Entropy and Gibbs energy — a statistical argument that gives the universe a direction

Entropy is a measure of how many microscopic arrangements are consistent with the macroscopic state — informally, how spread out matter and energy are. The hard part is that it is not a substance or a force; it is a counting argument about probability, and it gives the universe a preferred direction. Gibbs energy ΔG = ΔH − TΔS then combines two things that feel unrelated (heat release and disorder) into one criterion for whether something happens.

Students find this hard because it is the first time in chemistry that a statistical argument determines a definite outcome, and because "spontaneous" is a technical term meaning "thermodynamically allowed", carrying no implication about rate (diamond → graphite has ΔG < 0 and takes geological time).