  We consider a universe filled by a modified generalized Chaplygin gas
together with a pressureless dark matter component. We get a thermodynamical
interpretation for the modified generalized Chaplygin gas confined to the
apparent horizon of FRW universe, whiles dark sectors do not interact with each
other. Thereinafter, by taking into account a mutual interaction between the
dark sectors of the cosmos, we find a thermodynamical interpretation for
interacting modified generalized Chaplygin gas. Additionally, probable relation
between the thermal fluctuations of the system and the assumed mutual
interaction is investigated. Finally, we show that if one wants to solve the
coincidence problem by using this mutual interaction, then the coupling
constants of the interaction will be constrained. The corresponding constraint
is also addressed. Moreover, the thermodynamic interpretation of using either a
generalized Chaplygin gas or a Chaplygin gas to describe dark energy is also
addressed throughout the paper.
