where β β = ( k B T ) − − 1 is the inverse temperature, Tr is the trace (corresponding to an integral over phase space in the classical case) and H is the Hamiltonian. ρ ρ ¯ ¯ is the relevant probability operator (or density operator for quantum systems). It is chosen in such a way that it can be written as a function of the relevant variables only, but is a good approximation for the actual density, in particular such that it gives the correct mean values.