  Boltzmannian statistical mechanics partitions the phase space of a system
into macro-regions, and the largest of these is identified with equilibrium.
What justifies this identification? Common answers focus on Boltzmann's
combinatorial argument, the Maxwell-Boltzmann distribution, and maximum entropy
considerations. We argue that they fail and present a new answer. We
characterise equilibrium as the macrostate in which a system spends most of its
time and prove a new theorem establishing that equilibrium thus defined
corresponds to the largest macro-region. Our derivation is completely general,
and does not rely on assumptions about the dynamics or internal interactions.
