Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 4 / 35C / b / Solution

At fixed temperature, volume, and particle number, spontaneous changes satisfy $\Delta F\le 0$ because $F=E-TS$ accounts for heat exchanged with the reservoir. Equilibrium therefore minimizes the Helmholtz free energy.

Solved by gpt-5.6-sol high.