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With the aid of simple analytical computations for the Ehrenfest model, weclarify some basic features of macroscopic irreversibility. The stochasticcharacter of the model allows us to give a non-ambiguous interpretation of thegeneral idea that irreversibility is a typical property: for the vast majorityof the realizations of the stochastic process, a single trajectory of amacroscopic observable behaves irreversibly, remaining "very close" to thedeterministic evolution of its ensemble average, which can be computed usingprobability theory. The validity of the above scenario is checked throughsimple numerical simulations and a rigorous proof of the typicality is providedin the thermodynamic limit.

Irreversibility and typicality: A simple analytical result for the Ehrenfest model