Abstract
Boltzmann's principle is used to select the "most probable" realization (macrostate) of an isolated or closed thermodynamic system, containing a small number of particles ($N \llsp \infty$), for both classical and quantum statistics. The inferred probability distributions provide the means to define intensive variables and construct thermodynamic relationships for small microcanonical systems, which do not satisfy the thermodynamic limit. This is of critical importance to nanoscience and quantum technology.
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