Chapter 2.6, Problem 29P

Consider a system of two Einstein solids, with ${\text{N}}_{\text{A}}=\text{3}00,{\text{N}}_{\text{B}}=\text{2}00,{\text{q}}_{\text{total}}=\text{1}00$ (as discussed in Section 2.3). Compute the entropy of the most likely macrostate and of the least likely macrostate. Also compute the entropy over long time scales, assuming that all microstates are accessible. (Neglect the factor of Boltzmann’s constant in the definition of entropy; for systems this small it is best to think of entropy as a pure number.)