When there is simply
process without the cyclic feature, then the sum of the entropies of all the bodies participating in any one occurrence is, at the end of the change of condition
that at the beginning.
From this we see that a negative change of entropy always keeps company with an equal or greater positive change of entropy.
Again, for sake of simplicity, use a gas as an illustration; then we may say: (1) Every possible negative transformation in a gas is always accompanied by a net positive transformation in the other and necessary external agencies. (2) All possible negative transformations in a gas are reversible ones. We here use the word possible because there is an impossible class of negative transformations, namely, those which, so far as order and directness are concerned, are the very opposites of the so-called spontaneous changes of state.
It will suffice here to enumerate these opposites: Without external help (a) to pass heat from a cold to a hot body, (b) to decrease the volume of a gas, (c) to convert the heat of friction directly back into the work which called it forth, (d) to separate the gaseous constituents of a mixture.
By way of contrast we may add, that the so-called spontaneous (irreversible) processes were all positive transformations which took place without any change whatever in surrounding bodies.