The mean-field thermodynamic limit is studied for a class of isolated Newtonian N-body systems whose Hamiltonian admits several invariants of motion. It is shown that the macrostates of individual members of a statistical equilibrium ensemble are not necessarily themselves in a state of global thermal equilibrium in the strict sense. Yet they are always locally in thermodynamic equilibrium, and always global maximizers of the pertinent maximum entropy principle.

Minor slips of pen have been corrected compared to the version published in the proceedings of the workshop "Dynamics and Thermodynamics of Systems with Long Range Interactions: Theory and Experiment," Assisi, Italy, 2007; A. Campa, A. Giansanti, G. Morigi, F. Sylos Labini (Eds.). See http://scitation.aip.org/dbt/dbt.jsp?KEY=APCPCS&Volume=970&Issue=1