I'm struggling to understand Sakharov's third condition for baryogenesis, i.e., a departure from thermal equilibrium. I don't understand what thermal equilibrium means in this context or proofs that it is neccessary for baryogenesis.
Trodden and Carroll's TASI lecture notes outline a common argument. They begin by writing the expected baryon number in thermal equilibrium as $$ \langle B \rangle = \text{Tr}\left(e^{\beta H} B\right) = \cdots = 0 $$ The result that it equals zero follows quickly for a CPT invariant Hamiltonian. However, why does thermal equilibrium imply Gibbs' canonical ensemble, as in the above formula?
Gibbs' ensemble is useful in situations in which only the expected energy (or temperature) adequately describe, for our purposes, the probability of states. I cannot see why Gibbs' ensemble would be appropriate for understanding systems with more macroscopic parameters of interest, in this case temperature and baryon number, nor why it would be the only distribution for thermal equilibrium.