  In this note, we explore the thermodynamic properties of the universe in the
background of the generalized energy-momentum-squared gravity. We derive the
energy density of matter from the non-standard continuity equation and use it
in our analysis. We consider two types of models depending on the nature of
coupling between curvature and matter and perform thermodynamic analysis on
them using the cosmic apparent horizon. The models are kept as generic as
possible from the mathematical point of view in order to gain a wide
applicability of the work. In this work we have considered power law and
exponential form of models. All the thermodynamic parameters are expressed in
terms of the cosmic apparent horizon radius and its time derivatives and their
time evolution are studied. By using temperature, heat capacity analysis and
the evolution trend of Helmholtz free energy the conditions for thermodynamic
stability of the models are derived. It is seen that our stability analysis
considerably constrain the parameter space of the model.
