ABSTRACT
The concept of ergodicity is one of the most fundamental in probability, since it links the mathematical theory of probability to what can be observed in a deterministic mechanical world. It also plays an important role in theoretical physics and, in fact, the term ergodic was coined by Ludwig Boltzmann in 1887 in his study of the time development of mechanical particle systems. The term itself stems from the Greek ergos = “work” and hodos = “path,” possibly meaning that ergodic theory codifies how the energy in a system evolves with time. Ergodicity in itself is not a probabilistic concept and it can be studied within a purely deterministic framework, but in its stochastic setting, it helps in the interpretation of probabilities and expectations as long run relative frequencies.
