= Solution
For a <hard disc> configuration, the potential energy is zero if no particles overlap and infinite otherwise. All allowed configurations therefore have the same configurational Boltzmann factor. At fixed $N,A,T$, their relative free energies differ through the volume of accessible configuration space:
$$
F=U-TS,\qquad U_{\rm configurational}=0,\qquad\boxed{\text{equilibrium maximizes accessible configurational entropy}.}
$$
The kinetic contribution is common to the phases at the same temperature. “Entropy-driven crystallization” does not mean that particles develop an energetic attraction; excluded volume changes the number of possible many-particle arrangements.
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