That statement is essentially the content of the Second Law. The
second inequality is less obvious, for it says that, if the entropy and volume of the
system are constant, then the internal energy must decrease in a spontaneous change.
Do not interpret this criterion as a tendency of the system to sink to lower energy. It is
a disguised statement about entropy and should be interpreted as implying that, if
the entropy of the system is unchanged, then there must be an increase in entropy of
the surroundings, which can be achieved only if the energy of the system decreases
as energy flows out as heat.