Thermodynamic constraints and observational validation of the deceleration parameter

In this work, we propose a two-parameter parametrization for the deceleration parameter $q\left(z\right)$ grounded in thermodynamic constraints and applied it to explore the evolution of the universe. The second law of thermodynamics imposes essential conditions to ensure that the system approaches equilibrium in late times, requiring $q\left(z\right)\ge -1$ and $\frac{dq}{dz}>0$ as $z\to -1$. These constraints ensure that entropy does not decrease, stabilize the system, and facilitate a smooth transition from deceleration to acceleration, consistent with the observed cosmic expansion. Furthermore, the model avoids the phantom regime ($\omega <-1$), preventing catastrophic future scenarios such as the Big Rip. Using the combined CC, Pantheon, SH0ES, and BAO datasets, we constrain the model parameters and compare the results with the standard ΛCDM model. Our findings indicate $H_0=70.82\pm 0.88$, with a transition redshift of $z_t=0.597\pm 0.214$, suggesting an earlier onset of acceleration compared to ΛCDM. The present deceleration parameter, $q_0=-0.364\pm 0.032$, implies a weaker acceleration than in ΛCDM. Moreover, we analyze the evolution of total energy density, pressure, and the effective equation of state parameter, confirming a quintessence-like behavior with ${\omega }_0=-0.570\pm 0.056$. Our results provide a thermodynamically consistent framework for cosmic expansion, supporting a dark-energy-driven acceleration.