Interacting Generalized Chaplygin-Jacobi gas: Thermodynamics approach

This work investigates a cosmological model featuring an interaction between dark energy and dark matter, where the dark energy component is described by the Generalized Chaplygin-Jacobi gas (GCJG). In this study, we establish a system in which the GCJG and a pressureless dark matter fluid exchange energy via a linear interaction term, $Q \propto \rho_x$, being $\rho_{x}$ the dark energy density. By solving the conservation equations, we derive analytical expressions for the evolution of the dark energy and dark matter densities. The thermodynamic properties of this interacting system are then thoroughly analyzed. The thermodynamic analysis reveals that both dark components maintain positive temperatures, ensuring stability. Notably, the dark energy component transitions to a phantom regime in the past, a feature of interest for recent cosmological observations, without violating thermodynamic principles. The total entropy production is shown to be in agreement with the second law of thermodynamics. Furthermore, an analysis of the specific heats suggests that while the dark matter sector remains thermodynamically stable, the dark energy sector undergoes a late-time phase transition, consistent with its entering into the phantom domain at effective level.