Constructions of Variable Modified Chaplygin-Jacobi and Chaplygin-Abel Gases from Geometrothermodynamics

Abstract

Understanding the physical origin of the Universe's late-time accelerated expansion remains one of the central open problems in modern cosmology. Geometrothermodynamics (GTD) offers a compelling route to this problem, providing a geometric framework that unifies thermodynamics with contact and Riemannian geometry to encode the equilibrium properties of a physical system directly into its underlying geometric structure. In this work, we employ the GTD formalism to investigate cosmological models capable of explaining the observed accelerated expansion of the Universe. As an important outcome, our simple model exhibits dynamical behavior that provides a reasonable description of the late-time evolution of the Universe. We study the Chaplygin-Jacobi and Chaplygin-Abel gas models and their variable forms within geometrothermodynamics by deriving their thermodynamic relations, entropy, and equations of state. The free parameters of the models are constrained through a Markov Chain Monte Carlo (MCMC) analysis using several observational datasets, including cosmic chronometers combined with baryon acoustic oscillations (CC+BAO), DESI DR2 BAO data, DESI DR2 combined with the DES-SN5YR and Union3 Type Ia supernova compilations. The statistical performance of the models is assessed using the Akaike and Bayesian Information Criteria (AIC and BIC). We further examine their cosmological evolution through the deceleration parameter, the dark-energy equation-of-state parameter, and higher-order kinematic diagnostics, including the jerk and snap parameters. The perturbative stability of the models is also investigated through the squared sound speed.