The conditions for macroscopic motion to be compatible with statistical equilibrium are reviewed for a totally isolated macroscopic system (fixed energy, momentum, and angular momentum). The analysis clarifies the general definition of internal energy, the implications of macroscopic motion on the chemical potential, and the status of momentum and angular momentum conservation in statistical mechanics. Two important consequences follow: The temperature is necessarily positive, and the microcanonical ensemble (equiprobability of all accessible microstates) can be applied, as it is usually done, to systems that are only partially isolated (constant energy, but not momentum or angular momentum).

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