Lorenz Attractor Java applet. The Lorenz attractor is a classic example of a strange attractor. The time evolution of this hops between two minima. For any given moment, the time which the point stays in one minimum or the other is not predictable. However, the distribution of total time spent in either minima is, at least in principle, predictable.
Molecular dynamics shows similar behavior.
Thermodynamic properties are approximated by a time average over a simulation of a local or kinetic representation of a kinetic system. The Rossler system shown here is simpler, but similar to the Lorenz system. Above a critical energy many paths are chaotic. This is one such path. While almost periodic in the beginning, and occasionally during the run, the long term behavior of this system is unpredictable.