"Suppose we claim... heat flowing in the wrong direction, such as... ice forming in a glass of water... in an oven. ...Energy left the cool... water as heat, so the entropy went down. Because the temperature is low... in the denominator... that decrease in entropy is large. The same energy enters the hot region (...oven), so the entropy of that region increases. However... its temperature is high, [so] that increase in entropy is small. The net effect... a net decrease overall. ...[But] entropy never decreases, so heat cannot flow spontaneously... hot to cold..."