Time, scale of, macroscopic

In performing measurements of the properties of a system, experimentalists often find that the values of the measured properties are constant over the time seale At = t - to of their measurements and independent of the starting time to of the measurements. When sueh results are obtained, the system is said to be in the state of equilibrium. Of course, we know from mieroseopie considerations that the properties of a system that are not fixed by external restraints mnst be a function of time. Thus, the appearance of equihbrinm must be due to the smoothing out of fluctuations on the time scale of macroscopic measurements. 

The time interval At is assumed to represent the time scale of macroscopic measurements, i.e., the time resolution of the observer. It is also assumed that At is short on the time scale ts characterizing the motion of the JV particles (the system) and long on the time scale ts characterizing the response of the environment (the bath) to the motion of the system and its re-equilibration. This assumption requires the existence of a separation in the time scales ts and ts for the evolution of the system and bath, the latter being faster (ts ts), so that ig A/ < ts. 

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