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Whereas ergodic theories relate to limiting cases of infinite thermal reservoirs and infinitely long times, some ergodicity tendencies may appear also for finite reservoirs and time durations. These tendencies are here explored and found to exist, but only for extremely long times and very soft ergodic criteria. “Weak ergodicity breaking” is obviated by a judicious time-weighting, as found in a previous work [Found. Phys. (2015) 45: 673–690]. The treatment is based on an N-oscillator (classical) and an N-spin (quantal) model. The showing of ergodicity is facilitated by pictorial presentations.

Ergodic Tendencies in Sub-Systems Coupled to Finite Reservoirs—Classical and Quantal