The authors investigate the impact of the Dark Energy Spectroscopic Instrument (DESI) 2024 data on various dark energy models. They analyze three types of models: those related to thermodynamics, Taylor expansions of the barotropic factor, and ad hoc dark energy parameterizations. Using Monte Carlo Markov chain analyses with the Metropolis-Hastings algorithm, they infer kinematic quantities and predict early-time cosmological behavior. The results show that the best-fitting model is not the Chevallier-Polarski-Linder (CPL) parametrization but a more complex log-corrected dark energy contribution. Further analysis, including the correlation \( r_d h_0 \), reveals that the $\Lambda$CDM model aligns well with the data, suggesting that the tension between the concordance paradigm and the CPL model can be alleviated. The study concludes that future data will be crucial in clarifying whether dynamical dark energy is truly in tension with the $\Lambda$CDM model.The authors investigate the impact of the Dark Energy Spectroscopic Instrument (DESI) 2024 data on various dark energy models. They analyze three types of models: those related to thermodynamics, Taylor expansions of the barotropic factor, and ad hoc dark energy parameterizations. Using Monte Carlo Markov chain analyses with the Metropolis-Hastings algorithm, they infer kinematic quantities and predict early-time cosmological behavior. The results show that the best-fitting model is not the Chevallier-Polarski-Linder (CPL) parametrization but a more complex log-corrected dark energy contribution. Further analysis, including the correlation \( r_d h_0 \), reveals that the $\Lambda$CDM model aligns well with the data, suggesting that the tension between the concordance paradigm and the CPL model can be alleviated. The study concludes that future data will be crucial in clarifying whether dynamical dark energy is truly in tension with the $\Lambda$CDM model.