Strange systems in statistical mechanics

A number of rather unexpected behaviours in various systems are reviewed. Namely, it is shown that a macroscopic system having chaotic dynamics may nevertheless display undamped harmonic radial oscillations. Next, we show that small systems in an external field may have spatially dependent kinetic temperatures in equilibrium. Further, we can also show that the kinetic temperatures of different particle species in the same region of space will in general not assume the same values. Finally, we discuss the remarkable way in which the zero'th law of thermodynamics can sometimes appear to be violated in systems having long-range interactions.