Depending on the initial conditions (filled or open circles) and microscopically allowed processes, the reservoirs can exchange entropy advectively and diffusively, tracing out various paths through state space with the constraints that atom number and energy are conserved d N /d t = d U /d t = 0 and the entropy production is positive definite d S /d t >= 0. This evolution halts (stars) by reaching either a non-equilibrium steady state (Δ N , Δ S != 0) or equilibrium (Δ N = Δ S = 0) where the total entropy S = S L + S R has a global maximum.
