On the definition of equilibrium

Boltzmann's approach to statistical mechanics is widely believed to be conceptually superior to Gibbs' formulation. However, the microcanonical distribution often fails to behave as expected: the ergodicity of the motion relative to it can rarely be established for realistic systems; worse, it can often be proved to fail. Also, the approach involves idealizations that have little physical basis. Here we take Khinchin's advice and propose a definition of equilibrium that is more realistic: the definition reflects the fact that the system is made of a great number of particles, and implies that all measurable macroscopic observables have steady values.