontaneous.
