In stochastic processes the future is not uniquely determined, but we have at least probability relations enabling us to make predictions. - William Feller

Physical irreversibility manifests itself in the fact that, whenever the system is in a state far removed from equilibrium, it is much more likely to move toward equilibrium, than in the opposite direction.

The fact that the mean recurrence time is infinite implies that the chance fluctuations in an individual prolonged coin-tossing game are far removed from the familiar pattern governed by the normal distribution.

It is a common fallacy to believe that the law of large numbers acts as a force endowed with memory seeking to return to the original state, and many wrong conclusions have been drawn from this assumption.