  The property of Tsallis entropy is examined when considering tow systems with
different temperatures to be in contact with each other and to reach the
thermal equilibrium. It is verified that the total Tsallis entropy of the two
systems cannot decrease after the contact of the systems. We derived an
inequality for the change of Tsallis entropy in such an example, which leads to
a generalization of the principle of entropy increase in the framework of
nonextensive statistical mechanics.
