Physical insights of squared speed of sound parameterized Brans-Dicke gravity through cosmic parameters and thermodynamics

In this work, we investigate the cosmic analysis in detail by assuming squared speed of sound parameterizations in the framework of Brans-Dicke theory. For this purpose, we extract various cosmological parameters such as Hubble, deceleration, equation of state, Om diagnostic and jerk. We also explore the viability of the universe through the $\omega -{\omega }^{\prime }$ plane and the statefinder plane. We present the analytical and graphical solutions for all of the above-mentioned parameters. From the graphical analysis, it is noted that the deceleration parameter demonstrates the deceleration to acceleration expansions of the universe. In most cases, the Om diagnostic shows a quintessence-like era, the jerk parameter and statefinder parameter show the ΛCDM limit and the $\omega -{\omega }^{\prime }$ plane indicates a freezing region of the universe. Our investigation reveals that the squared speed of sound demonstrates stable behavior across all considered parameterizations. To analyze the thermodynamic properties of the proposed models, we examine the validity of the generalized second law of thermodynamics with generalized six parameters entropy as horizon entropy. We found the validity of this law for all squared speed of sound parameterizations.