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On the validity of the second law of thermodynamics in the mesoscopic realm

We describe the entropy evolution of an isolated thermodynamical system, consisting of an ideal gas contained in an adiabatic cylinder partitioned by a movable frictionless adiabatic piston, and show that, under appropriate initial conditions, the entropy can decrease. This remarkable exception to the second law of thermodynamics (which we show not to contradict Boltzmann H-theorem) would actually take place over an extremely long, in practice unobservable, time for an ordinary macroscopic system. However, there is a range of physical parameters, pertaining to mesoscopic systems, where the decrease can occur on a realistic time scale.