Statistical mechanics in just one equation

This semester, I am giving four lectures in a third-year undergraduate course on statistical mechanics. Last year, I gave a guest lecture on the Ising model.The first thing I want to emphasise is that the whole course is built around just one equation. exp(−F(T, V)/kT) = ∑s exp(−Es/kT) ≡ Z(T, V) This connects macroscopic thermodynamic properties (contained in the Helmholtz free energy F(T,V)) to microscopic properties (the energies E_s of all possible states s of the system).[Note that from equilibrium thermodynamics, partial derivatives of F(T,V) give the entropy (and specific heat capacity) and the pressure (equation of state)].I think that we are so used to this equation that we may miss just how amazing and profound it is.First, the equation is incredibly simple.Second, it is universal. It applies to any system in thermodynamic equilibrium regardless of its chemical or physical composition.Third, in the context of the theory of emergent phenomena, it is exceptional because it…