What physical state transformation requires the smallest amount of energy?

Freezing requires the smallest amount of energy because it is a process where a liquid turns into a solid. This transformation typically releases energy from the liquid as it cools, meaning it does not require an input of energy in the same way as the other processes mentioned.

In contrast, evaporation involves converting a liquid into a gas, which requires a significant amount of energy to overcome molecular attractions. Melting requires energy to break the bonds that hold molecules in a rigid structure when transitioning from solid to liquid. Sublimation, which is the transition from solid directly to gas, also requires a substantial amount of energy, as it involves overcoming the forces that hold molecules tightly packed in a solid state.

Thus, during the freezing process, the energy is released rather than absorbed, making it the physical state transformation that requires the least energy input.