I've recently been reading a bit into the thermalisation of a system of particles and I'm unsure on a couple of concepts. Firstly, if a system of particles are out of mutual thermal equilibrium, does this essentially correspond to the particles in the system having randomly distributed momenta, such that each has a different magnitude and a different direction?! Secondly, once the system has reached thermal equilibrium, does this then correspond to each of the particles having the same magnitude of momentum (although their momentum will in general be different as even though each as the same magnitude, they will all point in different directions)?! Finally, is the process of thermalisation then literally a redistribution of momentum between the particles through mutual interactions, such that the magnitudes of their momenta are all equal?!