Use the Gibbs distribution to calculate thermodynamic
properties (including entropy, all relevant thermodynamic
potentials, and heat capacity), of an ensemble of similar two-level
systems, in thermodynamic equilibrium at temperature T that is
comparable with the energy gap (delta). For each variable, sketch
its temperature dependence, and find its asymptotic values (or
trends) in the low- temperature and high-temperature limits.
Also, calculate the probabilities of the energy level
occupation, and give physical interpretations of your results, in
both temperature limits.