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.

在这篇笔记中，我们在广义能量 - 动量平方引力的背景下探索宇宙的热力学性质。我们从非标准连续性方程推导出物质的能量密度，并将其用于我们的分析。我们根据曲率和物质之间耦合的性质考虑两种类型的模型，并使用宇宙视界对它们进行热力学分析。从数学的角度来看，模型尽可能保持通用，以获得工作的广泛适用性。在这项工作中，我们考虑了幂律和指数形式的模型。所有的热力学参数都用宇宙视视界半径表示，并研究了它的时间导数和时间演化。通过使用温度，热容量分析和亥姆霍兹自由能的演化趋势推导出模型的热力学稳定性条件。可以看出，我们的稳定性分析极大地限制了模型的参数空间。